When factored completely, z2 - 9 equals?, №18010895, 02.05.2023 14:54

Mathematics

When factored completely, z2 - 9 equals?

Step-by-step answer

P Answered by Specialist

Let's see

$\\ \bf\bull\rightarrowtail z^2-9$

$\\ \bf\bull\rightarrowtail z^2-3^2$

(a+b)(a-b)=a^2-b^2

$\\ \bf\bull\rightarrowtail (z+3)(z-3)$

Mathematics

1) Which is a binomial factor of 8x2 + 26x + 15? A) x − 5 B) 2x − 5 C) 2x + 3 D) 4x + 3 2) Factor x2 + 5x - 24 A) (x + 8)(x - 3) B) (x + 3)(x - 8) C) (x + 6)(x + 4) D) (x + 2)(x - 12) 3) Factor the polynomial. 8x2 - 50 A) 2(4x - 5)(x - 5) B) 2(2x - 5)(2x - 5) C) 2(2x + 5)(2x + 5) D) 2(2x - 5)(2x + 5) 4) Which binomial is a factor of the polynomial? 3x2 + 7x + 2 A) (x − 1) B) (x − 2) C) (x − 2) D) (3x + 1) 5) Solve. x2 − 5x = 14 A) x = 0, x = 5 B) x = 0, x = −5 C) x = 2, x = −7 D) x = 7, x = −2 6) Factor x2 + 5x - 50 A) (x + 25)(x - 2) B) (x - 5)(x

Step-by-step answer

P Answered by PhD

14

Following are the calculation to the given points:

For point 1:

$\bold{8x^2+26x+15}\\\\\bold{8x^2+(20+6)x+15}\\\\\bold{8x^2+20x+6x+15}\\\\\bold{4x(2x+5)+3(2x+5)}\\\\\bold{(2x+5)(4x+3)}\\\\$

Therefore, the answer is "Option D".

For point 2:

$\bold{x^2 + 5x - 24}\\\\\bold{x^2 + (8-3)x - 24}\\\\\bold{x^2 + 8x-3x - 24}\\\\\bold{x(x + 8)-3(x +8)}\\\\\bold{(x + 8) (x-3)}\\\\$

Therefore, the answer is "Option A".

For point 3:

$\bold{8x2 - 50}\\\\\bold{2(4x2 - 25)}\\\\\bold{2((2x)^2 - 5^2)}\\\\\therefore \ \ x^2-y^2=(x+y) (x-y)\\\\\bold{2((2x - 5)(2x+5)}\\\\$

Therefore, the answer is "Option D".

For point 4:

$\bold{3x^2 + 7x + 2}\\\\\bold{3x^2 +(6+1)x + 2}\\\\\bold{3x^2 +6x+1x + 2}\\\\\bold{3x(x +2)+1(x + 2)}\\\\\bold{(x +2) (3x+1)}\\\\$

Therefore, the answer is "Option D".

For point 5:

$\bold{x^2 - 5x = 14}\\\\\bold{x^2 - 5x -14= 0}\\\\\bold{x^2 - (7-2)x -14= 0}\\\\\bold{x^2 -7x+2x -14= 0}\\\\\bold{x(x -7)+2(x -7)= 0}\\\\\bold{(x -7) (x+2)= 0}\\\\\bold{x -7=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x+2= 0}\\\\\bold{x =7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x= -2}\\\\$

Therefore, the answer is "Option D".

For point 6:

$\bold{x^2 + 5x - 50}\\\\\bold{x^2 + (10-5)x - 50}\\\\\bold{x^2 + 10x-5x - 50}\\\\\bold{x(x+ 10)-5(x +10)}\\\\\bold{(x+ 10)(x -5)}\\\\$

Therefore, the answer is "Option B".

For point 7:

$\bold{16x^2 + 24x + 9}\\\\\bold{16x^2 + (12+12)x + 9}\\\\\bold{16x^2 + 12x+12x + 9}\\\\\bold{4x(4x +3)+3(4x + 3)}\\\\\bold{(4x +3)(4x + 3)}\\\\\bold{(4x +3)^2}\\\\$

Therefore, the answer is "Option A".

For point 8:

$\bold{32x^2 - 50}\\\\\bold{2(16x^2 - 25)}\\\\\bold{2((4x)^2 - (5)^2)}\\\\\bold{2((4x-5)(4x+5))}\\\\$

Therefore, the answer is "Option B".

For point 9:

$\bold{x^2 + 7x - 18}\\\\\bold{x^2 + (9-2)x - 18}\\\\\bold{x^2 + 9x-2x - 18}\\\\\bold{x(x+ 9)-2(x +9)}\\\\\bold{(x+ 9)(x-2)}\\\\$

Therefore, the answer is "Option C".

For point 10:

$\bold{x^2 + 5x - 14}\\\\\bold{x^2 + (7-2)x - 14}\\\\\bold{x^2 + 7x-2x - 14}\\\\\bold{x(x+7)-2(x +7)}\\\\\bold{(x+7)(x -2)}\\\\$

Therefore, the answer is "Option C".

For point 11:

$\bold{25x^2 - 64}\\\\\bold{(5x)^2 - (8)^2}\\\\\bold{(5x-8)(5x+8)}\\\\$

Therefore, the answer is "Option C".

For point 12:

$\bold{x^2 - 81}\\\\\bold{x^2 - 9^2}\\\\\bold{(x - 9)(x+9)}\\\\$

Therefore, the answer is "Option A".

For point 13:

$\bold{8x^2 + 16x + 8 = 0}\\\\\bold{8(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + x+x + 1) = 0}\\\\\bold{(x(x +1)1(x + 1)) = 0}\\\\\bold{(x +1)(x + 1) = 0}\\\\\bold{(x +1)^2 = 0}\\\\\bold{x +1 = 0}\\\\\bold{x=-1}\\\\$

Therefore, the answer is "Option B".

For point 14:

$\bold{x^2 -x -12 = 0}\\\\\bold{x^2 -(4-3)x -12 = 0}\\\\\bold{x^2 -4x+3x -12 = 0}\\\\\bold{x(x -4)+3(x -4) = 0}\\\\\bold{(x -4) (x+3) = 0}\\\\\bold{(x -4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x+3) = 0}\\\\\bold{x =4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = -3}\\\\$

Therefore, the answer is "Option C".

For point 15:

$\bold{6x^2 + 8x - 28 = 2x^2 + 4}\\\\\bold{6x^2 + 8x - 28 - 2x^2 - 4=0}\\\\\bold{4x^2 + 8x - 32=0}\\\\\bold{4(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + (4-2)x - 8)=0}\\\\\bold{(x^2 + 4x-2x - 8)=0}\\\\\bold{(x(x + 4)-2(x +4))=0}\\\\\bold{(x + 4)(x -2)=0}\\\\\bold{(x + 4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x -2)=0}\\\\\bold{x =-4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x =2}\\\\$

Therefore, the answer is "Option B".

For point 14:

$\bold{6z^2 + 18z}\\\\\bold{6z(z + 3)}\\\\$

Therefore, the answer is "Option B".

Learn more:

link

1) Which is a binomial factor of 8x2 + 26x + 15? A) x − 5 B) 2x − 5 C) 2x + 3 D) 4x + 3 2) Facto

Mathematics

1) Which is a binomial factor of 8x2 + 26x + 15? A) x − 5 B) 2x − 5 C) 2x + 3 D) 4x + 3 2) Factor x2 + 5x - 24 A) (x + 8)(x - 3) B) (x + 3)(x - 8) C) (x + 6)(x + 4) D) (x + 2)(x - 12) 3) Factor the polynomial. 8x2 - 50 A) 2(4x - 5)(x - 5) B) 2(2x - 5)(2x - 5) C) 2(2x + 5)(2x + 5) D) 2(2x - 5)(2x + 5) 4) Which binomial is a factor of the polynomial? 3x2 + 7x + 2 A) (x − 1) B) (x − 2) C) (x − 2) D) (3x + 1) 5) Solve. x2 − 5x = 14 A) x = 0, x = 5 B) x = 0, x = −5 C) x = 2, x = −7 D) x = 7, x = −2 6) Factor x2 + 5x - 50 A) (x + 25)(x - 2) B) (x - 5)(x

Step-by-step answer

P Answered by PhD

14

Following are the calculation to the given points:

For point 1:

$\bold{8x^2+26x+15}\\\\\bold{8x^2+(20+6)x+15}\\\\\bold{8x^2+20x+6x+15}\\\\\bold{4x(2x+5)+3(2x+5)}\\\\\bold{(2x+5)(4x+3)}\\\\$

Therefore, the answer is "Option D".

For point 2:

$\bold{x^2 + 5x - 24}\\\\\bold{x^2 + (8-3)x - 24}\\\\\bold{x^2 + 8x-3x - 24}\\\\\bold{x(x + 8)-3(x +8)}\\\\\bold{(x + 8) (x-3)}\\\\$

Therefore, the answer is "Option A".

For point 3:

$\bold{8x2 - 50}\\\\\bold{2(4x2 - 25)}\\\\\bold{2((2x)^2 - 5^2)}\\\\\therefore \ \ x^2-y^2=(x+y) (x-y)\\\\\bold{2((2x - 5)(2x+5)}\\\\$

Therefore, the answer is "Option D".

For point 4:

$\bold{3x^2 + 7x + 2}\\\\\bold{3x^2 +(6+1)x + 2}\\\\\bold{3x^2 +6x+1x + 2}\\\\\bold{3x(x +2)+1(x + 2)}\\\\\bold{(x +2) (3x+1)}\\\\$

Therefore, the answer is "Option D".

For point 5:

$\bold{x^2 - 5x = 14}\\\\\bold{x^2 - 5x -14= 0}\\\\\bold{x^2 - (7-2)x -14= 0}\\\\\bold{x^2 -7x+2x -14= 0}\\\\\bold{x(x -7)+2(x -7)= 0}\\\\\bold{(x -7) (x+2)= 0}\\\\\bold{x -7=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x+2= 0}\\\\\bold{x =7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x= -2}\\\\$

Therefore, the answer is "Option D".

For point 6:

$\bold{x^2 + 5x - 50}\\\\\bold{x^2 + (10-5)x - 50}\\\\\bold{x^2 + 10x-5x - 50}\\\\\bold{x(x+ 10)-5(x +10)}\\\\\bold{(x+ 10)(x -5)}\\\\$

Therefore, the answer is "Option B".

For point 7:

$\bold{16x^2 + 24x + 9}\\\\\bold{16x^2 + (12+12)x + 9}\\\\\bold{16x^2 + 12x+12x + 9}\\\\\bold{4x(4x +3)+3(4x + 3)}\\\\\bold{(4x +3)(4x + 3)}\\\\\bold{(4x +3)^2}\\\\$

Therefore, the answer is "Option A".

For point 8:

$\bold{32x^2 - 50}\\\\\bold{2(16x^2 - 25)}\\\\\bold{2((4x)^2 - (5)^2)}\\\\\bold{2((4x-5)(4x+5))}\\\\$

Therefore, the answer is "Option B".

For point 9:

$\bold{x^2 + 7x - 18}\\\\\bold{x^2 + (9-2)x - 18}\\\\\bold{x^2 + 9x-2x - 18}\\\\\bold{x(x+ 9)-2(x +9)}\\\\\bold{(x+ 9)(x-2)}\\\\$

Therefore, the answer is "Option C".

For point 10:

$\bold{x^2 + 5x - 14}\\\\\bold{x^2 + (7-2)x - 14}\\\\\bold{x^2 + 7x-2x - 14}\\\\\bold{x(x+7)-2(x +7)}\\\\\bold{(x+7)(x -2)}\\\\$

Therefore, the answer is "Option C".

For point 11:

$\bold{25x^2 - 64}\\\\\bold{(5x)^2 - (8)^2}\\\\\bold{(5x-8)(5x+8)}\\\\$

Therefore, the answer is "Option C".

For point 12:

$\bold{x^2 - 81}\\\\\bold{x^2 - 9^2}\\\\\bold{(x - 9)(x+9)}\\\\$

Therefore, the answer is "Option A".

For point 13:

$\bold{8x^2 + 16x + 8 = 0}\\\\\bold{8(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + x+x + 1) = 0}\\\\\bold{(x(x +1)1(x + 1)) = 0}\\\\\bold{(x +1)(x + 1) = 0}\\\\\bold{(x +1)^2 = 0}\\\\\bold{x +1 = 0}\\\\\bold{x=-1}\\\\$

Therefore, the answer is "Option B".

For point 14:

$\bold{x^2 -x -12 = 0}\\\\\bold{x^2 -(4-3)x -12 = 0}\\\\\bold{x^2 -4x+3x -12 = 0}\\\\\bold{x(x -4)+3(x -4) = 0}\\\\\bold{(x -4) (x+3) = 0}\\\\\bold{(x -4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x+3) = 0}\\\\\bold{x =4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = -3}\\\\$

Therefore, the answer is "Option C".

For point 15:

$\bold{6x^2 + 8x - 28 = 2x^2 + 4}\\\\\bold{6x^2 + 8x - 28 - 2x^2 - 4=0}\\\\\bold{4x^2 + 8x - 32=0}\\\\\bold{4(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + (4-2)x - 8)=0}\\\\\bold{(x^2 + 4x-2x - 8)=0}\\\\\bold{(x(x + 4)-2(x +4))=0}\\\\\bold{(x + 4)(x -2)=0}\\\\\bold{(x + 4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x -2)=0}\\\\\bold{x =-4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x =2}\\\\$

Therefore, the answer is "Option B".

For point 14:

$\bold{6z^2 + 18z}\\\\\bold{6z(z + 3)}\\\\$

Therefore, the answer is "Option B".

Learn more:

link

Mathematics

1. which of the following is the factored form of the expression: 3x2 – 4x? a. x(3x - 4) b. x(3 – 4x) c. (3x -1) (x -1) d. (3x +1)(x -1) 2. which is a completely factored form of the expression: x2 + 21x +20 ? a. (x + 5)(x + 4) b. (x + 10)(x + 2) c. (x + 20)(x + 1) d. (x + 21)(x - 1) 3. which expression is factored form of 4x2 -9? a. 2(x - 3)2 b. (x - 3)2 c. 2(x + 3)(x - 3) d. (2x + 3)(2x - 3) 4. below are factored forms of the expression: 12x3 – 36x2 . which expression has the greatest common factor as the first term? a. 3x (4x2 – 12x) b. 4x2(3x

Step-by-step answer

P Answered by PhD

34

1. 3x^2-4x=x(3x-4) - A.

2. x^2 + 21x +20=(x-x_1)(x-x_2)

Find the roots:

$D=21^2-4\cdot 20=441-80=361, \ \sqrt{D}=19,\\ \\x_1=\dfrac{-21-19}{2}=-20, \ x_2=\dfrac{-21+19}{2}=-1$ ,

then

x^2 + 21x +20=(x+20)(x+1) - C.

3. 4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3) - D.

4. 12x^3-36x^2=12x^2(x-3) - C.

5. x^2 -5x -6=(x-x_1)(x-x_2)

Find the roots:

$D=(-5)^2-4\cdot (-6)=25+24=49, \ \sqrt{D}=7,\\ \\x_1=\dfrac{5-7}{2}=-1, \ x_2=\dfrac{5+7}{2}=6$ ,

then

x^2 -5x -6=(x-6)(x+1) and the width of the lawn is x-6 - A.

6. Since x^2 + 5x -24=(x+8)(x-3) the length and width are x+8 and x-3 - A.

7. 32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z) - B.

8. $12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \\24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \\ 46xy=2\cdot 23\cdot x\cdot y$ .

So the greatest common divisor is $2\cdot x=2x$ - D.

9. 2x^2 -3x -35=2(x-x_1)(x-x_2)

Find the roots:

$D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ \sqrt{D}=17,\\ \\x_1=\dfrac{3-17}{2\cdot 2}=-\dfrac{7}{2}, \ x_2=\dfrac{3+17}{2\cdot 2}=5$ ,

then

$2x^2 -3x -35=2(x+\dfrac{7}{2})(x-5)=(2x+7)(x-5)$ - A.

10. $81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2$ - B.

11. $18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+\dfrac{5}{2})(x+\dfrac{4}{3})=(6x+15)(3x+4)$ , the length is 6x+15.

12. $(x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x$ - C.

13. 30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2) .

14. x^2 -16=(x-4)(x+4) - B.

15. $81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2$ , the length of one side is 9p+5.

Mathematics

1. which of the following is the factored form of the expression: 3x2 – 4x? a. x(3x - 4) b. x(3 – 4x) c. (3x -1) (x -1) d. (3x +1)(x -1) 2. which is a completely factored form of the expression: x2 + 21x +20 ? a. (x + 5)(x + 4) b. (x + 10)(x + 2) c. (x + 20)(x + 1) d. (x + 21)(x - 1) 3. which expression is factored form of 4x2 -9? a. 2(x - 3)2 b. (x - 3)2 c. 2(x + 3)(x - 3) d. (2x + 3)(2x - 3) 4. below are factored forms of the expression: 12x3 – 36x2 . which expression has the greatest common factor as the first term? a. 3x (4x2 – 12x) b. 4x2(3x

Step-by-step answer

P Answered by PhD

34

1. 3x^2-4x=x(3x-4) - A.

2. x^2 + 21x +20=(x-x_1)(x-x_2)

Find the roots:

$D=21^2-4\cdot 20=441-80=361, \ \sqrt{D}=19,\\ \\x_1=\dfrac{-21-19}{2}=-20, \ x_2=\dfrac{-21+19}{2}=-1$ ,

then

x^2 + 21x +20=(x+20)(x+1) - C.

3. 4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3) - D.

4. 12x^3-36x^2=12x^2(x-3) - C.

5. x^2 -5x -6=(x-x_1)(x-x_2)

Find the roots:

$D=(-5)^2-4\cdot (-6)=25+24=49, \ \sqrt{D}=7,\\ \\x_1=\dfrac{5-7}{2}=-1, \ x_2=\dfrac{5+7}{2}=6$ ,

then

x^2 -5x -6=(x-6)(x+1) and the width of the lawn is x-6 - A.

6. Since x^2 + 5x -24=(x+8)(x-3) the length and width are x+8 and x-3 - A.

7. 32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z) - B.

8. $12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \\24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \\ 46xy=2\cdot 23\cdot x\cdot y$ .

So the greatest common divisor is $2\cdot x=2x$ - D.

9. 2x^2 -3x -35=2(x-x_1)(x-x_2)

Find the roots:

$D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ \sqrt{D}=17,\\ \\x_1=\dfrac{3-17}{2\cdot 2}=-\dfrac{7}{2}, \ x_2=\dfrac{3+17}{2\cdot 2}=5$ ,

then

$2x^2 -3x -35=2(x+\dfrac{7}{2})(x-5)=(2x+7)(x-5)$ - A.

10. $81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2$ - B.

11. $18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+\dfrac{5}{2})(x+\dfrac{4}{3})=(6x+15)(3x+4)$ , the length is 6x+15.

12. $(x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x$ - C.

13. 30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2) .

14. x^2 -16=(x-4)(x+4) - B.

15. $81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2$ , the length of one side is 9p+5.

Mathematics

Which of the following is equivalent to xy3z2 + y2z + xyz when it is completely factored? * a. xyz(y2z + y + 1) * b. xy2z(yz + 1 + 1) * c. yz(xy2z + y + x) * d. z(xy3z + y2 + xy)

Step-by-step answer

P Answered by Specialist

40

The correct answer among the choices presented above is option C. The expression yz(xy2z + y + x) is the completely factored form of the given equation xy3z2 + y2z + xyz. When you distribute yz in option c, you will see that the answer is equal to the given equation.

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Mathematics

Anthony received $150 for his birthday this year. This was $10 less than half the amount he received last year. How much money did Anthony receive for his birthday last year?

Step-by-step answer

P Answered by PhD

The answer is in the image