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".

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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".

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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

Imran is paid ?286 per week Every week he puts 20% of his wage into a savings account How much does he put into his savings each week

Step-by-step answer

P Answered by PhD

The answer is in the image

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

Deanna gets 3 problems incorrect on a math quiz. Her score is 85%. How many questions are on the quiz?

Step-by-step answer

P Answered by PhD

The answer is in the image