25.04.2021

Which two polynomials have a sum of 4x-6 ?

. 4

Faq

Mathematics
Step-by-step answer
P Answered by Specialist

there's one more screen shot but the limit is 5... so ill type it out!

7. Are the two products the same when you multiply them vertically? (1 point)

Yes they are

Making a Decision:

8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)

They were both correct

9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)

I prefer the first one, Table method. To me it is easier and the fastest out of them all.


Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Mathematics
Step-by-step answer
P Answered by Specialist

there's one more screen shot but the limit is 5... so ill type it out!

7. Are the two products the same when you multiply them vertically? (1 point)

Yes they are

Making a Decision:

8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)

They were both correct

9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)

I prefer the first one, Table method. To me it is easier and the fastest out of them all.


Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Scenario: Multiplying Polynomials

Instructions:
View the video found on page 1 of this Journal acti
Mathematics
Step-by-step answer
P Answered by Specialist

Step-by-step explanation:

We have the polynomial

16n^3+13n^2+7n-10   ( 1 )

To solve this problem we have to take into account that only we can sum term with the same order in the variable. We have the polynomials

8n_{3}-5n+11n^{2}-5\\7n^2 + 8n - n^3 + 2\\15n^2 - 10n + 3n^3 - 4\\2n^2 + 12n - 5 + 8n^3

we can note (by summing term by term) that only the sum of the first and the fourth equation correspond to the given polynomial ( 1 ) of the problem. If we organize these polynomials (that is, write the equation down in a form where higher order appears first ) we have

8n^3 +11n^2 - 5n  - 5\\ 8n^3+2n^2 + 12n - 5\\

and if we sum we obtain

16n^3+13n^2+7n-10

that is what we was looking for

I hope this is useful for you

regards

Mathematics
Step-by-step answer
P Answered by PhD
There are infinitely many ways to do this. One such way is 
(x^2 + 10x + 4) plus (-x^2 - 10x)
note how the x^2 terms combine to 0x^2 or just 0. The same applies to the x terms as well. The only thing left is 4

So as you can see, the goal is to get everything to cancel but the 4. You can also have something like 
(2x^2-7x+2) plus (-2x^2 + 7x + 2)
and we have the same cancellations going on. This time we have 2+2 = 4 left over. 
Mathematics
Step-by-step answer
P Answered by Master

Step-by-step explanation:

We have the polynomial

16n^3+13n^2+7n-10   ( 1 )

To solve this problem we have to take into account that only we can sum term with the same order in the variable. We have the polynomials

8n_{3}-5n+11n^{2}-5\\7n^2 + 8n - n^3 + 2\\15n^2 - 10n + 3n^3 - 4\\2n^2 + 12n - 5 + 8n^3

we can note (by summing term by term) that only the sum of the first and the fourth equation correspond to the given polynomial ( 1 ) of the problem. If we organize these polynomials (that is, write the equation down in a form where higher order appears first ) we have

8n^3 +11n^2 - 5n  - 5\\ 8n^3+2n^2 + 12n - 5\\

and if we sum we obtain

16n^3+13n^2+7n-10

that is what we was looking for

I hope this is useful for you

regards

Mathematics
Step-by-step answer
P Answered by PhD
There are infinitely many ways to do this. One such way is 
(x^2 + 10x + 4) plus (-x^2 - 10x)
note how the x^2 terms combine to 0x^2 or just 0. The same applies to the x terms as well. The only thing left is 4

So as you can see, the goal is to get everything to cancel but the 4. You can also have something like 
(2x^2-7x+2) plus (-2x^2 + 7x + 2)
and we have the same cancellations going on. This time we have 2+2 = 4 left over. 
Mathematics
Step-by-step answer
P Answered by PhD

Part 1 is explained in 1) of the explanation.

Part 2 is explained in 2) of the explanation.

Step-by-step explanation:

1) So you choose 45 and to write it as 50-5.

We want to square 45 without using a calculator.

That is we want to find 45^2 without a calculator.

45^2=(50-5)^2

45^2=(50)^2-2(50)(5)+(5)^2 by your identity (x-y)^2=x^2-2xy+y^2.

45^2=50(50)-100(5)+25

45^2=2500-500+25

45^2=2000+25

45^2=2025

-----------

2) Choose two numbers for a and b between 8 and 15. I will choose 10 (a=10) and 12 (b=12).

a^3+b^3=(a+b)(a^2-ab+b^2)

10^3+12^3=(10+12)(10^2-10(12)+(12)^2

10^3+12^3=(22)(100-120+144)

10^3+12^3=(22)(-20+144)

10^3+12^3=22(124)

Now we have to multiply 22 and 124 without a calculator...

22(124)

(20+2)(124)

124(20)+124(2)

124(10+10)+124(2)

1240+1240+248

2480+248

2728

Mathematics
Step-by-step answer
P Answered by PhD

Part 1 is explained in 1) of the explanation.

Part 2 is explained in 2) of the explanation.

Step-by-step explanation:

1) So you choose 45 and to write it as 50-5.

We want to square 45 without using a calculator.

That is we want to find 45^2 without a calculator.

45^2=(50-5)^2

45^2=(50)^2-2(50)(5)+(5)^2 by your identity (x-y)^2=x^2-2xy+y^2.

45^2=50(50)-100(5)+25

45^2=2500-500+25

45^2=2000+25

45^2=2025

-----------

2) Choose two numbers for a and b between 8 and 15. I will choose 10 (a=10) and 12 (b=12).

a^3+b^3=(a+b)(a^2-ab+b^2)

10^3+12^3=(10+12)(10^2-10(12)+(12)^2

10^3+12^3=(22)(100-120+144)

10^3+12^3=(22)(-20+144)

10^3+12^3=22(124)

Now we have to multiply 22 and 124 without a calculator...

22(124)

(20+2)(124)

124(20)+124(2)

124(10+10)+124(2)

1240+1240+248

2480+248

2728

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