SOLUTION: What is the coefficient of x in (x^3 + x^2 + x + 1)(7x^6 - 3x^5 + 8x - 10)?

Algebra.Com
Question 1209341: What is the coefficient of x in (x^3 + x^2 + x + 1)(7x^6 - 3x^5 + 8x - 10)?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

The term with 'x' in the product of polynomials comes 


        from x * (-10)   (where x is from first polynomial and -10 is from second polynomial)

    and

        from 1 * (8x)   (where 1 is from first polynomial and 8x is from second polynomial).


Therefore, the term with 'x' is -10x + 8x = -2x.


Coefficient at 'x' in the product is -2.    ANSWER

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The other tutor provides the fastest route.
My method isn't exactly efficient but I'll discuss it anyway.

f(x) = x^3 + x^2 + x + 1
g(x) = 7x^6 - 3x^5 + 8x - 10
The goal is to find the x coefficient in f(x)*g(x)

I'll use the box method
Place the terms of f(x) along the top.
Place the terms of g(x) along the left side.
x^3x^2x1
7x^6
-3x^5
8x
-10


To fill in each cell, you multiply the headers.
Example: x^3 times 7x^6 = 7x^9 goes in the top left corner.
We could fill this entire table but instead I'll only fill out the cells that have an x term
That would be -10x and 8x shown below
x^3x^2x1
7x^6
-3x^5
8x8x
-10-10x

Combine like terms to get -2x


Answer: -2
RELATED QUESTIONS

What is the coefficient of x^-5 in the expansion of (x^3 -... (answered by robertb)
1. Let f(x) = x^3 + 3x ^2 + 4x - 7 and g(x) = -7x^4 + 5x^3 +x^2 - 7. What is the... (answered by Edwin McCravy)
Let f(x) = x^3 + 3x^2 + 4x - 7 and g(x) = 2x^4 - 8x^3 + 4x^2 - 1. What is the... (answered by ikleyn,math_tutor2020)
What is the coefficient of x in (x^4 + x^3 + x^2 + x +... (answered by Edwin McCravy)
Please check my answer, I am not sure which is correct Problem:... (answered by Alan3354)
What is the numerical coefficient of x^27 in the complete expansion of (x^2 + 5x + 2)^5 (answered by Edwin McCravy)
Let f(x) = x^3 + 3x ^2 + 4x - 7 and g(x) = -7x^4 + 5x^3 + x^2 - 7. What is the... (answered by Edwin McCravy)
Find the coefficient of x^22 in the expansion of... (answered by KMST)
Expand (1/2-2x)^5 up to the term in x^3. If the coefficient of x^2 in the expansion of... (answered by greenestamps)