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

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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(52782) About Me  (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) About Me  (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