+0

# Algebra

0
6
1
+867

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

Jun 12, 2024

#1
+1252
+1

There are 2 ways to do the problem.

First, we could take a look at all the possible conbinations we could have to give us x^2.

First off, we have 8x*x = 8x^2.

Next, we have 7x*x=x^2

Lastly, we have x^2*1 = x^2

Adding all the coefficients up, we get \(8+7+1=16\)

We could also just factor it, which isn't reccomended, but we get

\(x^{7}+4x^{6}+4x^{5}+19x^{4}+19x^{3}+16x^{2}+16x+1\)

Which shows the coefficient of x^2 is 16.

So our final answer is 16

Thanks! :)

Jun 12, 2024

#1
+1252
+1

There are 2 ways to do the problem.

First, we could take a look at all the possible conbinations we could have to give us x^2.

First off, we have 8x*x = 8x^2.

Next, we have 7x*x=x^2

Lastly, we have x^2*1 = x^2

Adding all the coefficients up, we get \(8+7+1=16\)

We could also just factor it, which isn't reccomended, but we get

\(x^{7}+4x^{6}+4x^{5}+19x^{4}+19x^{3}+16x^{2}+16x+1\)

Which shows the coefficient of x^2 is 16.

So our final answer is 16

Thanks! :)

NotThatSmart Jun 12, 2024