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# Algebra

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

Jun 12, 2024

#1
+1250
+1

We could probably do this really hard way.

By distributing every number, we get

$${x^{3}\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+x^{2}\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+x\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+1\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)}$$

Simplfying, we have

$$x^{7}+4x^{6}+8x^{5}+16x^{4}+22x^{3}+19x^{2}+15x+7$$

As it clear shows$$15$$ is the coefficient of x.

So our final answer is 15.

Thanks! :)

Jun 12, 2024

#1
+1250
+1

We could probably do this really hard way.

By distributing every number, we get

$${x^{3}\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+x^{2}\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+x\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+1\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)}$$

Simplfying, we have

$$x^{7}+4x^{6}+8x^{5}+16x^{4}+22x^{3}+19x^{2}+15x+7$$

As it clear shows$$15$$ is the coefficient of x.

So our final answer is 15.

Thanks! :)

NotThatSmart Jun 12, 2024