+1222 What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?
+1910 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! :)
+1910 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! :)
