Question

When (x^2+3x+4)(x^2+2+1) is simplified what is the coefficient of the x^3 term

Answer 1

(I wrote this up assuming the "2" term in the second trinomial was meant to be a "2x") You can find the answer by expanding the expression in the usual way, by repeated application of the distributive property:


`(x^2+3x+4)(x^2+2x+1)=\\(x^2+3x+4)x^2+(x^2+3x+4)2x+(x^2+3x+4)1=\\ x^2(x^2)+3x(x^2)+4(x^2)+x^2(2x)+3x(2x)+4(2x)+x^2+3x+4=\\ x^4+3x^3+4x^2+2x^3+6x^2+8x+x^2+3x+4\\ x^4+(3x^3+2x^3)+(4x^2+6x^2+x^2)+(8x+3x)+4=\\\\ x^4+5x^3+11x^2+11x+4`

So the coefficient of your x³ term would be 5 in this case.