Question

The product of the polynomials (3x + 2) and (-x^3-3) is ______.When this product is multiplied by (3 + x), the coefficient of x^4 in the result is______.

Answer 1

The product of the polynomials (3x+2) and (-x^3-3) is:

(3x+2)*(-x^3-3) = (3x)*(-x^3) + (3x)*(-3) + 2*(-x^3) + 2*(-3) = -3x^4 - 2x^3 -9x - 6

Multiplying it by (3 + x), we got:

(3 + x)*(-3x^4 - 2x^3 -9x - 6) = 3*(-3x^4) + 3(-2x^3) + 3*(-9x) +3*(-6) + x*(-3x^4) + x*(-2x^3) + x*(-9x) + x*(-6) = -3x^5 -11x^4 -6x^3 -9x^2 - 33x - 18

Therefore, the coefficient of x^4 is -11.