Question

The product of the polynomials (3x 2) and (-x^3 – 3) is . when this product is multiplied by (3 x), the coefficient of x4 in the result is

Answer 1

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

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

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

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Explanation:

Answer 2

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

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

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

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Explanation: