Question

What is the product of the following two polynomials?

(2x3+3x2)(4x4−5x3−6x2)

Answer 1

Compute termwise:

(2x^3+3x^2)(4x^4−5x^3−6x^2)
= 2x^3(4x^4−5x^3−6x^2) + 3x^2(4x^4−5x^3−6x^2)
= (8x^7 − 10x^6 − 12x^5) + (12x^6 − 15x^5 − 18x^4)

Combine like terms:
= 8x^7 + 2x^6 − 27x^5 − 18x^4

You can also factor: x^4(8x^3 + 2x^2 − 27x − 18).