Question

50 Points!

What is the product of -2x^3 +x - 5 and x^3 - 3x - 4?

(a) show your work
(b) Is the product of -2x^3 + x - 5 and x^3 - 3x - 4 equal to the product of x^3 - 3x - 4 and -2x^3 + x - 5? Explain.

Answer 1

Answer:
`\bold{a)\quad -2x^6+3x^4+3x^3-3x^2+11x+20\qquad b)\quad YES}`

Explanation:

a)

`(-2x^6+x-5)(x^3-3x-4)\\\\\text{Use distributive Property to multiply:}\\-2x^3(x^3-3x-4)+x(x^3-3x-4)-5(x^3-3x-4)\\\\.\ -2x^6+2x^4+8x^3\\+\qquad \quad +x^4\qquad \quad -3x^2-4x\\+ \underline{\qquad \qquad \qquad -5x^3\quad \quad+15x+20}\\= -2x^6+3x^4+3x^3-3x^2+11x+20`

b)

When multiplying, the order doesn't matter: 2 × 3 = 3 × 2

This is referred to as "Commutative Property of Multiplication"

So, (-2x⁶+x-5)(x³-3x-4) = (x³-3x-4)(-2x⁶+x-5)