Question

PLEASE HELP ME I BEG YOU I REALLY NEED!!!!

Answer 1

Polynomial that represents a difference in cubes.

x³ - 64 = 0
x³ = 64
∛x³ = ∛64
x = 4

Correct Steps for factoring the polynomial 5x³ - 40
5(x³ - 8)
5((x)³ - (2)³)
5(x - 2)(x² + 2x + 4)

To check:
5(x - 2)(x² + 2x + 4)
(5x - 10) (x² + 2x + 4)
5x(x² + 2x + 4) - 10(x² + 2x + 4)
5x³ + 10x² + 20x - 10x² - 20x - 40
5x³ + 10x² - 10x² + 20x - 20x - 40
5x³ - 40

Answer 2

Difference of cubes: a³ - b³

A) x³ - 64 = x³ - 4³

In B, 4 is not a cube number.

In C, this is the sum of a cubes. 8x³ + 27 = (2x)³ = 3³

In D, 4 is not a cube number.

Your answer is A.

Question #6

5x³ - 40
5[x³ - 8]
5[x³ - 2³]

Note: x³ - y³ = (x-y)(x² + xy + b²)

5[(x-2)(x² + 2x + 2²)]
5[(x-2)(x² + 2x + 4)]

Your answer is B.