Question

help

Answer 1

With?

Answer 2

read the attachment

Answer 3

Part A) P(x) = x^3 + 6x^2 - x - 30, D(x) = x - 2
x goes into x ^3 x^2 times
so x^3 + 6x^2 - x - 30 - x^3 +2x^2 = 8x^2-x-30
x goes into 8x^2 8x times
8x^2 - x - 30 - 8x^2 +16x = 15x - 30
x goes into 15 x 15 times
15x-30-15x+30 = 0, meaning the remainder will be zero, Q(x) = x^2 + 8x +15
so P(x) = (x-2)(x^2 + 8x + 15)

Answer 4

Part B)
P(x) = x^3 + 6x^2 - x - 30, D(x) =x-3
x goes into x^3 x^2 times
x^3 + 6x^2 - x - 30 - x^3 + 3x^2 = 9x^2 - x - 30
x goes into 9x^2 9x times
9x^2 - x - 30 - 9x^2 + 27x = 26x - 30
x goes into 26x 26 times
26x - 30 - 26x + 78 = remainder of 48, with Q(x) = x^2 + 9x + 26
P(x) = (x-3)(x^2 + 9x +26) + 48