Question

Divide. (–10x3 + 30x – 20) ÷ (–5x + 5)

Answer 1

@dpaInc help

Answer 2

For dividend,
Consider f(x) = -10x^3 + 30x - 20
f(1) = -10(1)^3 + 30(1) - 20 = 0
so, (x-1) is a factor of f(x)
f(x) = -10x^3 + 30x - 20 = -10 (x^3 -3x +2)
By long division,
x^2 + x - 2
-----------------------
x-1 ) x^3 - 3x + 2
x^3 - x^2
---------------------
x^2 - 3x
x^2 - x
----------------
- 2x +2
- 2x +2
------------

f(x) = -10x^3 + 30x - 20
= -10 (x^3 -3x +2)
= -10 (x-1)(x^2 + x -2)
= -10 (x-1) (x-2)(x+1)

For divisor,
-5x + 5 = -5 (x-1)

(–10x3 + 30x – 20) ÷ (–5x + 5)
= -10 (x-1) (x-2)(x+1) ÷ -5 (x-1)
\[ = \frac{-10 (x-1) (x-2)(x+1)}{ -5 (x-1)}\]
Can you cancel the common factors there?