Question

In factoring by group how do you solve:

x^3+8x^2-x-8
Also:
y^3-y^2+2y-2

Answer 1

(x + 8) (x + 1) (x − 1)

(y − 1) (y² + 2)

Explanation:

x³ + 8x² − x − 8

Factor from the first two terms:

x² (x + 8) − x − 8

And from the last two terms:

x² (x + 8) − (x + 8)

Factor:

(x + 8) (x² − 1)

Factor the difference of squares:

(x + 8) (x + 1) (x − 1)

y³ − y² + 2y − 2

Factor from the first two terms:

y² (y − 1) + 2y − 2

And from the last two terms:

y² (y − 1) + 2 (y − 1)

Factor:

(y − 1) (y² + 2)