Question

Factorize x³ - 8x² + 17x – 10​

Answer 1

Step-by-step explanation:

In this case the factors of 10 are ±1,±2,±5

Substituting 1 into the expression x

2

−8x+17x−10

gives 1−8+17−10=0

so x=1 is a root and (x−1) is a factor of this expression.

Using synthetic division to divide

x−1

x

3

−8x

2

+17x−10

we get x

2

−7x+10

(sorry I can't see any way to neatly demonstrate synthetic division here)

with obvious factors (x−2)(x−5)

So

(x

3

−8x

2

+17x−10)=(x−1)(x−2)(x−5)

Late addition: Here is an image to help explain the synthetic division