# How do you factor # x^4 - 8x^3 + 12x^2#?

##### 2 Answers

#### Explanation:

Take out the common factor of

Find factors of 12 which add to 8.

6 x 2 = 12 and 6 + 2 = 8. The factors we need are 6 and 2.

The signs are both negative.

#### Explanation:

The first step in factorising is to take out the common factor

#x^2#

#rArrx^2(x^2-8x+12)# Now we require to factorise the quadratic inside the bracket.

For the standard quadratic function

#color(red)(|bar(ul(color(white)(a/a)color(black)(ax^2+bx+c)color(white)(a/a)|)))# Consider the factors which multiply to give ac and sum to give b.

For

#x^2-8x+12# a = 1 , b = -8 and c = 12

Require factors of product

#ac=1xx12=12# which sum to -8In this case these are -6 and -2 as product = 12 and sum = -8

#rArrx^2-8x+12=(x-6)(x-2)#

#rArrx^4-8x^3+12x^2=x^2(x-6)(x-2)#