# How do you factor #5x^3+6x^2-45x-54#?

##### 1 Answer

May 22, 2016

(5x +6)(x-3)(x+3)

#### Explanation:

Group the terms in 'pairs'

thus

#[5x^3+6x^2]+[-45x-54]# now factorise each pair

#rArrx^2(5x+6)-9(5x+6)# We now have a common factor of (5x + 6) and taking it out leaves.

#(5x+6)(x^2-9)# Now

#x^2-9" is a difference of squares"# In general a difference of squares factorises as.

#color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))# here

#x^2=(x)^2" and " 9=(3)^2rArra=x ,b=3#

#rArrx^2-9=(x-3)(x+3)# Putting this altogether to obtain.

#5x^3+6x^2-45x-54=(5x+6)(x-3)(x+3)#