# How do you factor the expression #56x^3 +43x^2+5x#?

##### 1 Answer

#### Explanation:

First separate out the common factor

#56x^3+43x^2+5x = x(56x^2+43x+5)#

To factor the remaining quadratic expression, use an AC method.

Find a pair of factors of

To help find the appropriate pair you can proceed as follow:

Find the prime factorisation of

#280 = 2*2*2*5*7#

Next note that

As a result, the prime factors must be split between the pair in such a way that all factors of

This leaves the following possibilities to check the sum:

#1 + 5*7*2^3 = 1 + 280 = 281#

#5 + 7*2^3 = 5 + 56 = 61#

#7 + 5*2^3 = 7 + 40 = 47#

#5*7 + 2^3 = 35 + 8 = 43#

The last pair

Use this pair to split the middle term and factor by grouping:

#56x^2+43x+5#

#=56x^2+35x+8x+5#

#=(56x^2+35x)+(8x+5)#

#=7x(8x+5)+1(8x+5)#

#=(7x+1)(8x+5)#

Putting it all together:

#56x^3+43x^2+5x = x(7x+1)(8x+5)#