# How do you factor completely #8u^2 (u+1) + 2u (u+1) -3 (u+1)#?

##### 2 Answers

#### Explanation:

The key realization here is that every term has a

What I have in blue, we can factor by grouping. Here, I'll split the

What I have underlined is the same as

I can factor a

Both the underlined terms have a

Hope this helps!

#### Explanation:

#"take out the "color(blue)"common factor "(u+1)#

#=(u+1)(8u^2+2u-3)#

#"factor the quadratic using the a-c method"#

#"the factors of the product "8xx-3=-24#

#"which sum to + 2 are - 4 and + 6"#

#"split the middle term using these factors"#

#8u^2-4u+6u-3larrcolor(blue)"factor by grouping"#

#=color(red)(4u)(2u-1)color(red)(+3)(2u-1)#

#"take out the "color(blue)"common factor "(2u-1)#

#=(2u-1)(color(red)(4u+3))#

#"putting it together"#

#=(u+1)(2u-1)(4u+3)#