# How do you factor completely: #5x^2 + 6x − 8#?

##### 2 Answers

#### Explanation:

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

#"the factors of the product "5xx-8=-40#

#"which sum to + 6 are + 10 and - 4"#

#"split the middle term using these factors"#

#5x^2+10x-4x-8larrcolor(blue)"factor by grouping"#

#=color(red)(5x)(x+2)color(red)(-4)(x+2)#

#"take out the "color(blue)"common factor "(x+2)#

#=(x+2)(color(red)(5x-4))#

#5x^2+6x-8=(x+2)(5x-4)#

#### Explanation:

A quadratic equation

- No (real) roots exist. In this case, the polynomial cannot be factorized any further
#x_1=x_2=\hat{x}# . In this case, the polynomial is the squared binomial#a(x-\hat{x})^2# #x_1 \ne x_2# . In this case, the polynomial can be factored as#a(x-x_1)(x-x_2)#

Let's look for the solutions of your equation:

So,