Question

How do you factor the trinomial `2x^2+15x+7`?

Answer 1

`2x^2+15x+7=(x+7)(2x+1)`

Explanation:

Given quadratic polynomial:

`2x^2+15x+7`

`=2x^2+14x+x+7`

`=2x(x+7)+(x+7)`

`=(x+7)(2x+1)`

Answer 2

`(x+7)(2x+1)`

Explanation:

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

`"the factors of the product "2xx7=14`

`"which sum to "+15" are "+14" and "+1`

`"use these factors to split the middle term"`

`2x^2+14x+x+7larrcolor(blue)"factor by grouping"`

`=color(red)(2x)(x+7)color(red)(+1)(x+7)`

`"take out the "color(blue)"common factor "(x+7)`

`=(x+7)(color(red)(2x+1))`

`2x^2+15x+7=(x+7)(2x+1)`