Question

How do you factor completely `6x^2+7x+2`?

Answer 1

`(2x+1)(3x+2)`

Explanation:

`"for a quadratic in "color(blue)"standard form"`

`•color(white)(x)ax^2+bx+c color(white)(x);a!=0`

`6x^2+7x+2larr"is in standard form"`

`"with "a=6, b=7" and "c=2`

`color(blue)"to factorise"`

`"consider the factors of the product ac which sum to b"`

`rArrac=6xx2=12" and + 4, + 3 sum to + 7"`

`6x^2+3x+4x+2larrcolor(blue)"split middle term"`

`=color(red)(3x)(2x+1)color(red)(+2)(2x+1)larrcolor(blue)"factor in groups"`

`"take out a common factor "(2x+1)`

`=(2x+1)(color(red)(3x+2))`

`rArr6x^2+7x+2=(2x+1)(3x+2)`

Answer 2

`(2x+1)(3x+2)`

Explanation:

By sum & product

= `6x^2+4x+3x+2`

= `2x(3x+2)+1(3x+2)`

= `(2x+1)(3x+2)`

Hope this helps!