Question

How do you factor by grouping `3x^2 - 17x + 10`?

Answer 1

`3x^2-17x+10=(3x-2)(x-5)`

Explanation:

In the quadratic polynomial `3x^2-17x+10`, the coefficient of `x^2` and constant term are of same sign and their product is `30`,

hence we should split `-17`, the coefficient of `x`. in two parts, whose sum is `17` and product is `30`. These are `2` and`15` and hence

`3x^2-17x+10`

= `3x^2-15x-2x+10`

= `3x(x-5)-2(x-5)`

= `(3x-2)(x-5)`

Note - If sign of coefficient of `x^2` and constant term are different, find two numbers whose difference is equal to the coefficient of `x`.

Answer 2

`(x-5)(3x-2)`

Explanation:

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

`"the factors of the product "3xx10=30`

`"which sum to "-17" are "-15" and "-2`

`"split the middle term using these factors"`

`3x^2-15x-2x+10larrcolor(blue)"factor by grouping"`

`=color(red)(3x)(x-5)color(red)(-2)(x-5)`

`"take out the "color(blue)"common factor "(x-5)`

`=(x-5)(color(red)(3x-2))`

`3x^2-17x+10=(x-5)(3x-2)`