Question

How do you factor `3x^2 +10x - 8`?

Answer 1

`(3x-2)(x+4)`

Explanation:

`3x^2+10x-8`

first multiply `3` with `-8` and we get `-24`

then find two numbers that if we add or subtract we get `+10` and if we multiply we get `-24`

and the numbers are `+12` and `-2`

then we place those numbers as follow :-

`3x^2+12x-2x-8`

then we group them

`(3x^2+12x)(-2x-8)`

now take the common factor out.

`3x(x+4)-2(x+4)`

then group the numbers outside of the brackets

`(3x-2)(x+4)`

and that is the answer

Proper Solution:-

`3x^2+10x-8`

`3x^2+12x-2x-8`

`(3x^2+12x)(-2x-8)`

`3x(x+4)-2(x+4)`

`(3x-2)(x+4)`

Answer 2

`(x+4)(3x-2)`

Explanation:

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

`•color(white)(x)ax^2+bx+c ;a!=0`

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

`3x^2+10x-8larrcolor(blue)"is in standard form"`

`"with "a=3,b=10" and "c=-8`

`"consider factors of "3xx-8=-24" which sum to + 10"`

`"the required factors are "+12" and "-2`

`color(blue)"split the middle term using these factors"`

`3x^2+12x-2x-8larrcolor(blue)"factor by grouping"`

`=color(red)(3x)(x+4)color(red)(-2)(x+4)`

`"take out the common factor "(x+4)`

`=(x+4)(color(red)(3x-2))`

`rArr3x^2+10x-8=(x+4)(3x-2)`