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

2 Answers
Apr 1, 2018

(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)

Apr 1, 2018

(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)