How do you factor 3x^2 - 5x - 12?

3 Answers

The answer is (x-3)(3x+4).

Explanation:

![https://useruploads.socratic.org/uA9v8owQVa0rRLtH5qXG_1501845782432413515707.jpg)

3x^2−5x−12

=(x-3)(3x+4)

Explanation:

Another Method
Using Quadratic Formula,
(-b+-sqrt(b^2-4ac))/(2a)

a=3
b=-5
c=-12

Applying Formula we get,

(-(-5)+-sqrt(-5^2-4(3)(-12)))/(2(3)
(+5+-sqrt(25+144))/(6)
(5+-sqrt(169))/(6)

(5+-(13))/(6)

x=(5+13)/(6)=18/6=3 _ here (x-3)
and
x=(5-13)/(6)=-8/6=-4/3 _ here (3x+4)

Aug 4, 2017

(x-3)(3x+4)

Explanation:

3x^2 -5x -12 is a quadratic trinomial.

Find factors of 3 and 12 whose products differ by 5

" "3 " & " 12
" "darr" "darr

" "1" "3" "rarr3 xx 3 =9
" "3" "4" "rarr1xx4 = ul4
color(white)(w.wwwwwwwwww..wwww)5

We have correct factors, now fill in the signs to get-5 and 12

" "1" "-3" "rarr3 xx -3 =-9
" "3" "+4" "rarr1xx+4 = +ul4
color(white)(w.wwwwwwwwwwwwww.wwww)-5

3x^2 -5x -12

=(x-3)(3x+4)