Explain how to use grouping to factor each polynomial. 3x^2-5x-12

Question

Explain how to use grouping to factor each polynomial. 3x²-5x-12

Answer 1

This method is also called splitting the middle term or the British method.

Factor by grouping is a method best for an even number of terms. In your problem the polynomial has only 3 terms so we split the linear term in two by answering the key question:

What multiplies to a×c and adds to b?

For your problem a=3, b=-5, and c=-12.

So what multiplies to -36 and adds to -5?

-9x4=36

-9+4=-5

Then make the following substitution -5x=-9x+4x into your original problem to get:

3x²-9x+4x-12.

From here factor by grouping as usual.

Answer 2

3x^2 -5x -12

=3x^2 +4x -9x -12

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

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

or

3x^2-5x-12

=3x^2 -9x +4x -12

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

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

either way works