Please use this form if you would like to have this math solver on your website, free of charge.

Factoring by Grouping

WHAT TO DO:

HOW TO DO IT:

Given a trinomial of type ax^{2} + bx + c that has
no common factor, where signs may be positive or
negative. Separate the signs from the coefficients.
[Read Â± as + or - ]

Read the â€œclues of the signsâ€.

Find product of first and last coefficients.
This is the grouping number (GN)

GN

AÂ·C = P

Find all possible factors of GN = P
whose sum or difference is B
(depending on the sign before C.)

+ sum

or

- difference

P = rÂ·s
, r > s

(r + s) = B

(r - s) = B

Example:

Given: 10x^{2} + 11x - 6

GN

10Â·6 = 60

The last sign is â€œ−â€ so find the pair of factors
of 60 that has a difference of 11.

The largest factor of the pair gets middle sign, +

+ 15 and
- 4

The trinomial can be arranged in four terms using
these values as coefficients of x, grouped 2 Ã— 2