Factoring Trinomials Formula

Polynomial expression in the form of $ax^{2}+bx+c$ is known as a Trinomial.

$\large a^{2} + 2ab + b^{2} = (a+b)^{2}$

$\large a^{2} – 2ab + b^{2} = (a-b)^{2}$

$\large a^{2} – b^{2} = (a+b)(a-b)$

$\large a ^{3} + b ^{3} = (a + b) (a ^{2} – a b + b ^{2})$

$\large a ^{3} – b ^{3} = (a – b) (a ^{2} + a b + b ^{2})$

Solved Examples

Question 1: Factor $2 x ^{2} – 5 x – 12$.

Solution:

$2 x ^{2} – 5 x – 12$

= $2 x^{2} + 3x – 8x – 12$

= $x (2x + 3) – 4 (2x + 3)$

= $(2x + 3) (x – 4)$