EDGE Math 8

Factoring Other Trinomials

Trinomials in the Form $a x^{2} + b x + c$

To factor trinomials in the form $a x^{2} + b x y + c y^{2},$ the steps are the same as when factoring the trinomial $a x^{2} + b x + c .$ The only difference is that the variable y is included as a literal coefficient in the second term of the binomial factors.

In the preceding example, you factored the given trinomials as follows:

$5 x^{2} - 7 x + 2$	$=$	$(5 x - 2) (x - 1)$

$4 x^{2} - 31 x - 8$	$=$	$(4 x + 1) (x - 8)$

$12 x^{2} + 28 x + 15$	$=$	$(6 x + 5) (2 x + 3)$

$6 x^{2} + 25 x + 14$	$=$	$(2 x + 7) (3 x + 2)$

If the trinomials above have y as a second variable, then they can be factored as follows:

$5 x^{2} - 7 x + 2 y^{2}$	$=$	$(5 x - 2 y) (x - y)$

$4 x^{2} - 31 x - 8 y^{2}$	$=$	$(4 x + y) (x - 8 y)$

$12 x^{2} + 28 x + 15 y^{2}$	$=$	$(6 x + 5 y) (2 x + 3 y)$

$6 x^{2} + 25 x + 14 y^{2}$	$=$	$(2 x + 7 y) (3 x + 2 y)$