6.7.1 Factoring Strategies for Polynomials

Algebra 16.7.1 Factoring Strategies for Polynomials

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Warm Up

In this unit, remember to double click on mathematical expressions/equations to enlarge, if needed.

Working with a partner, list as many strategies as you can for factoring polynomials.

Your answers may vary, but here are some examples:

Factoring by finding the GCF of an expression and using reverse distribution
Factoring using grouping
Factoring trinomials of the form $x^{2} + b x + c$ (undo FOIL)
Factoring trinomials of the form $a x^{2} + b x + c$ using trial and error
Factoring trinomials using the “ $a c$ ” method
Factoring using substitution
Factoring the difference of squares
Factoring perfect square trinomials

Work with your partner to write a sample polynomial that would be fitting for each strategy listed.

Compare your answers:

Factoring Strategy	Sample Polynomial
Factoring by finding the GCF of an expression and using reverse distribution	$14 a + 8 a b + 12$
Factoring using grouping	$x^{2} + 2 x - 5 x - 10$
Factoring trinomials of the form $x^{2} + b x + c$ (undo FOIL)	$t^{2} + 14 t + 24$
Factoring trinomials of the form $a x^{2} + b x + c$ using trial and error	$18 x^{2} - 3 x y - 10 y^{2}$
Factoring trinomials using the “ $a c$ ” method	$16 x^{2} - 32 x + 12$
Factoring using substitution	$(x - 2)^{2} + 7 (x - 2) + 12$
Factoring the difference of squares	$81 y^{2} - 1$
Factoring perfect square trinomials	$25 v^{2} + 20 v + 4$

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