6.5.1 Undoing FOIL

Algebra 16.5.1 Undoing FOIL

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Warm Up

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

We are going to factor the trinomial $q^{2} + 10 q + 24$ by reversing the process of FOIL.

Find all the different combinations of factors of $24$ . One example is provided in the table.

Factors of 24	Sum of factors
$1, 24$	$1 + 24 = 25$

Compare your answers:

Factors of 24	Sum of factors
$1$ , $24$	$1 + 24 = 25$
$2$ , $12$	$2 + 12 = 14$
$3$ , $8$	$3 + 8 = 11$
$4$ , $6$	$4 + 6 = 10$

We’re going to look at these factors to see which of them would fit in the boxes and multiply to make the trinomial $q^{2} + 10 q + 24$ that we started with in the beginning.

$(q + ◻) (q + ◻)$

Which pair of factors fits the situation? What is the factored expression?

Compare your answer:

$4$ , $6$

$(q + 4) (q + 6)$

So, by undoing FOIL, we found that the trinomial $q^{2} + 10 q + 24$ factors to the expression $(q + 4) (q + 6)$ .

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