Problem of the Week

Updated at Sep 24, 2018 4:13 PM

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Mar 31, 2025

This week we have another algebra problem:

How would you find the factors of $35{q}^{2}-6q-9$ ?

Let's start!

35{q}^{2}-6q-9

Split the second term in

35{q}^{2}-6q-9

into two terms.

Multiply the coefficient of the first term by the constant term.

35\times -9=-315

Ask: Which two numbers add up to

-6

and multiply to

-315

15

and

-21

Split

-6q

as the sum of

15q

and

-21q

35{q}^{2}+15q-21q-9

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35{q}^{2}+15q-21q-9

Factor out common terms in the first two terms, then in the last two terms.

5q(7q+3)-3(7q+3)

Factor out the common term

7q+3

(7q+3)(5q-3)

Done