Problem of the Week

Updated at Feb 13, 2023 2:18 PM

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Mar 24, 2025

This week we have another algebra problem:

How can we factor $6{y}^{2}-48y+42$ ?

Let's start!

6{y}^{2}-48y+42

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

6{y}^{2}

-48y

, and

42

It is

6

What is the highest degree of $y$ that divides evenly into

6{y}^{2}

-48y

, and

42

It is 1, since

y

is not in every term.

Multiplying the results above,

The GCF is

6

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GCF =

6

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

6(\frac{6{y}^{2}}{6}+\frac{-48y}{6}+\frac{42}{6})

Simplify each term in parentheses.

6({y}^{2}-8y+7)

Factor

{y}^{2}-8y+7

Ask: Which two numbers add up to

-8

and multiply to

7

-7

and

-1

Rewrite the expression using the above.

(y-7)(y-1)

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6(y-7)(y-1)

Done