Problem of the Week

Updated at Jun 5, 2023 9:31 AM

Recent Posts

Mar 24, 2025

For this week we've brought you this algebra problem.

How would you find the factors of $20{u}^{2}+4u-24$ ?

Here are the steps:

20{u}^{2}+4u-24

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

20{u}^{2}

4u

, and

-24

It is

4

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

20{u}^{2}

4u

, and

-24

It is 1, since

u

is not in every term.

Multiplying the results above,

The GCF is

4

To get access to all 'How?' and 'Why?' steps, join Cymath Plus!

GCF =

4

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

4(\frac{20{u}^{2}}{4}+\frac{4u}{4}-\frac{24}{4})

Simplify each term in parentheses.

4(5{u}^{2}+u-6)

Split the second term in

5{u}^{2}+u-6

into two terms.

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

5\times -6=-30

Ask: Which two numbers add up to

1

and multiply to

-30

6

and

-5

Split

u

as the sum of

6u

and

-5u

5{u}^{2}+6u-5u-6

To get access to all 'How?' and 'Why?' steps, join Cymath Plus!

4(5{u}^{2}+6u-5u-6)

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

4(u(5u+6)-(5u+6))

Factor out the common term

5u+6

4(5u+6)(u-1)

Done