Problem of the Week

Updated at Jun 29, 2020 2:29 PM

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May 5, 2025

To get more practice in algebra, we brought you this problem of the week:

How can we compute the factors of $30{x}^{2}-44x+16$ ?

Check out the solution below!

30{x}^{2}-44x+16

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

30{x}^{2}

-44x

, and

16

It is

2

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

30{x}^{2}

-44x

, and

16

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

2

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

GCF =

2

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

2(\frac{30{x}^{2}}{2}+\frac{-44x}{2}+\frac{16}{2})

Simplify each term in parentheses.

2(15{x}^{2}-22x+8)

Split the second term in

15{x}^{2}-22x+8

into two terms.

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

15\times 8=120

Ask: Which two numbers add up to

-22

and multiply to

120

-10

and

-12

Split

-22x

as the sum of

-10x

and

-12x

15{x}^{2}-10x-12x+8

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

2(15{x}^{2}-10x-12x+8)

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

2(5x(3x-2)-4(3x-2))

Factor out the common term

3x-2

2(3x-2)(5x-4)

Done