GCF and Factoring Out a Monomial

Find the Greatest Common Factor:

28x⁶ and 40x

• 1120x⁷

• 4x

• 7x⁶

• answer not here

Find the Greatest Common Factor:

32x³y⁸ and 48xy³

• 8x³y³

• 8xy

• 16xy³

• 16x³y⁸

Find the Greatest Common Factor:

17x and 22y²

• 2

• xy²

• 17x

• 1

Find the Greatest Common Factor:

26x²y and 30xy²

Mathematical Equivalence

ON

Answer explanation

In expanded form, the terms would be (2)(13)xxy and (2)(15)xyy. The only factors they have in common are 2xy.

Factor out the Greatest Common Factor to write an equivalent expression:

12a³b² + 20ab²

• 4ab²(3a² + 5)

• 4ab(3a²b + 5b)

• 2ab²(6a² + 10)

Factor out the Greatest Common Factor to write an equivalent expression:

11a³b² + 12cd²

• 11abcd(a²b + 12d)

• The expression is prime and cannot be factored.

• (11+12)(abcd)

Factor out the Greatest Common Factor to write an equivalent expression:

24x⁴y⁴ + 30x⁹y²

^{***Hint #1: "GCF(Leftovers)"}

^{***Hint #2: Use the button next to the division sign when you need to type an exponent, the press the right arrow when you're ready to type in the next symbol, number, etc.}

^{ALSO... If you make a mistake, click right after the part you want to change and use BACKSPACE (not DELETE).}

Mathematical Equivalence

OFF

Answer explanation

Everything that BOTH terms are divisible by should be in the front. It is the GCF. The terms in the parentheses are the "leftovers" after you have divided each term by the GCF.

{It's like you UN-distributed the monomial.}

Factor out the Greatest Common Factor to write an equivalent expression:

44f³g⁷ + 56fg⁴

• 4(11f³g⁷ + 14fg⁴)

• 4fg⁴(11f²g³ + 14)

• fg⁴(44f²g³ + 56)

Answer explanation

Always divide out the largest coefficient possible without getting decimals or fractions. Remember... you're limited to the smallest of each exponent because that IS the greatest amount of variables they have in common.

Which TWO expressions would be considered prime?

• 3xy + 5xy³

• 15xy³ + 22

• 18a⁴c - 25b²

• 17ab² - 119a³

Mason factored the expression 25x⁴y⁵ - 75x²y⁸ and wrote this:

5xy(5x³y⁴ - 15xy⁷)

He is ​ (a)   because ​ (b)  

• incorrect
• he could have factored out a larger value.
• correct
• 5xy is the GCF.