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Math 7 · Unit 4, Lesson 4: Factoring Out the GCF · Tile 2 of 3

Pull It Out

Divide every term, then check

Divide every term, then check

To factor, write the GCF outside the parentheses. Inside, write what's left of each term after you divide it by the GCF. Then check: expand your answer, and you should land right back where you started.

  1. Find the GCF of the numbers
  2. Divide each term by the GCF
  3. Write GCF( what is left )
  4. Check by expanding

Watch it work

12x + 18GCF 612x ÷ 6 = 2x, 18 ÷ 6 = 36(2x + 3)check: 6(2x + 3) = 12x + 18
10y − 25GCF 55(2y − 5)check: 10y − 25
8a + 20b + 4GCF 44(2a + 5b + 1)check: 8a + 20b + 4

When a term is the GCF itself, a 1 is left behind, not nothing.

12x + 18 = 2(6x + 9) is true, but it is not finished, because 6x and 9 still share a 3. Always pull out the greatest. If the terms inside still share a factor, keep going.

Elle and Finn

ElleMath-speak

Factoring rewrites a sum as a product. 12x + 18 and 6(2x + 3) are equivalent expressions.

FinnPlain English

Factoring turns adding into multiplying. Same value, it just comes in a neater package.

Elle and Finn talk it over

Finn

I factored 8a + 20b + 4 and got 4(2a + 5b).

Elle

Expand it and see what you get.

Finn

8a + 20b. Hey, where did my 4 go?

Elle

It left a 1 behind when it came out. Leave the 1 in.

Let me try a few

NC standard: NC.7.EE.1.

Where to go next

Let me try a few7 problems on pull it out. Next: Tile 3, Pulling Out a NegativeWhen the first term is negative All tilesAll 3 parts of this lesson. Tell us what you thought about this tileA few quick questions about just this tile. It takes a few minutes, and opens in a new tab so you keep your place.