Math 7 · Unit 4, Lesson 4: Factoring Out the GCF · Tile 3 of 3
Pulling Out a Negative
When the first term is negative
When the first term is negative
When the first term is negative, you can pull out a negative GCF. Then every sign inside flips. Both ways are right, but pulling out the negative makes the first term inside positive, which is usually neater.
−8x + 12pull out 4: 4(−2x + 3)or pull out −4: −8x ÷ (−4) = 2x, 12 ÷ (−4) = −3−4(2x − 3)check: −4(2x − 3) = −8x + 12
−6a − 9pull out −3−3(2a + 3)check: −6a − 9
Which expressions are equivalent to 12 − 4x?
A. 4(3 − x)B. −4(x − 3)C. −4(−3 + x)D. 2(6 − 2x)
Answer: all four. Expand each to check. D is equivalent, but it is not fully factored, because 6 and 2x still share a 2.
Elle and Finn
ElleMath-speak
When factoring out a negative common factor, divide each term by the negative factor. The sign of every term inside changes.
FinnPlain English
Pull out a negative, and every sign inside flips. Expand to check, and the signs flip right back.
NC standard: NC.7.EE.1.