1Cademy - Factoring $$-8y

Learn Before

Factoring the Greatest Common Factor from a Polynomial

Example

Factoring $-8y - 24$

Factor $-8y - 24$ by extracting the greatest common factor, noting that the leading coefficient is negative.

Step 1 — Find the GCF: Ignoring the signs, find the GCF of $8y$ and $24$ . Factor each into primes: $8y = 2 \cdot 2 \cdot 2 \cdot y$ and $24 = 2 \cdot 2 \cdot 2 \cdot 3$ . The common factors are three $2$ s, so the numerical GCF is $2 \cdot 2 \cdot 2 = 8$ . Because the expression has a negative leading coefficient, use $-8$ as the GCF.

Step 2 — Rewrite each term using the GCF: Express $-8y = (-8) \cdot y$ and $-24 = (-8) \cdot 3$ , giving $(-8) \cdot y + (-8) \cdot 3$ .

Step 3 — Factor out the GCF: $-8(y + 3)$ .

Step 4 — Check by multiplying: $-8(y + 3) = -8 \cdot y + (-8) \cdot 3 = -8y - 24$ ✓.

The factored form is $-8(y + 3)$ . Factoring out the negative GCF reverses the signs inside the parentheses — both terms that were originally negative appear as positive inside $(y + 3)$ .

Updated 2026-04-21

Contributors are:

Who are from:

References

OpenStax Elementary Algebra

Learn Before

Related

Learn After