Math Snap

STEP 1

1. We are given a polynomial expression with three terms.
2. We need to identify the greatest common factor (GCF) of the terms.
3. We will factor out the GCF from the expression.

STEP 2

1. Identify the GCF of the coefficients and the variables in the expression.
2. Factor the GCF out of the expression.

STEP 3

Identify the GCF of the coefficients $22$, $10$, and $-16$.
- The prime factors of $22$ are $2 \times 11$.
- The prime factors of $10$ are $2 \times 5$.
- The prime factors of $-16$ are $2^4$.
The GCF of the coefficients is $2$.

STEP 4

Identify the GCF of the variables in each term:
- For $a$, the powers are $2$, $9$, and $5$. The GCF is $a^2$.
- For $b$, the powers are $6$, $3$, and $1$. The GCF is $b^1$.
- For $c$, the powers are $8$, $0$, and $7$. The GCF is $c^0$ (since $c$ is not present in the second term).
The GCF of the entire expression is $2a^2b$.

Factor the GCF $2a^2b$ out of each term in the expression:
\[
22a^2b^6c^8 + 10a^9b^3 - 16a^5bc^7 $$ becomes:
\[
2a^2b(11b^5c^8 + 5a^7b - 8a^3c^7) $$ The GCF is: $2a^2b$
The factored expression is: $2a^2b(11b^5c^8 + 5a^7b - 8a^3c^7)$