Lesson 3: Distribution and Factoring — Practice Questions

1. 1. What is the greatest common factor (GCF) of all the terms in the polynomial $18p^4q^2 - 30p^3q^3 + 6p^2q^4$?

   • A. $6p^2q^2$
   • B. $6pq$
   • C. $3p^2q^2$
   • D. $18p^4q^4$

2. 2. Factor the polynomial completely by finding its greatest common factor: $14a^2b + 21ab^2 - 7ab$.

   • A. $7ab(2a + 3b - 1)$
   • B. $7ab(2a + 3b)$
   • C. $7a(2ab + 3b^2 - b)$
   • D. $14ab(a + 2b - 1)$

3. 3. Which expression correctly shows the terms of $15m^3 + 5m^2 - 10m$ rewritten as products of the GCF?

   • A. $5(3m^3 + m^2 - 2m)$
   • B. $5m(3m^2) + 5m(m) - 5m(2)$
   • C. $m(15m^2 + 5m - 10)$
   • D. $5m(3m^3 + m^2 - 2m)$

4. 4. Simplify the rational expression $\frac{4x-20}{x^2-5x}$. The simplified form is ___.

5. 5. Which expression is the simplified form of $\frac{z^2-16}{z^2+8z+16}$?

   • A. $\frac{z-4}{z+4}$
   • B. $\frac{z+4}{z-4}$
   • C. $-1$
   • D. $\frac{z-2}{z+2}$

6. 6. Simplify the expression $\frac{p^2+2p-8}{p^2-p-2}$. The simplified form is ___.

7. 7. To simplify the expression $\frac{m^2-4m}{7m-28}$, what is the common factor that can be canceled?

   • A. $m$
   • B. $m-4$
   • C. $7$
   • D. $m+4$

8. 8. Simplify the rational expression $\frac{3w^2+9w-54}{2w+12}$ completely. The result is ___.