Lesson 6: Factoring ax² + bx + c — 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. The trinomial $4x^2 + 11x + 6$ can be factored into two binomials. If one of the factors is $(x+2)$, what is the other factor? ___

5. 5. Which of the following represents the correct factorization of the trinomial $8x^2 - 14x + 3$?

   • A. (2x - 1)(4x - 3)
   • B. (2x + 1)(4x - 3)
   • C. (2x - 3)(4x - 1)
   • D. (8x - 1)(x + 3)

6. 6. Factor the trinomial $6x^2 + x - 12$. One of the binomial factors is $(3x-4)$. The other factor is ___.

7. 7. When factoring $10x^2 - 21x - 10$, you test combinations of factors. If you use the factors $(2, 5)$ for $a=10$, which pair of factors for $c=-10$ will produce the correct middle term?

   • A. (-2, 5)
   • B. (2, -5)
   • C. (1, -10)
   • D. (-1, 10)