9-6 Factoring Quadratic Trinomials Practice — Grade 9 math

9-6 Factoring Quadratic Trinomials — Practice Questions

1. Factor the trinomial $4c - 60 + c^2$.
- A. (c + 10)(c - 6)
- B. (c - 10)(c + 6)
- C. (c + 12)(c - 5)
- D. (c - 15)(c + 4)
2. Factor the trinomial $a^2 + 48 - 2a$.
- A. (a - 8)(a + 6)
- B. (a - 8)(a - 6)
- C. (a - 12)(a - 4)
- D. Cannot be factored
3. Factor the trinomial $32 - 12b + b^2$.
- A. (b - 4)(b - 8)
- B. (b + 4)(b + 8)
- C. (b - 16)(b + 2)
- D. (b - 2)(b - 16)
4. Factor the expression $3b^2 - 33b + 72$ completely.
- A. 3(b - 3)(b - 8)
- B. 3(b - 6)(b - 4)
- C. (b - 3)(b - 8)
- D. 3(b - 12)(b + 1)
5. Solve the quadratic equation $n^2 - 14n + 49 = 0$. The solution is $n = $ ___.
6. Factor the expression $4x^2 - 20x - 144$ completely.
- A. 4(x - 9)(x + 4)
- B. 4(x + 9)(x - 4)
- C. 4(x - 12)(x + 3)
- D. (x - 9)(x + 4)
7. To factor the trinomial $6x^2 + 19x + 10$ using the 'ac' method, which pair of numbers should be used to split the middle term?
- A. Two numbers that multiply to 60 and add to 19
- B. Two numbers that multiply to 10 and add to 19
- C. Two numbers that multiply to 60 and add to 10
- D. Two numbers that multiply to 16 and add to 19
8. Factor the trinomial $4n^2 + 5n - 6$. The result is ___.
9. Completely factor the expression $20x^2 + 14x - 12$. The factored form is ___.
10. When factoring $5p^2 - 17p + 6$, the middle term is split into two terms. Which expression represents the correct next step in the 'ac' method?
- A. $5p^2 - 15p - 2p + 6$
- B. $5p^2 + 15p + 2p + 6$
- C. $5p^2 - 10p - 7p + 6$
- D. $5p^2 - 30p + p + 6$