When factoring the trinomial $x^2 - 9x - 22$, what can you conclude about the signs of the two numbers in the binomial factors?

One number is positive and one is negative.

It is impossible to determine the signs.

Factoring x² + bx + c Practice — Grade 8 math

1. Which of the following is the correct factorization of the trinomial $x^2 - 10x + 24$?
- A. (x + 4)(x + 6)
- B. (x - 4)(x - 6)
- C. (x - 2)(x - 12)
- D. (x + 2)(x - 12)
2. When factoring the trinomial $x^2 - 9x - 22$, what can you conclude about the signs of the two numbers in the binomial factors?
- A. Both numbers are positive.
- B. Both numbers are negative.
- C. One number is positive and one is negative.
- D. It is impossible to determine the signs.
3. When factoring $x^2 + 3x - 18$ into $(x+p)(x+q)$, one of the numbers, say $p$, is 6. What is the value of $q$? ___
4. Factor the trinomial $x^2 - 4x - 21$. If the factored form is $(x+p)(x+q)$, what is the value of the smaller number between $p$ and $q$? ___
5. 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)
6. 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
7. 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)
8. 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)
9. Solve the quadratic equation $n^2 - 14n + 49 = 0$. The solution is $n = $ ___.