Answer key for factoring trinomials worksheet with problems and solutions.

To solve these problems, we need to factor each trinomial. Factoring a trinomial in the form $x^2 + bx + c$ means finding two numbers that:
1. Multiply to give the last number ($c$).
2. Add to give the middle number ($b$).

Once we find those two numbers, we write the answer as $(x + \text{number}_1)(x + \text{number}_2)$. Then, we match the factors to the letters provided in the key at the bottom of the page.

Here is the step-by-step solution for each problem:

Problem 1: $x^2 + 2x - 8$
* We need numbers that multiply to $-8$ and add to $2$.
* The numbers are $4$ and $-2$ because $(4)(-2) = -8$ and $4 + (-2) = 2$.
* Factors: $(x + 4)(x - 2)$
* Looking at the key: $(x - 2)$ is A and $(x + 4)$ corresponds to the remaining part. The box shows A.

Problem 2: $x^2 + 2x - 3$
* We need numbers that multiply to $-3$ and add to $2$.
* The numbers are $3$ and $-1$.
* Factors: $(x + 3)(x - 1)$
* Looking at the key: $(x - 1)$ is G. The box shows G.

Problem 3: $x^2 + 11x + 18$
* We need numbers that multiply to $18$ and add to $11$.
* The numbers are $9$ and $2$.
* Factors: $(x + 9)(x + 2)$
* Looking at the key: $(x + 9)$ is D. The box shows D.

Problem 4: $x^2 + 7x - 60$
* We need numbers that multiply to $-60$ and add to $7$.
* The numbers are $12$ and $-5$.
* Factors: $(x + 12)(x - 5)$
* Looking at the key: $(x + 12)$ is E. The box shows E.

Problem 5: $x^2 - 18x + 77$
* We need numbers that multiply to $77$ and add to $-18$. Since they multiply to a positive but add to a negative, both numbers must be negative.
* The numbers are $-11$ and $-7$.
* Factors: $(x - 11)(x - 7)$
* Looking at the key: $(x - 11)$ is B. The box shows B.

Problem 6: $x^2 - 13x + 30$
* We need numbers that multiply to $30$ and add to $-13$. Both numbers must be negative.
* The numbers are $-10$ and $-3$.
* Factors: $(x - 10)(x - 3)$
* Looking at the key: $(x - 10)$ is H. The box shows H.

Problem 7: $x^2 - 11x - 12$
* We need numbers that multiply to $-12$ and add to $-11$.
* The numbers are $-12$ and $1$.
* Factors: $(x - 12)(x + 1)$
* Looking at the key: $(x - 12)$ is I. The box shows I.

Problem 8: $x^2 - x - 30$
* We need numbers that multiply to $-30$ and add to $-1$ (since $-x$ is $-1x$).
* The numbers are $-6$ and $5$.
* Factors: $(x - 6)(x + 5)$
* Looking at the key: $(x - 6)$ is C. The box shows C.

Problem 9: $x^2 + 15x + 56$
* We need numbers that multiply to $56$ and add to $15$.
* The numbers are $7$ and $8$.
* Factors: $(x + 7)(x + 8)$
* Looking at the key: $(x + 7)$ is F. The box shows F.

Final Answer:
1. A
2. G
3. D
4. E
5. B
6. H
7. I
8. C
9. F