Test Your Skills: Factoring Trinomials with a ≠ 1 (Algebra 1 Questions)

📚 Quick Study Guide

🔍 Standard Form: A trinomial is in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants and $a \neq 0$. 🧮 The 'ac' Method: Multiply $a$ and $c$ to get $ac$. Find two numbers that multiply to $ac$ and add up to $b$. ➗ Decomposition: Rewrite the middle term ($bx$) using the two numbers you found in the previous step. This decomposes the trinomial into four terms. 🤝 Factoring by Grouping: Group the first two terms and the last two terms. Factor out the greatest common factor (GCF) from each group. ✏️ Final Factorization: If done correctly, the expressions in the parentheses will be the same. Factor out this common binomial factor. 💡 Check Your Answer: Multiply the factors to make sure you get the original trinomial.

🧪 Practice Quiz

1. What are the factors of $2x^2 + 5x + 2$?
1. (2x + 1)(x + 2)
2. (2x + 2)(x + 1)
3. (x + 1)(x + 2)
4. (2x - 1)(x - 2)
2. Factor $3x^2 - 10x + 8$.
1. (3x - 4)(x - 2)
2. (3x - 2)(x - 4)
3. (3x + 4)(x + 2)
4. (3x + 2)(x + 4)
3. Factor $4x^2 + 8x + 3$.
1. (2x + 1)(2x + 3)
2. (2x - 1)(2x - 3)
3. (4x + 1)(x + 3)
4. (4x - 1)(x - 3)
4. Factor $5x^2 - 17x + 6$.
1. (5x - 2)(x - 3)
2. (5x - 3)(x - 2)
3. (5x + 2)(x + 3)
4. (5x + 3)(x + 2)
5. Factor $6x^2 + 11x - 10$.
1. (2x + 5)(3x - 2)
2. (2x - 5)(3x + 2)
3. (6x - 5)(x + 2)
4. (6x + 5)(x - 2)
6. Factor $8x^2 - 14x + 3$.
1. (4x - 1)(2x - 3)
2. (4x + 1)(2x + 3)
3. (8x - 1)(x - 3)
4. (8x + 1)(x + 3)
7. Factor $10x^2 + 13x - 3$.
1. (5x - 1)(2x + 3)
2. (5x + 1)(2x - 3)
3. (10x - 1)(x + 3)
4. (10x + 1)(x - 3)