Factoring quadratics examples

📚 Quick Study Guide

🔍 Factoring is the process of breaking down a quadratic expression into its constituent binomial factors.

💡 A quadratic expression is of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

📝 The goal is to find two binomials $(px + q)$ and $(rx + s)$ such that $(px + q)(rx + s) = ax^2 + bx + c$.

➕ If $a = 1$, we look for two numbers that add up to $b$ and multiply to $c$.

➗ For example, to factor $x^2 + 5x + 6$, we need two numbers that add to 5 and multiply to 6 (2 and 3).

✅ Thus, $x^2 + 5x + 6 = (x + 2)(x + 3)$.

⭐ When $a \neq 1$, use techniques like factoring by grouping.

Practice Quiz

1. What are the factors of $x^2 + 7x + 12$?
   1. (x + 1)(x + 12)
   2. (x + 2)(x + 6)
   3. (x + 3)(x + 4)
   4. (x + 1)(x + 7)
2. Factor $x^2 - 5x + 6$.
   1. (x - 1)(x - 6)
   2. (x - 2)(x - 3)
   3. (x + 2)(x + 3)
   4. (x + 1)(x + 6)
3. Factor $x^2 + 2x - 8$.
   1. (x + 4)(x - 2)
   2. (x - 4)(x - 2)
   3. (x + 4)(x + 2)
   4. (x - 4)(x + 2)
4. 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)
5. Factor $3x^2 - 10x + 3$.
   1. (3x - 1)(x - 3)
   2. (3x + 1)(x + 3)
   3. (3x - 3)(x - 1)
   4. (3x + 3)(x + 1)
6. What are the factors of $x^2 - 9$?
   1. (x - 3)(x - 3)
   2. (x + 3)(x + 3)
   3. (x + 3)(x - 3)
   4. (x - 9)(x + 1)
7. Factor $4x^2 - 4x + 1$.
   1. (2x + 1)(2x + 1)
   2. (2x - 1)(2x - 1)
   3. (2x + 1)(2x - 1)
   4. (4x - 1)(x - 1)