Solved examples for factoring simple quadratic trinomials

📚 Quick Study Guide

• 🔍 A quadratic trinomial is a polynomial with three terms, where the highest power of the variable is 2. It generally looks like $ax^2 + bx + c$.
• 💡 Factoring a simple quadratic trinomial (where $a = 1$) involves finding two numbers that multiply to $c$ and add up to $b$.
• 📝 The factored form will look like $(x + p)(x + q)$, where $p * q = c$ and $p + q = b$.
• ➗ When $c$ is positive, $p$ and $q$ have the same sign (both positive or both negative).
• ➖ When $c$ is negative, $p$ and $q$ have different signs (one positive and one negative).
• 🧠 Always check your work by expanding the factored form to ensure it matches the original trinomial.
• ➕ Remember to look for a greatest common factor (GCF) before attempting to factor the trinomial.

Practice Quiz

1. What are the factors of $x^2 + 5x + 6$?
   1. (x + 1)(x + 6)
   2. (x + 2)(x + 3)
   3. (x + 5)(x + 1)
   4. (x - 2)(x - 3)
2. What are the factors of $x^2 - 7x + 12$?
   1. (x - 3)(x - 4)
   2. (x + 3)(x + 4)
   3. (x - 2)(x - 6)
   4. (x + 2)(x + 6)
3. What are the factors of $x^2 + 2x - 15$?
   1. (x + 5)(x - 3)
   2. (x - 5)(x + 3)
   3. (x + 15)(x - 1)
   4. (x - 5)(x - 3)
4. What are the factors of $x^2 - 4x - 21$?
   1. (x - 7)(x + 3)
   2. (x + 7)(x - 3)
   3. (x - 7)(x - 3)
   4. (x + 7)(x + 3)
5. What are the factors of $x^2 + 8x + 16$?
   1. (x + 4)(x + 4)
   2. (x + 8)(x + 2)
   3. (x + 16)(x + 1)
   4. (x - 4)(x - 4)
6. What are the factors of $x^2 - 10x + 25$?
   1. (x - 5)(x - 5)
   2. (x + 5)(x + 5)
   3. (x - 10)(x - 5)
   4. (x + 25)(x + 1)
7. What are the factors of $x^2 + x - 20$?
   1. (x + 5)(x - 4)
   2. (x - 5)(x + 4)
   3. (x + 10)(x - 2)
   4. (x - 10)(x + 2)