Test Questions for Factoring Trinomials $ax^2+bx+c$ (Trial and Error Algebra 1)

📚 Quick Study Guide

• 🔍 Understanding Trinomials: A trinomial is a polynomial with three terms, generally in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.
• 🔢 Trial and Error Method: This method involves finding two binomials that, when multiplied together (using the FOIL method), result in the original trinomial.
• 💡 Steps for Factoring $ax^2 + bx + c$:
  • Find two numbers that multiply to $ac$ and add up to $b$.
  • Rewrite the middle term $bx$ using these two numbers.
  • Factor by grouping.
• ➕ Signs Matter: Pay close attention to the signs of $b$ and $c$. If $c$ is positive, both factors have the same sign as $b$. If $c$ is negative, the factors have opposite signs.
• ✅ Verification: Always check your answer by multiplying the factored binomials back together to ensure they equal 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. $(x + 1)(2x + 2)$
   4. $(x + 2)(x + 1)$
2. Factor the trinomial: $3x^2 - 10x + 3$
   1. $(3x - 1)(x - 3)$
   2. $(3x + 1)(x + 3)$
   3. $(x - 1)(3x - 3)$
   4. $(3x - 3)(x - 1)$
3. Which of the following is a factor of $5x^2 + 11x + 2$?
   1. $(5x + 1)$
   2. $(x + 3)$
   3. $(5x - 1)$
   4. $(x - 2)$
4. Factor $2x^2 - 7x + 3$
   1. $(2x - 1)(x - 3)$
   2. $(2x + 1)(x + 3)$
   3. $(x - 1)(2x - 3)$
   4. $(2x - 3)(x - 1)$
5. What are the factors of $4x^2 + 8x + 3$?
   1. $(2x + 1)(2x + 3)$
   2. $(4x + 1)(x + 3)$
   3. $(2x - 1)(2x - 3)$
   4. $(4x - 1)(x - 3)$
6. Factor: $6x^2 - 5x - 4$
   1. $(2x + 1)(3x - 4)$
   2. $(2x - 1)(3x + 4)$
   3. $(6x + 1)(x - 4)$
   4. $(6x - 1)(x + 4)$
7. Which of the following is a factor of $7x^2 - 9x + 2$?
   1. $(7x - 2)$
   2. $(x + 1)$
   3. $(7x + 2)$
   4. $(x - 2)$