Test Questions on Factoring Perfect Square Trinomials (Algebra 1)

📚 Quick Study Guide

• 🔍 Definition: A perfect square trinomial is a trinomial that can be factored into the square of a binomial.
• ➕ Formulas:
  • $(a + b)^2 = a^2 + 2ab + b^2$
  • $(a - b)^2 = a^2 - 2ab + b^2$
• 📝 Steps to Identify and Factor:
  1. Check if the first and last terms are perfect squares.
  2. Verify if the middle term is twice the product of the square roots of the first and last terms.
  3. Factor using the appropriate formula.
• 💡 Example 1: Factor $x^2 + 6x + 9$. Here, $a = x$ and $b = 3$. Since $2ab = 2(x)(3) = 6x$, the trinomial is a perfect square. Thus, $x^2 + 6x + 9 = (x + 3)^2$.
• 🧪 Example 2: Factor $4x^2 - 12x + 9$. Here, $a = 2x$ and $b = 3$. Since $-2ab = -2(2x)(3) = -12x$, the trinomial is a perfect square. Thus, $4x^2 - 12x + 9 = (2x - 3)^2$.

✍️ Practice Quiz

1. What is the factored form of $x^2 + 10x + 25$?
   1. (x + 3)^2
   2. (x + 4)^2
   3. (x + 5)^2
   4. (x + 6)^2
2. What is the factored form of $x^2 - 8x + 16$?
   1. (x - 2)^2
   2. (x - 3)^2
   3. (x - 4)^2
   4. (x - 5)^2
3. What is the factored form of $4x^2 + 4x + 1$?
   1. (x + 1)^2
   2. (2x + 1)^2
   3. (3x + 1)^2
   4. (4x + 1)^2
4. What is the factored form of $9x^2 - 12x + 4$?
   1. (3x - 1)^2
   2. (3x - 2)^2
   3. (3x - 3)^2
   4. (3x - 4)^2
5. Factor $x^2 + 14x + 49$:
   1. (x + 6)^2
   2. (x + 7)^2
   3. (x + 8)^2
   4. (x + 9)^2
6. Factor $25x^2 - 20x + 4$:
   1. (4x - 1)^2
   2. (5x - 2)^2
   3. (6x - 3)^2
   4. (7x - 4)^2
7. Which of the following is a perfect square trinomial?
   1. $x^2 + 4x + 3$
   2. $x^2 + 6x + 8$
   3. $x^2 + 10x + 25$
   4. $x^2 + 8x + 15$