Test questions on recognizing and factoring perfect square trinomials

📚 Quick Study Guide

• 🔍 Definition: A perfect square trinomial is a trinomial that can be factored into the square of a binomial.
• 💡 Formulas:
  • $(a + b)^2 = a^2 + 2ab + b^2$
  • $(a - b)^2 = a^2 - 2ab + b^2$
• 📝 Recognizing Perfect Square Trinomials:
  • The first and last terms are perfect squares.
  • The middle term is twice the product of the square roots of the first and last terms.
• ➗ Factoring Steps:
  1. Check if the trinomial fits the form $a^2 + 2ab + b^2$ or $a^2 - 2ab + b^2$.
  2. Identify $a$ and $b$.
  3. Factor as $(a + b)^2$ or $(a - b)^2$, respectively.

🧪 Practice Quiz

1. What is the factored form of $x^2 + 6x + 9$?
   1. (A) $(x + 2)^2$
   2. (B) $(x - 3)^2$
   3. (C) $(x + 3)^2$
   4. (D) $(x - 2)^2$
2. Which of the following is a perfect square trinomial?
   1. (A) $x^2 + 4x + 2$
   2. (B) $x^2 - 6x + 9$
   3. (C) $x^2 + 2x - 1$
   4. (D) $x^2 - 4x - 4$
3. Factor $4x^2 - 12x + 9$.
   1. (A) $(2x + 3)^2$
   2. (B) $(2x - 3)^2$
   3. (C) $(4x - 3)^2$
   4. (D) $(2x - 9)^2$
4. What is the value of $c$ that makes $x^2 + 10x + c$ a perfect square trinomial?
   1. (A) 5
   2. (B) 10
   3. (C) 20
   4. (D) 25
5. Which expression is equivalent to $(x - 5)^2$?
   1. (A) $x^2 - 10x + 25$
   2. (B) $x^2 + 10x + 25$
   3. (C) $x^2 - 25$
   4. (D) $x^2 + 25$
6. Factor $9x^2 + 24x + 16$.
   1. (A) $(3x + 4)^2$
   2. (B) $(3x - 4)^2$
   3. (C) $(9x + 4)^2$
   4. (D) $(3x + 16)^2$
7. What is the factored form of $16x^2 - 8x + 1$?
   1. (A) $(4x + 1)^2$
   2. (B) $(4x - 1)^2$
   3. (C) $(16x - 1)^2$
   4. (D) $(4x - 2)^2$