Perfect Square Trinomials

Show your work for each problem.

1.
Which expression is a perfect square trinomial?
1. a)
2. b)
3. c)
4. d)
Answer:
because , , and matches the middle term.
2.
What is the factored form of ?
1. a)
2. b)
3. c)
4. d)
Answer:
because , , and .
3.
Factor . Write your answer in the form . What is ?
Answer: 4
because and .
4.
Factor . Write your answer in the form . What is ?
Answer: 3
because and (negative in the middle).
5.
Factor:
Answer: (x + 6)^2
1. What is the square root of the first term ? x
2. What is the square root of the last term ? 6
3. Is ? yes
4. What is the factored form? (x + 6)^2
6.
Factor:
Answer: (x - 7)^2
1. What is the square root of ? 7
2. Is the middle term positive or negative? negative
3. Check: Is ? yes
4. Write the factored form (x - 7)^2
7.
Which is the factored form of ?
1. a)
2. b)
3. c)
4. d)
Answer:
because , , and .
8.
Is a perfect square trinomial?
1. a)No, because the middle term is wrong
2. b)No, because 12 is not a perfect square
3. c)Yes, it factors to
4. d)Yes, it factors to
Answer: No, because 12 is not a perfect square
is NOT a perfect square trinomial because is not a perfect square. It factors as instead.
9.
Factor . The answer is . What is ?
Answer: 3
because , , and .
10.
Factor . The answer is . What is ?
Answer: 5
because , , and .
11.
Factor:
Answer: (5x - 3)^2
1. What is the square root of ? 5x
2. What is the square root of ? 3
3. What is ? 30x
4. Since the middle term is negative, what is the factored form? (5x - 3)^2
12.
Factor:
Answer: (6x + 7)^2
1. What is the square root of ? 6x
2. What is the square root of ? 7
3. What is ? 84x
4. Write the factored form (6x + 7)^2
13.
Which expression equals ?
1. a)
2. b)
3. c)
4. d)
Answer:
14.
Factor . Write your answer in the form . What is ?
Answer: 11
. So , , and .
15.
Factor:
Answer: (8x - 5)^2
1. What is the square root of ? 8x
2. What is the square root of ? 5
3. Calculate 80x
4. Does this match the middle term (ignoring sign)? yes
5. Write the factored form (8x - 5)^2
16.
Factor:
Answer: (9x + 5)^2
1. What is the square root of ? 9x
2. What is the square root of ? 5
3. Calculate 90x
4. Does this match the middle term? yes
5. Write the factored form (9x + 5)^2