Factoring Trinomials (a=1)

Show your work for each problem.

1.
What two numbers add to 7 and multiply to 12?
1. a)2 and 5
2. b)1 and 6
3. c)2 and 6
4. d)3 and 4
Answer: 3 and 4
and . The other pairs multiply to 12 but don't add to 7.
2.
Factor:
1. a)
2. b)
3. c)
4. d)
Answer:
and , so
3.
Factor . Write just the two numbers (smaller first, comma separated).
Answer: 3, 5
and , so
4.
Factor:
Answer: (x + 3)(x + 6)
1. What is the sum we need (the middle coefficient)? 9
2. What is the product we need (the constant)? 18
3. What two numbers add to 9 and multiply to 18? 3 and 6
4. Write the factored form: (x + 3)(x + 6)
5.
Factor:
1. a)
2. b)
3. c)
4. d)
Answer:
and , so
6.
Factor . Write the factored form.
Answer: (x - 3)(x - 8)
and , so
7.
Factor:
1. a)
2. b)
3. c)
4. d)
Answer:
and , so
8.
Factor:
Answer: (x + 4)(x - 6)
1. What sum do we need? -2
2. What product do we need? -24
3. Since the product is negative, the factors have different signs. The sum is negative, so which factor is larger in absolute value? negative
4. What two numbers work? (larger absolute value first) -6 and 4
5. Write the factored form: (x + 4)(x - 6)
9.
Factor . Write the factored form.
Answer: (x + 4)(x - 3)
and , so
10.
Factor:
Answer: (x + 4)(x - 5)
1. What is the sum (middle coefficient)? -1
2. What is the product (constant)? -20
3. List factor pairs of 20: (1,20), (2,10), (4,5)
4. Which pair can give a sum of -1 with opposite signs? 4 and 5
5. Write the factored form: (x + 4)(x - 5)
11.
Which trinomial CANNOT be factored using integers?
1. a)
2. b)
3. c)
4. d)
Answer:
For : factors of 7 are (1,7). . This is prime. The others: , , .
12.
Factor . Write the factored form.
Answer: (x - 4)(x - 9)
and , so
13.
Factor:
Answer: (x + 11)(x - 5)
1. What sum and product do we need? sum 6, product -55
2. List factor pairs of 55: (1,55), (5,11)
3. Which pair, with opposite signs, gives sum 6? 11 and -5
4. Write the factored form: (x + 11)(x - 5)
14.
Factor . Write the factored form.
Answer: (x - 7)(x - 9)
and , so
15.
A rectangle has area square units. Find its dimensions.
Answer: (x + 7) and (x - 5)
1. What is area as a product? length times width
2. What sum and product do we need? sum 2, product -35
3. Factor pairs of 35: (1,35), (5,7)
4. Which pair with opposite signs sums to 2? 7 and -5
5. What are the dimensions? (x + 7) and (x - 5)
16.
If factors as , what is ?
1. a)
2. b)
3. c)
4. d)
Answer:
Since , we need , so . This gives .