How do you factor x² + bx + c?

Find two numbers with product c and sum b, then write (x + p)(x + q).

What is a difference of squares?

a² minus b² factors as (a + b)(a − b), like x² − 25 = (x + 5)(x − 5).

For x² + bx + c, find two numbers that multiply to c and add to b.

By Nethanel Bar, Co-founder & CEO

Last updated October 18, 2026

Factor completely.

12 problems

1.
x² + 8x + 12
Solve on the board
Answer(x+2)×(x+6)
1. Factor
  (x+2)×(x+6)
2.
x² + 16x + 15
Solve on the board
Answer(x+1)×(x+15)
1. Factor
  (x+1)×(x+15)
3.
x² + 17x + 16
Solve on the board
Answer(x+1)×(x+16)
1. Factor
  (x+1)×(x+16)
4.
x² + 13x + 22
Solve on the board
Answer(x+2)×(x+11)
1. Factor
  (x+2)×(x+11)
5.
x² + 6x − 7
Solve on the board
Answer(x−1)×(x+7)
1. Factor
  (x−1)×(x+7)
6.
x² − 6x − 27
Solve on the board
Answer(x−9)×(x+3)
1. Factor
  (x−9)×(x+3)
7.
x² − 16x + 15
Solve on the board
Answer(x−15)×(x−1)
1. Factor
  (x−15)×(x−1)
8.
x² − 2x − 8
Solve on the board
Answer(x−4)×(x+2)
1. Factor
  (x−4)×(x+2)
9.
x² − 8x + 7
Solve on the board
Answer(x−7)×(x−1)
1. Factor
  (x−7)×(x−1)
10.
x² − 25
Solve on the board
Answer(x+5)×(x−5)
1. Factor
  (x+5)×(x−5)
11.
x² + 18x + 81
Solve on the board
Answer(x+9)²
1. Factor
  (x+9)²
12.
x² − 6x + 9
Solve on the board
Answer(x−3)²
1. Factor
  (x−3)²

x² + 8x + 12: 2 and 6 multiply to 12 and add to 8, so it factors as (x + 2)(x + 6). Multiply back out to check.

How do you factor x² + bx + c?: Find two numbers with product c and sum b, then write (x + p)(x + q).
What is a difference of squares?: a² minus b² factors as (a + b)(a − b), like x² − 25 = (x + 5)(x − 5).

Name: ____________________ Date: ____________

Factor completely.

(x+2)×(x+6)
(x+1)×(x+15)
(x+1)×(x+16)
(x+2)×(x+11)
(x−1)×(x+7)
(x−9)×(x+3)
(x−15)×(x−1)
(x−4)×(x+2)
(x−7)×(x−1)
(x+5)×(x−5)
(x+9)²
(x−3)²