Worked example
Solve (x − 2)(x − 5) = 0.
Answer & why
Answer: 2 and 5
Set each factor to zero: x = 2 or x = 5.
Grade 9 · Math
Solve a factored quadratic
Use the zero-product property to find both roots.
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8 reproducible examples from this math generator. Choose New examples for another set.
Question 1
Solve (x − 7)(x − 13) = 0. Which pair lists both solutions?
- -7 and 13
- 7 and -13
- 7 and 13
- -7 and -13
A hint
Set each factor equal to zero.
Answer & why
Answer: 7 and 13
A product is zero when a factor is zero. x − 7 = 0 or x − 13 = 0, giving 7 and 13.
Question 2
Solve (x − 5)(x − 8) = 0. Which pair lists both solutions?
- -5 and -8
- -5 and 8
- 5 and 8
- 5 and -8
A hint
Set each factor equal to zero.
Answer & why
Answer: 5 and 8
A product is zero when a factor is zero. x − 5 = 0 or x − 8 = 0, giving 5 and 8.
Question 3
Solve (x − 6)(x − 11) = 0. Which pair lists both solutions?
- -6 and 11
- 6 and -11
- -6 and -11
- 6 and 11
A hint
Set each factor equal to zero.
Answer & why
Answer: 6 and 11
A product is zero when a factor is zero. x − 6 = 0 or x − 11 = 0, giving 6 and 11.
Question 4
Solve (x − 4)(x − 12) = 0. Which pair lists both solutions?
- 4 and 12
- 4 and -12
- -4 and 12
- -4 and -12
A hint
Set each factor equal to zero.
Answer & why
Answer: 4 and 12
A product is zero when a factor is zero. x − 4 = 0 or x − 12 = 0, giving 4 and 12.
Question 5
Solve (x − 2)(x − 11) = 0. Which pair lists both solutions?
- -2 and -11
- 2 and -11
- -2 and 11
- 2 and 11
A hint
Set each factor equal to zero.
Answer & why
Answer: 2 and 11
A product is zero when a factor is zero. x − 2 = 0 or x − 11 = 0, giving 2 and 11.
Question 6
Solve (x − 9)(x − 14) = 0. Which pair lists both solutions?
- 9 and 14
- 9 and -14
- -9 and 14
- -9 and -14
A hint
Set each factor equal to zero.
Answer & why
Answer: 9 and 14
A product is zero when a factor is zero. x − 9 = 0 or x − 14 = 0, giving 9 and 14.
Question 7
Solve (x − 9)(x − 11) = 0. Which pair lists both solutions?
- 9 and 11
- -9 and 11
- -9 and -11
- 9 and -11
A hint
Set each factor equal to zero.
Answer & why
Answer: 9 and 11
A product is zero when a factor is zero. x − 9 = 0 or x − 11 = 0, giving 9 and 11.
Question 8
Solve (x − 7)(x − 10) = 0. Which pair lists both solutions?
- 7 and 10
- -7 and 10
- 7 and -10
- -7 and -10
A hint
Set each factor equal to zero.
Answer & why
Answer: 7 and 10
A product is zero when a factor is zero. x − 7 = 0 or x − 10 = 0, giving 7 and 10.