Grade 9 · Math · Algebra 1

9th grade Solve a quadratic by factoring (zero product property) worksheet

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Solve a quadratic by factoring (zero product property)

Grade 9 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Jun solves 2x² + x - 15 = 0 on graph paper. It factors as (2x - 5)(x + 3) = 0. What is the positive solution?
Luz solves 4x² + 4x - 15 = 0 with a sharp pencil. It factors as (2x - 3)(2x + 5) = 0. What is the positive solution?
In math club, Milo solves 5x² - 13x - 6 = 0. It factors as (5x + 2)(x - 3) = 0. What is the negative solution?
Noah's puzzle card says x(x - 5) = 36. What is the larger solution?
Pia solves (x + 2)(x + 5) = 28 (it looks friendly, but there is a trap). What is the smaller solution?
Ren's robot solves (x - 1)(x + 6) = 30. What is the larger solution?
7.
Zee's puzzle card says x² - 10x + 25 = 0. Which gives every solution?
- x = 5 or x = -5
- x = -5 only
- x = 5 only
- No real solution
8.
Ari solves x² + 14x + 49 = 0 in pencil. Which gives every solution?
- No real solution
- x = -7 only
- x = -7 or x = 7
- x = 7 only
9.
Bo's robot solves 4x² + 12x + 9 = 0 and wants a fraction. Which gives every solution?
- x = 3/2 only
- x = -3/2 or x = 3/2
- x = -3 only
- x = -3/2 only
10.
Esme's math book shows 9x² - 24x + 16 = 0. Which gives every solution?
- x = -4/3 only
- x = 4/3 only
- x = 4 only
- x = 4/3 or x = -4/3

Solve a quadratic by factoring. Every version has 10 questions, and the answer key prints on the second page.

Standard: A-REI.B.4b, A-APR.B.3

zero product rule: If a product is 0, one of its factors is 0.

factor: One of the brackets that multiply together.

solution: An input whose output is 0.

perfect square: A bracket times itself, like (x - 5)².

standard form: Everything on one side and 0 on the other.

Your child read the solution straight off the bracket, so the sign came out wrong.

Your child set only one bracket to 0.

Your child picked the input 0 instead of the input that makes the output 0.

Ask: what makes x + 4 equal 0?

Ask: if a product is 0, which of the two brackets could be 0?

Ask: put x = 0 in. Is the answer 0?

What is the most common mistake with solve a quadratic by factoring (zero product property)?

Your child read the solution straight off the bracket, so the sign came out wrong.

How can I help my child with solve a quadratic by factoring (zero product property)?

Ask: what makes x + 4 equal 0?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records