Grade 9 · Math · Algebra 1

9th grade Factor ax² + bx + c worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Factor ax^2 + bx + c

Grade 9 Math Worksheet

NameDate

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

To split the middle of 6x² − x − 2, Milo needs two numbers that multiply to 6 × (−2) and add to −1. Type them like 1, -9. What are they?
Pia wants two numbers that multiply to 3 × (−8) and add to 2, to split 3x² + 2x − 8. Type them like 1, -9. What are they?
Ren cuts the middle of 4x² + 4x − 3 using two numbers that multiply to 4 × (−3) and add to 4. Type them like 1, -9. What are they?
4.
Tala wants to factor 3x² − 7x − 6. Which answer is right?
- (3x − 2)(x + 3)
- (3x + 2)(x − 3)
- (3x + 1)(x − 6)
- (3x − 3)(x + 2)
5.
Zee and a friend disagree about 2x² + 3x − 20. Which is 2x² + 3x − 20 factored?
- (2x + 5)(x − 4)
- (2x − 1)(x + 20)
- (2x − 5)(x + 4)
- (2x + 4)(x − 5)
6.
Ari tries four pairs of sides for 5x² − 14x − 3. Which one is right?
- (5x + 1)(x − 3)
- (5x − 1)(x + 3)
- (5x + 3)(x − 1)
- (5x − 3)(x + 1)
7.
Bo needs the sides of 4x² + 5x − 6 for a puzzle. Which is 4x² + 5x − 6 factored?
- (4x − 1)(x + 6)
- (4x − 3)(x + 2)
- (4x + 2)(x − 3)
- (4x + 3)(x − 2)
Esme has one side of 2x² − x − 15: 2x² − x − 15 = (2x + 5)(x + ▢). It may be negative. What number goes in the box?
Kira has one side of 4x² − 17x + 15: 4x² − 17x + 15 = (4x − 5)(x + ▢). It may be negative. What number goes in the box?
Luz has one side of 5x² − 18x − 8: 5x² − 18x − 8 = (5x + 2)(x + ▢). It may be negative. What number goes in the box?

Factor ax^2 + bx + c. Every version has 10 questions, and the answer key prints on the second page.

I can split the middle term of ax² + bx + c with two numbers that multiply to a × c and add to b.
I can factor ax² + bx + c and check the middle by multiplying back.
I can take out −1 first when the x² term is negative.

Standard: A-SSE.B.3a

leading coefficient: The number in front of x², like 3 in 3x² + 14x + 8.

split the middle: Write bx as two x terms so the pieces can be grouped.

a × c: The first number times the last number; the split numbers multiply to it.

trial and check: Try a pair of sides, multiply back, and look at the middle.

Your child looked for two numbers that multiply to the last number, instead of the first number times the last.

Your child found two numbers with the right product but the wrong sum.

Your child had the right numbers but with the signs flipped. Try: multiply the brackets back and look at the sign of the middle term.

Ask: what is the first number times the last number here?

Ask: do your two numbers also add to the middle number?

What is the most common mistake with factor ax² + bx + c?

Your child looked for two numbers that multiply to the last number, instead of the first number times the last.

How can I help my child with factor ax² + bx + c?

Ask: what is the first number times the last number here?

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