Grade 9 · Math · Algebra 1

9th grade Factor ax² + bx + c worksheet

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Factor ax^2 + bx + c

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Milo takes out −1 first: −3x² + 10x + 8 = −(3x + 2)(x + ▢). It may be negative. What number goes in the box?
Noah takes out −1 first: −2x² + 7x + 15 = −(2x + 3)(x + ▢). It may be negative. What number goes in the box?
Tala factors 2x² + xy − 15y², which has two letters: 2x² + xy − 15y² = (2x − 5y)(x + ▢y). It may be negative. What number goes in the box?
Zee factors 3x² − 14xy + 8y², which has two letters: 3x² − 14xy + 8y² = (3x − 2y)(x + ▢y). It may be negative. What number goes in the box?
Ari factors 5x² + 13xy − 6y², which has two letters: 5x² + 13xy − 6y² = (5x − 2y)(x + ▢y). It may be negative. What number goes in the box?
Bo factors 2x² + 13xy + 20y², which has two letters: 2x² + 13xy + 20y² = (2x + 5y)(x + ▢y). It may be negative. What number goes in the box?
Esme's garden bed is a rectangle of 6x² + 17x + 12 square feet. One side is 2x + 3 feet. When x = 4, how long is the other side, in feet?
Jun plans a school garden of 10x² + 19x + 6 square feet with one side 5x + 2 feet. When x = 5, how long is the other side, in feet?
Kira's new vegetable bed covers 6x² + 19x + 10 square feet, and one side is 3x + 2 feet. When x = 4, how many feet long is the other side?
Luz's flower bed has an area of 12x² + 17x + 6 square feet and one side of 4x + 3 feet. When x = 6, how long is the other side?

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.

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