Grade 9 · Math · Algebra 1

9th grade Factor x² + bx + c worksheet

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Factor x^2 + bx + c

Grade 9 Math Worksheet

NameDate

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

For x² − 3x − 28, Jun needs two side numbers that multiply to −28 and add to −3. Type them like 1, -9. What are they?
Kira wants the sides of x² + 4x − 45. The side numbers multiply to −45 and add to 4. Type them like 1, -9. What are they?
Luz factors x² − 13x + 40 with two side numbers that multiply to 40 and add to −13. Type them like 1, -9. What are they?
Milo has a puzzle card for x² + x − 42: two numbers with product −42 and sum 1. Type them like 1, -9. What are they?
5.
Pia and a friend disagree about x² − 4x − 32. Which is x² − 4x − 32 factored?
- (x + 8)(x + 4)
- (x − 16)(x + 2)
- (x + 8)(x − 4)
- (x − 8)(x + 4)
6.
Ren checks four answers for x² − x − 56. Which one is right?
- (x − 14)(x + 4)
- (x + 8)(x + 7)
- (x + 8)(x − 7)
- (x − 8)(x + 7)
Zee has one side of x² − x − 30: x² − x − 30 = (x + 5)(x + ▢). It may be negative. What number goes in the box?
Ari has one side of x² + 3x − 40: x² + 3x − 40 = (x − 5)(x + ▢). It may be negative. What number goes in the box?
Bo has one side of x² − 12x + 27: x² − 12x + 27 = (x − 3)(x + ▢). It may be negative. What number goes in the box?
Esme has one side of x² + 5x − 36: x² + 5x − 36 = (x + 9)(x + ▢). It may be negative. What number goes in the box?

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

I can find two numbers that multiply to c and add to b.
I can factor x² + bx + c, with plus and minus signs, and check it by multiplying back.
I can tell when x² + bx + c cannot be factored with whole numbers.

Standard: A-SSE.B.3a

factor (verb): Write as a product: find the sides from the pieces.

side numbers: The p and q in (x + p)(x + q).

trinomial: A polynomial with three terms, like x² + 9x + 20.

multiply back: Multiply the brackets to check you get the start again.

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

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

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

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

Ask: do your two numbers also multiply to the last number?

What is the most common mistake with factor x² + bx + c?

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

How can I help my child with factor x² + bx + c?

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

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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