Grade 9 · Math · Algebra 1

9th grade Factor x² + bx + c worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Factor x^2 + bx + c

Grade 9 Math Worksheet - Building Confidence

NameDate

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

Jun draws x² + 9x + 20 as a rectangle. Its two side numbers multiply to 20 and add to 9. Type them like 1, -9. What are the two numbers?
Kira lays tiles for x² + 13x + 30 in a rectangle. The side numbers multiply to 30 and add to 13. Type them like 1, -9. What are they?
Luz sketches x² + 12x + 32 as a quilt block. The side numbers multiply to 32 and add to 12. Type them like 1, -9. What are they?
Milo cuts x² + 14x + 45 into four pieces of paper. The side numbers multiply to 45 and add to 14. Type them like 1, -9. What are they?
5.
Pia is very sure that x² + 10x + 16 = (x + 4)(x + 4). Is Pia right?
- No. It multiplies back to x² + 8x + 16.
- Yes. Both brackets start with x, so the factoring works.
- Yes. 4 × 4 = 16.
- No. The numbers must add to 16.
6.
Ren writes x² + 11x + 30 = (x + 5)(x + 6) on the board. Is Ren right?
- Yes. It multiplies back to x² + 11x + 30.
- No. The two numbers must be the same.
- No. The numbers must add to 30.
- No. It multiplies back to x² + 30x + 11.
7.
Tala checks a friend's answer: x² + 15x + 54 = (x + 3)(x + 18). Is the friend right?
- No. It multiplies back to x² + 21x + 54.
- Yes. Both brackets start with x, so the friend is right.
- No. The numbers must add to 54.
- Yes. 3 × 18 = 54.
8.
Zee draws x² + 11x + 18 as a rectangle and needs its two sides. Which is x² + 11x + 18 factored?
- (x + 4)(x + 7)
- (x + 2)(x + 9)
- (x + 3)(x + 6)
- (x − 2)(x − 9)
9.
Bo builds x² + 16x + 28 from tiles. Which pair of sides fits?
- (x + 2)(x + 14)
- (x + 4)(x + 7)
- (x + 6)(x + 10)
- (x − 2)(x − 14)
10.
Esme needs the sides of a tabletop of x² + 17x + 42 square units. Which is x² + 17x + 42 factored?
- (x + 8)(x + 9)
- (x + 3)(x + 14)
- (x − 3)(x − 14)
- (x + 6)(x + 7)

9th grade Factor x² + bx + c worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

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

What your child will learn

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

Words to know

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.

Common mistakes

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.

What to say

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

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

Questions parents ask

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.

More algebra 1

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