Grade 11 · Math · Algebra 2

11th grade Zeros of a polynomial and its factors, in both directions worksheet

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Zeros of a polynomial and its factors, in both directions

Grade 11 Math Worksheet

NameDate

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

Jun solves a puzzle card: p(x) = (2x − 7)(x + 3)². Which zero of p comes from the factor 2x − 7?
Kira's robot graphs p(x) = (3x + 4)(x − 2)³. Which zero of p comes from the factor 3x + 4?
Milo marks p(x) = (5x + 2)(x − 4)² on a grid map. Which zero of p comes from the factor 5x + 2?
4.
Noah designs a puzzle: a polynomial with leading coefficient 1 and only the zeros -2 (multiplicity 2), 3 and 5. Which polynomial is it?
- 2(x + 2)(x − 3)(x − 5)
- (x + 2)(x − 3)(x − 5)
- (x + 2)²(x − 3)(x − 5)
- (x − 2)²(x + 3)(x + 5)
5.
Ren's robot needs a polynomial with leading coefficient 1 and only the zeros 4 (multiplicity 3) and -1. Which polynomial is it?
- (x − 4)(x + 1)
- 3(x − 4)(x + 1)
- (x + 4)³(x − 1)
- (x − 4)³(x + 1)
6.
Tala graphs a polynomial with leading coefficient 1 and only the zeros 0 (multiplicity 2), -6 and 2. Which polynomial is it?
- x²(x − 6)(x + 2)
- x(x + 6)(x − 2)
- x²(x + 6)(x − 2)
- 2x(x + 6)(x − 2)
7.
Zee writes a math club card: leading coefficient 1, only the zeros -5 (multiplicity 2), 1 and 6. Which polynomial is it?
- (x + 5)²(x − 1)(x − 6)
- (x − 5)²(x + 1)(x + 6)
- 2(x + 5)(x − 1)(x − 6)
- (x + 5)(x − 1)(x − 6)
Bo knows x = 3 is a zero of p(x) = x³ − 2x² − 5x + 6. What is p(x) ÷ (x − 3)?
Esme's robot finds that x = -4 is a zero of p(x) = x³ − 3x² − 18x + 40. What is p(x) ÷ (x + 4)?
Kira reads that x = 3 is a zero of p(x) = x⁴ − 10x² + 9. What is p(x) ÷ (x − 3)?

Zeros of a polynomial and its factors. Every version has 10 questions, and the answer key prints on the second page.

I can read every zero of a factored polynomial, with the right sign and its multiplicity.
I can write a polynomial from its zeros, in factored form or multiplied out.
I can divide out a zero I know and find the other zeros.

Standard: A-APR.B.3

zero: An input whose output is 0; a row of the table with output 0.

factor: A bracket that multiplies, like x − 3; it is 0 at its zero.

multiplicity: How many times a factor appears: the power on it.

leading coefficient: The number in front of the highest power of x.

quotient: What is left after dividing; here one degree lower.

Read the zero straight off a factor with the sign kept, so x + 3 became x = 3.

Gave the output at x = 0 instead of an input whose output is 0.

Counted a repeated factor once, so a power like (x − 3)² was lost.

Ask: what number makes x + 3 equal 0?

Ask: which column of the table has to show 0?

Ask: how many times does x − 3 appear in (x − 3)²?

What is the most common mistake with zeros of a polynomial and its factors, in both directions?

Read the zero straight off a factor with the sign kept, so x + 3 became x = 3.

How can I help my child with zeros of a polynomial and its factors, in both directions?

Ask: what number makes x + 3 equal 0?

Are these 11th 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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