Grade 11 · Math · Precalculus

11th grade Solve inequalities with a polynomial of degree 3 or more worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Solve inequalities with a polynomial of degree 3 or more

Grade 11 Math Worksheet - Building Confidence

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

Ari starts a sign chart for f(x) = (x + 2)(x − 1)(x − 3). Separating them with commas, what are all the zeros of f?
Bo starts a sign chart for f(x) = (x + 4)(x + 1)(x − 2). Separating them with commas, what are all the zeros of f?
Esme starts a sign chart for f(x) = x(x + 5)(x − 2). Separating them with commas, what are all the zeros of f?
Jun starts a sign chart for f(x) = x(x − 4)(x + 1). Separating them with commas, what are all the zeros of f?
Luz tests one number in each interval of a sign chart for f(x) = (x + 2)(x − 3)(x − 6). What is f(-1)?
Milo tests one number in each interval of a sign chart for f(x) = (x + 4)(x + 1)(x − 2). What is f(-3)?
7.
Pia finished the sign chart shown for f(x) = (x + 2)(x − 1)(x − 3). Which x-values make f(x) > 0?
- x < -2 or 1 < x < 3
- -2 ≤ x ≤ 1 or x ≥ 3
- x < -2 or x > 3
- -2 < x < 1 or x > 3
8.
Ren finished the sign chart shown for f(x) = (x + 4)(x − 1)(x − 5). Which x-values make f(x) ≤ 0?
- -4 ≤ x ≤ 5
- x < -4 or 1 < x < 5
- -4 ≤ x ≤ 1 or x ≥ 5
- x ≤ -4 or 1 ≤ x ≤ 5
9.
Tala finished the sign chart shown for f(x) = (x + 3)(x + 1)(x − 2). Which x-values make f(x) < 0?
- -3 < x < 2
- x ≤ -3 or -1 ≤ x ≤ 2
- x < -3 or -1 < x < 2
- -3 < x < -1 or x > 2
10.
Zee finished the sign chart shown for f(x) = (x + 1)(x − 2)(x − 6). Which x-values make f(x) ≥ 0?
- x ≤ -1 or x ≥ 6
- x ≤ -1 or 2 ≤ x ≤ 6
- -1 < x < 2 or x > 6
- -1 ≤ x ≤ 2 or x ≥ 6

Inequalities with a polynomial of degree 3 or more. Every version has 10 questions, and the answer key prints on the second page.

I can find every zero of a factored polynomial, including x = 0 from a lone x.
I can make a sign chart, test one number in each interval, and read off where the polynomial is positive or negative.
I can solve a cubic or quartic inequality, keeping or leaving out the zeros, even when a factor is squared.

Standard: A-APR.B.3, A-CED.A.1

zero: An x that makes the polynomial equal 0.

sign chart: A number line split at the zeros, with + or − in each piece.

interval: The stretch of the number line between two zeros, or past the last one.

test point: One number you pick inside an interval to find its sign.

double root: A zero from a squared factor, such as (x − 2)².

strict: < or >: the zeros themselves are left out.

Read a factor such as (x − 3) as giving the zero −3 instead of 3.

Added the values of the factors instead of multiplying them. Point out that factors side by side, like (x + 3)(x − 1), are multiplied.

Took out a common factor of x and then forgot that x = 0 is a zero too.

Ask: what number makes x − 3 equal 0? Put it back in and check.

Ask: what x makes the lone x factor equal 0?

What is the most common mistake with solve inequalities with a polynomial of degree 3 or more?

Read a factor such as (x − 3) as giving the zero −3 instead of 3.

How can I help my child with solve inequalities with a polynomial of degree 3 or more?

Ask: what number makes x − 3 equal 0? Put it back in and check.

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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