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

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Solve inequalities with a polynomial of degree 3 or more

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer.

  1. Ari notices a squared factor in (x − 2)²(x + 3) > 0. Which x-values solve the inequality?

    • x ≥ -3
    • -3 < x < 2 or x > 2
    • x < -3 or x > 2
    • x < -3

  2. Bo notices a squared factor in (x + 1)²(x − 4) ≤ 0. Which x-values solve the inequality?

    • -1 ≤ x ≤ 4
    • x ≤ 4
    • x = -1 or x ≥ 4
    • x < -1 or -1 < x < 4

  3. Kira sees that x⁴ − 10x² + 9 factors like a quadratic in x². Which x-values solve x⁴ − 10x² + 9 < 0?

    • -3 < x < -1 or 1 < x < 3
    • -3 ≤ x ≤ -1 or 1 ≤ x ≤ 3
    • 1 < x < 3
    • x < -3 or -1 < x < 1 or x > 3

  4. Luz sees that x⁴ − 5x² + 4 factors like a quadratic in x². Which x-values solve x⁴ − 5x² + 4 ≥ 0?

    • x ≤ -2 or -1 ≤ x ≤ 1 or x ≥ 2
    • x < -2 or -1 < x < 1 or x > 2
    • -2 ≤ x ≤ -1 or 1 ≤ x ≤ 2
    • x ≤ 1 or x ≥ 2

  5. Milo sees that x⁴ − 13x² + 36 factors like a quadratic in x². Which x-values solve x⁴ − 13x² + 36 ≤ 0?

    • -3 < x < -2 or 2 < x < 3
    • x ≤ -3 or -2 ≤ x ≤ 2 or x ≥ 3
    • 2 ≤ x ≤ 3
    • -3 ≤ x ≤ -2 or 2 ≤ x ≤ 3

  6. Noah sees that x⁴ − 17x² + 16 factors like a quadratic in x². Which x-values solve x⁴ − 17x² + 16 > 0?

    • x < 1 or x > 4
    • -4 < x < -1 or 1 < x < 4
    • x < -4 or -1 < x < 1 or x > 4
    • x ≤ -4 or -1 ≤ x ≤ 1 or x ≥ 4

  7. Pia solves x³ > 4x with a sign chart. Which x-values make x³ > 4x true?

    • -2 < x < 0 or x > 2
    • x < -2 or 0 < x < 2
    • -2 ≤ x ≤ 0 or x ≥ 2
    • x < -2 or x > 2

  8. Ren solves x³ ≤ 9x with a sign chart. Which x-values make x³ ≤ 9x true?

    • -3 ≤ x ≤ 0 or x ≥ 3
    • -3 ≤ x ≤ 3
    • x < -3 or 0 < x < 3
    • x ≤ -3 or 0 ≤ x ≤ 3

  9. Tala solves x³ + 8x < 6x² with a sign chart. Which x-values make x³ + 8x < 6x² true?

    • 2 < x < 4
    • x < 0 or 2 < x < 4
    • x ≤ 0 or 2 ≤ x ≤ 4
    • 0 < x < 2 or x > 4

  10. Zee solves x³ ≥ 16x with a sign chart. Which x-values make x³ ≥ 16x true?

    • -4 < x < 0 or x > 4
    • x ≤ -4 or x ≥ 4
    • x ≤ -4 or 0 ≤ x ≤ 4
    • -4 ≤ x ≤ 0 or x ≥ 4
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11th grade Solve inequalities with a polynomial of degree 3 or more worksheet – printable
Print: 123456

About this worksheet

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

What your child will learn

  • 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

Words to know

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.

Common mistakes

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.

What to say

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

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

Questions parents ask

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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