Grade 11 · Math · Algebra 2

11th grade Solve cubic and quartic equations by factoring worksheet

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Solve cubic and quartic equations by factoring

Grade 11 Math Worksheet - Challenge Me

NameDate

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

Ren solves x⁴ + 5x² − 36 = 0 on a math club card. What are all the real solutions?
Tala's robot solves x⁴ − 12x² − 64 = 0 as a quadratic in x². What are all the real solutions?
Zee solves x⁴ − 24x² − 25 = 0 on graph paper. What are all the real solutions?
Esme factors 3x⁴ − 81x = 0 using a difference of cubes. How many real solutions does it have?
Jun's robot factors x⁴ + 8x = 0 using a sum of cubes. How many real solutions does it have?
Kira factors x⁵ − 81x = 0 on graph paper. How many real solutions does it have?
Luz factors x⁵ − 16x = 0 in a notebook. How many real solutions does it have?
Milo solves x³ + 7x² = 16x + 112 on a puzzle card. What is the largest solution?
Noah's robot solves x³ + 9x² = 25x + 225. What is the largest solution?
Ren solves x³ + 8x² = 36x + 288 on graph paper. What is the largest solution?

Solve cubic and quartic equations by factoring. Every version has 10 questions, and the answer key prints on the second page.

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

solution: An input that makes the equation true; a zero row of the table.

zero product rule: If a product is 0, one of its factors is 0.

grouping: Taking a common factor out of each pair of terms.

quadratic form: A quartic like x⁴ − 13x² + 36 that is a quadratic in x².

real solution: A solution that is a real number; it shows as a zero row.

Kept the sign from the factor, so x + 7 = 0 became x = 7.

Divided both sides by x, which throws away the solution x = 0.

Picked x = 0 because the equation ends in = 0.

Ask: what number makes x + 7 equal 0?

Ask: does x = 0 make the equation true?

Ask: what is the output when x = 0?

What is the most common mistake with solve cubic and quartic equations by factoring?

Kept the sign from the factor, so x + 7 = 0 became x = 7.

How can I help my child with solve cubic and quartic equations by factoring?

Ask: what number makes x + 7 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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