Cubes
X Puzzles
Factor by Grouping
Synthetic Division
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100

Factor x³ - 27

What is (x - 3)(x² + 3x + 9)?

100

Factor z³ − z² − 12z 

What is z(z + 3)(z - 4)?

100

Factor 3x³ + 5x² - 9x - 15 = 0

What is (3x + 5)(x² - 3)?

100

Factor g(x) = x3 − x2 − 20x if (x + 4) is a factor. 

What is g(x) = x(x + 4)(x − 5)?

100

Factor a6 + a5 - 30a4

What is a4(a + 6)(a - 5)?

200

Factor x³ + 216

What is (x+6)(x² - 6x + 36)?

200

Factor a³ − 4a² + 4a 

What is a(a - 2)2?

200

Factor 3x³ - x² - 12x + 4

What is (3x - 1)(x + 2)(x - 2)?

200

Factor t(x) = x3 − 5x² − 9x + 45 if (x − 5) is a factor. 

What is t(x) = (x − 5)(x − 3)(x + 3)?

200

Factor 8m3 - 343

What is (2m - 7)(4m2 + 14m + 49)?

300

Factor 8x³ + 125

What is (2x + 5)(4x² - 10x + 25)?

300

Solve 2x⁴ − 4x³ + 2x² = 0 

What is x = 0 and 1?

300

Factor 3x⁴ - x³ + 3x² - x = 0

What is x(3x + 1)(x² + 1)?

300

Factor f(x) = x4 − 6x3 − 8x + 48 given (x - 6) is a factor?

What is f (x) = (x − 6)(x − 2)(x2 + 2x + 4)?

300
Solve z3 - 7z2 - 9z + 63 = 0

What is z = 3, -3, and 7?

400

Factor 27x³ - 343

What is (3x - 7)(9x² + 21x + 49)?

400

Factor p⁴ - 14p+ 40 

What is (p - 2)(p + 2)(p - 10)

400

Factor x³ − 5x² − 4x + 20 

What is (x-5)(x+2)(x-2)?
400

Factor s(x) = x4 + 4x3 − 64x − 256 given (x + 4) is a factor

What is s(x) = (x + 4)(x − 4)(x2 + 4x + 16)?

400

Factor 2p8 - 12p5 + 16p2

What is 2p2(p3 - 2)(p3 - 4)?

500

Factor 125x³ + 1000

What is (5x + 10)(25x² - 50x + 100)?

500

Solve x⁴ + x³ − 6x² = 0

What is x = -3, 0, and 2?

500

Solve n3 + 12n2 + 48n + 64

What is n = -4?

500

Factor r(x) = x3 − 37x + 84 given (x + 7) is a factor

What is r(x) = (x + 7)(x − 3)(x − 4)?

500

Solve x4 - 13x2 + 36

What is x = 2, -2, 3, and -3?

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