Factor sums and differences of cubes, and higher-degree polynomials
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
In a notebook, Kira writes 27x³ + 8 as (3x + 2) times a quadratic. What is the quadratic?
Luz factors 64x³ − 1 in pencil. One factor is 4x − 1. What is the other factor?
On a puzzle card, 125x³ + 8 = (5x + 2)( ? ). Milo needs the second factor. What is it?
On a worksheet, Noah factors x³ − 5x² − 9x + 45 completely by grouping. Which answer is right?
- (x + 5)(x − 3)(x + 3)
- (x − 5)(x − 3)(x + 3)
- (x − 5)(x² − 9)
- (x − 5)(x² + 9)
In a notebook, Pia groups the four terms of x³ + 2x² − 16x − 32 and factors completely. Which answer is right?
- (x − 2)(x − 4)(x + 4)
- (x + 2)(x² − 16)
- (x + 2)(x − 4)(x + 4)
- (x + 2)(x² + 16)
Ren factors 2x³ − x² − 50x + 25 completely in pencil. Which answer is right?
- (2x + 1)(x − 5)(x + 5)
- (2x − 1)(x² + 25)
- (2x − 1)(x − 5)(x + 5)
- (2x − 1)(x² − 25)
On a puzzle card, Tala must factor x³ + 7x² − 4x − 28 completely. Which answer is right?
- (x + 7)(x² + 4)
- (x + 7)(x − 2)(x + 2)
- (x + 7)(x² − 4)
- (x − 7)(x − 2)(x + 2)
On a worksheet, Zee factors x⁴ − 13x² + 36 completely. Which answer is right?
- (x − 2)(x + 2)(x − 3)(x + 3)
- (x² − 4)(x² − 9)
- (x − 4)(x − 9)
- (x² − 2)(x² − 3)
In a notebook, Esme treats x⁴ − 10x² + 9 as a quadratic in x² and factors completely. Which answer is right?
- (x² − 1)(x² − 3)
- (x − 1)(x − 9)
- (x² − 1)(x² − 9)
- (x − 1)(x + 1)(x − 3)(x + 3)
Jun factors x⁴ − 5x² − 36 completely in pencil. Which answer is right?
- (x² − 3)(x² + 2)
- (x − 3)(x + 3)(x² + 4)
- (x − 9)(x + 4)
- (x² − 9)(x² + 4)