Algebra and Number Theory: Prime Factorization, GCF, LCM, Roots, and Factoring
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60 Terms
What is the prime factorization of 84?
2² × 3 × 7
What is the prime factorization of 180?
2² × 3² × 5
What is the GCF of 48 and 72?
24
What is the GCF of 18x³ and 30x²?
6x²
What is the GCF of 12x²y and 18xy²?
6xy
What is the LCM of 12 and 18?
36
What is the LCM of 8, 12, and 20?
120
What is the square root of 144?
12
What is the square root of 225?
15
What is the cube root of 64?
4
What is the cube root of 125?
5
What is x³ × x⁵ simplified?
x⁸
What is x⁷ ÷ x³ simplified?
x⁴
What is (x³)⁴ simplified?
x¹²
What is 5x² × 3x⁴ simplified?
15x⁶
What is 18x⁶ ÷ 6x² simplified?
3x⁴
What is 12x + 18 factored completely?
6(2x + 3)
What is 15x² − 25x factored completely?
5x(3x − 5)
What is 8x³ + 12x² factored completely?
4x²(2x + 3)
What is x² + 9x + 20 factored completely?
(x + 4)(x + 5)
What is x² + 11x + 24 factored completely?
(x + 3)(x + 8)
What is x² − 9x + 20 factored completely?
(x − 4)(x − 5)
What is x² + x − 20 factored completely?
(x + 5)(x − 4)
What is x² − 7x − 18 factored completely?
(x − 9)(x + 2)
What is x² − 13x + 40 factored completely?
(x − 5)(x − 8)
What is 2x² + 7x + 3 factored completely?
(2x + 1)(x + 3)
What is 3x² + 10x + 8 factored completely?
(3x + 4)(x + 2)
What is 4x² + 11x + 6 factored completely?
(4x + 3)(x + 2)
What is 6x² + 13x + 6 factored completely?
(3x + 2)(2x + 3)
What is 6x² − x − 2 factored completely?
(3x + 2)(2x − 1)
What is 8x² − 14x + 3 factored completely?
(4x − 1)(2x − 3)
What is x² − 36 factored completely?
(x − 6)(x + 6)
What is x² − 81 factored completely?
(x − 9)(x + 9)
What is 25x² − 49 factored completely?
(5x − 7)(5x + 7)
What is 16x² − 25 factored completely?
(4x − 5)(4x + 5)
What is x² + 10x + 25 factored completely?
(x + 5)²
What is x² − 12x + 36 factored completely?
(x − 6)²
What is 4x² + 12x + 9 factored completely?
(2x + 3)²
What is 9x² − 24x + 16 factored completely?
(3x − 4)²
What is −x² + 7x − 12 factored completely?
−(x − 3)(x − 4)
What is −2x² − 10x − 12 factored completely?
−2(x + 2)(x + 3)
What is (x + 4)(x + 7) expanded?
x² + 11x + 28
What is (x − 3)(x + 8) expanded?
x² + 5x − 24
What is (2x + 3)(x + 5) expanded?
2x² + 13x + 15
What is (3x − 4)(2x + 5) expanded?
6x² + 7x − 20
What is (4x + 1)(x − 6) expanded?
4x² − 23x − 6
What is (x + 3)(x² − 2x + 5) expanded?
x³ + x² − x + 15
What is (2x − 1)(x² + 3x − 4) expanded?
2x³ + 5x² − 11x + 4
What is 3x² + 12x + 9 factored completely?
3(x + 1)(x + 3)
What is 4x² − 36 factored completely?
4(x − 3)(x + 3)
What is 2x³ − 18x factored completely?
2x(x − 3)(x + 3)
What is 5x² − 45 factored completely?
5(x − 3)(x + 3)
What is the side length of a cube with a volume of 343 cm³?
7 cm
What is the volume of a cube with a side length of 8 cm?
512 cm³
What is the surface area of a cube with a side length of 6 cm?
216 cm²
What is the side length of a cube with a surface area of 294 cm²?
7 cm
What is 2x² + 8x + 6 factored completely?
2(x + 1)(x + 3)
What is 3x² − 15x + 18 factored completely?
3(x − 2)(x − 3)
What is 6x² + 18x + 12 factored completely?
6(x + 1)(x + 2)
What is 4x² − 20x + 24 factored completely?
4(x − 2)(x − 3)