Factoring Polynomials

Problem: 1

Find the prime factors of 315.

Problem: 3

Write all the positive factors of x · y.

Problem: 5

Write all the positive factors of x²y².

Problem: 7

Find the GCF and LCM of given monomial.

54, 42

Problem: 9

Find the GCF and LCM.

76xy²z, 57y²z²

Problem: 11

Find the GCF and LCM.

22x³y²z², 33x²y³z², 66x²y²z³

Problem: 13

Determine the greatest common factor of the terms in the polynomial.

4x⁴ – 20x³

Problem: 15

Determine the greatest common factor of the terms in the polynomial.

64x⁹ + 12x⁶ + 6x³

Problem: 17

Find whether the given pair of polynomials are relatively prime or not. If two polynomials have no common factors other than constants, they are relatively prime.

t³ – 9t, t³ – 9

Problem: 19

Find whether the given pair of polynomials are relatively prime or not. If two polynomials have no common factors other than constants, they are relatively prime.

3x⁴ + 6x² – 9x, 6x⁵ + 18x⁴ + 30x³ – 24

Problem: 21

Factor the given polynomial.

7x² + 21x + 56

Problem: 23

Factor the given polynomial.

63 y³ + 36y⁵

Problem: 25

Factor the polynomial.

x(y – 7) + 4(7 – y)

Problem: 27

Factor the polynomial.

t²+ 14t + 49

Problem: 29

Factor the trinomial.

x² + 6x + 9

Problem: 31

Factor the trinomial.

4x² + 4x + 1

Problem: 33

Factor the polynomial.

9k²– 4

Problem: 35

Factor the binomial.

x² – 4y²

Problem: 37

Factor the binomial.

64 m² – 81

Problem: 39

Factor the polynomial.

u² – v² + 6v – 9

Problem: 41

Factor the binomial.

64 x – 81x³

Problem: 43

Factor the binomial.

x⁴ – 81

Problem: 45

Factor the polynomial x³ – 27.

Problem: 47

Factor the polynomial 81 x³ – 3.

Problem: 49

Factor the binomial.

6x⁴ – 96

Problem: 51

Factor the given trinomial. First, factor out a common factor, if possible.

3x² – 12x + 12

Problem: 53

Factor the polynomial.

2(x + y)⁶– 2(x – y)⁶

Problem: 55

Factor the given polynomial, if possible.

64x² – 396

Problem: 57

Factor the given polynomial, if possible.

x² – 9x + 81

Problem: 59

Factor the trinomial.

b² + 2b – 35

Problem: 61

Factor the trinomial.

180y² – 36xy + x²

Problem: 63

Factor the trinomial.

112y² – 6x²y – x⁴

Problem: 65

Factor the polynomial by grouping.

x³ + 2x² + 4x + 8

Problem: 67

Factor the polynomial.

15x³ + 24x² – 35x + 56

Problem: 69

Factor the polynomial.

3x³ – 9x² – 8x + 24

Problem: 71

Factor the polynomial.

bx – ax + by – ay

Problem: 73

Factor the polynomial.

9x⁵ + 15x³ + 15x² + 25

Problem: 75

Factor the polynomial.

d⁶ – d⁴ – d² + 1

Problem: 77

Match the polynomial 3x⁵ + 9x⁴ – 9x³ – 27x² with its factorization:

A. 3x³(x + 3)(x – 3)(x² + 9)

B. (4x + 1)(x + 4)

C. 3x(x + 9)(x – 9)

D. 3x²(x² – 3)(x + 3)

E. (7x – 8)(49x² + 56x + 64)

F. (x² + 9)(x – 9)

Problem: 1

Find the prime factors of 315.

Problem: 3

Write all the positive factors of x · y.

Problem: 5

Write all the positive factors of x²y².

Problem: 7

Find the GCF and LCM of given monomial.

54, 42

Problem: 9

Find the GCF and LCM.

76xy²z, 57y²z²

Problem: 11

Find the GCF and LCM.

22x³y²z², 33x²y³z², 66x²y²z³

Problem: 13

Determine the greatest common factor of the terms in the polynomial.

4x⁴ – 20x³

Problem: 15

Determine the greatest common factor of the terms in the polynomial.

64x⁹ + 12x⁶ + 6x³

Problem: 17

Find whether the given pair of polynomials are relatively prime or not. If two polynomials have no common factors other than constants, they are relatively prime.

t³ – 9t, t³ – 9

Problem: 19

Find whether the given pair of polynomials are relatively prime or not. If two polynomials have no common factors other than constants, they are relatively prime.

3x⁴ + 6x² – 9x, 6x⁵ + 18x⁴ + 30x³ – 24

Problem: 21

Factor the given polynomial.

7x² + 21x + 56

Problem: 23

Factor the given polynomial.

63y³ + 36y⁵

Problem: 25

Factor the polynomial.

x(y – 7) + 4(7 – y)

Problem: 27

Factor the polynomial.

t²+ 14t + 49

Problem: 29

Factor the trinomial.

x² + 6x + 9

Problem: 31

Factor the trinomial.

4x² + 4x + 1

Problem: 33

Factor the polynomial.

9k²– 4

Problem: 35

Factor the binomial.

x² – 4y²

Problem: 37

Factor the binomial.

64m² – 81

Problem: 39

Factor the polynomial.

u² – v² + 6v – 9

Problem: 41

Factor the binomial.

64x – 81x³

Problem: 43

Factor the binomial.

x⁴ – 81

Problem: 45

Factor the polynomial x³ – 27.

Problem: 47

Factor the polynomial 81x³ – 3.

Problem: 49

Factor the binomial.

6x⁴ – 96

Problem: 51

Factor the given trinomial. First, factor out a common factor, if possible.

3x² – 12x + 12

Problem: 53

Factor the polynomial.

2(x + y)⁶– 2(x – y)⁶

Problem: 55

Factor the given polynomial, if possible.

64x² – 396

Problem: 57

Factor the given polynomial, if possible.

x² – 9x + 81

Problem: 59

Factor the trinomial.

b² + 2b – 35

Problem: 61

Factor the trinomial.

180y² – 36xy + x²

Problem: 63

Factor the trinomial.

112y² – 6x²y – x⁴

Problem: 65

Factor the polynomial by grouping.

x³ + 2x² + 4x + 8

Problem: 67

Factor the polynomial.

15x³ + 24x² – 35x + 56

Problem: 69

Factor the polynomial.

3x³ – 9x² – 8x + 24

Problem: 71

Factor the polynomial.

bx – ax + by – ay

Problem: 73

Factor the polynomial.

9x⁵ + 15x³ + 15x² + 25

Problem: 75

Factor the polynomial.

d⁶ – d⁴ – d² + 1

Problem: 77

Match the polynomial 3x⁵ + 9x⁴ – 9x³ – 27x² with its factorization:

A. 3x³(x + 3)(x – 3)(x² + 9)

B. (4x + 1)(x + 4)

C. 3x(x + 9)(x – 9)

D. 3x²(x² – 3)(x + 3)

E. (7x – 8)(49x² + 56x + 64)

F. (x² + 9)(x – 9)

Hotmath Practice Problems