ALEBRA 2 HELP PLEASE PLEASE! polynomials!?

Question

31. Provide the prime factorization for the integer: 756
32. Provide the prime factorization for the integer: 3,861
33. Find the GCF and LCM for the monomials: 30, 35, 36, 42
34. Find the GCF and LCM for the monomials: 52r2s, 78rs2t
35. Find the GCF and LCM for the monomials: 22xy2z2, 33x2yz2, 44x2yz

Answer 1

3.1The prime factorization for the integer :756 =1×2 ×2 ×3× 3×3×7

                                                                         = 1×2² ×3³ ×7

    The prime factorization for the integer :756 =2 ×2×3× 3×3×7

                                                                         =2²× 3³× 7

               Exponential form                                =  22×33×7.

Answer 2

3.2

The prime factorization for the integer :3861 =1×3 ×9 ×143

                                                                         = 1 ×3³ ×143

    The prime factorization for the integer :756 =3× 3×3×143

                                                                         = 3³× 143

               Exponential form                                =  33×143.

 

Comments

Prime factorization for the integer 3861 = 3 × 3 × 3 × 11 × 13.

= 3³ × 11 × 13.

Answer 3

3.2

The prime factorization for the integer :3861 =1×3 ×9 ×143

                                                                         = 1 ×3³ ×143

    The prime factorization for the integer :756 =3× 3×3×143

                 
                  Exponential form    
                                       = 3³× 143
              .

 

Comments

Prime factorization for the integer 3861 = 3 × 3 × 3 × 11 × 13.

= 3³ × 11 × 13.

 

Answer 4

3.3

GCF

The numbers are 30, 35, 36, 42

The prime factorization of 30 = 2×3×5

The prime factorization of 35 = 5×7

The prime factorization of 36 = 2×2×3×3=2^2×3^2                                    
 The prime factorization of 42 = 2×3×7             .

The greatest common factor = 2^2×3^2×5×7

                                              = 4×9×35 =36×35

GCF = 1620.

 

Answer 5

3.3

LCM :

LCM of 30, 35, 36, 42

  

The least common multiple (LCM)=1260

 

Answer 6

3.4

GCF

52r2s , 78rs2t

The prime factorization of monomial 52r2s =2×2×13×2×r×s

                                                                   =2^3×13×r×s

The prime factorization of monomial 78rs2t =2×3×13×2×s×t

                                                                    =2^2×3×13×s×t

The greatest common factor of two monomials =2^3×3×13×r×s×t

The greatest common factor of two monomials =2^3×39×rst

The greatest common factor of two monomials =8×39rst

The greatest common factor of two monomials =312rst

GCF = 312rst.

 

 

Answer 7

33) Greatest common factor of 30, 35, 36, 42

The GCF is the product of the common prime factors in each number.

Factor each number and Circle the common prime factors.

The product of common prime factors, 1 is called the greatest common factor of 30, 35, 36, 42.

Answer 8

34) Greatest common factor of 52r2s, 78rs2t

The GCF is the product of the common prime factors in each number.

Factor each monomial and Circle the common prime factors.

The product of common prime factors, 1 * 2 * 2 * 13 * r * s or 52rs is called the greatest common factor of 52r2s, 78rs2t.

Least common multiple of monomials 52r2s, 78rs2t.

LCM is the product of each factor the greatest number of times it occurs in any number.

Write the prime factorization of two monomials.

LCM = 1 * 2³ * 3 * 13 * r * s * t  = 312 rst

Least common multiple of monomials 52r2s, 78rs2t is 312rst.

Answer 9

35) Greatest common factor of the monomials 22xy2z2, 33x2yz2, 44x2yz

The GCF is the product of the common prime factors in each number.

Factor each monomial and Circle the common prime factors.

The product of common prime factors, 1 * 2 * 2 * x * y * z s or 4xyz is called the greatest common factor of 22xy2z2, 33x2yz2, 44x2yz

Least common multiple of monomials 22xy2z2, 33x2yz2, 44x2yz.

LCM is the product of each factor the greatest number of times it occurs in any number.

Write the prime factorization of three monomials.

LCM = 1 * 2³ * 3 * 11 * x * y * z = 264 xyz.

Least common multiple of monomials 22xy2z2, 33x2yz2, 44x2yz is 264 xyz.