Question

Gcf of 24x^5 - 56x^3 + 16x

Answer 1

8x

Explanation:

Greatest common factor is the factor of 24, 56 and 16. Since 16x only has the power of 1, then then the answer should be on power of 1.

Answer 2

Given the 24x⁵ - 56x³ + 16x contains numbers and variables, there are two steps to finding the GCF. Find the GCF for the numeric part, then find the GCF for the variable part.

Steps to find the LCD of 24x⁵ - 56x³ + 16x

1. Find the LCD for the numerical part 24, - 56, 16x
2. Find the LCD of the variable part x⁵, x³, x¹.
3. Multiply the values with each other

Find the common factors of the numerical part: 24, −56, 16

The factors for 24 are −24,−12,−8,−6,−4,−3,−2,−1,1,2,3,4,6,8,12,24.

The factors for −56 are−56,−28,−14,−8,−7,−4,−2,−1,1,1,2,2,4,4,7,7,8,8,14,14,28,28,56,56.

The factors for 16 are −16,−8,−4,−2,−1,1,2,4,8,16.

List all the factors 24,−56,16 to find the common factors.

• 24:−24,−12,−8,−6,−4,−3,−2,−1,1,2,3,4,6,8,12,24
• −56:−56,−28,−14,−8,-7,−4,−2,−1,1,1,2,2,4,4,7,7,8,8,14,14,28,28,56,56
• 16:−16,−8,−4,−2,−1,1,1,4,8,16

The common factors for 24,−56,16 are −8,−4,−2,−1.−8,−4,−2,−1

The GCF of the numerical part is 8.

`\bf{GCF_(Numerical)=8 }`

Then find the common factors for the variable part:

x⁵, x³, x

The factors for x⁵ are:

x · x · x · x · x

The factors for x³ are:

x · x · x

The factors for x¹ are:

x

List all the factors x⁵, x³, x¹ to find the common factors.

x⁵ = x · x · x · x · x

x³ = x · x · x

x¹ = x

The common factor of the variables x⁵, x³, x¹ is x.

The LCD of the variable part is x.

`\bf{GCF_(Numerical)=x }`

Multiply the LCD of the numerical part 8 and the GCF of the variable part x.

8x