What is the greatest common factor of the terms in the polynomial 4x⁴ - 32x³ - 60x²?

Solution:

The greatest common factor (GCF) of polynomials is the largest polynomial that divides evenly into the polynomials.

Given, the polynomial is 4x⁴ - 32x³ - 60x²

We have to find the GCF of polynomial for numerical part and variable part

First, find GCF of numerical part

The factors of 4 are 1, 2, 4

The factors of -32 are ±1, ±2, ±4, ±8, ±16, ±32.

The factors of -60 are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60.

The common factors are 1, 2, 4.

The greatest common factor is 4.

Now, find the GCF of variable part

The factors of x⁴ are x,x,x,x.

The factors of x³ are x,x,x

The factors of x² are x,x

The common factors are x, x

The greatest common is x².

Therefore, the GCF of the polynomial is 4x².

What is the greatest common factor of the terms in the polynomial 4x⁴ - 32x³ - 60x²?

Summary:

The greatest common factor of the terms in the polynomial 4x⁴ - 32x³ - 60x² is 4x².