Finding the HCF of Polynomials

The Highest Common Factor (HCF) of two or more polynomials is the polynomial that has the highest degree and is a factor of each of the given polynomials. The HCF can be found using the following steps:

1. Factorize each polynomial into its prime factors.
2. Identify the common factors in each polynomial.
3. Multiply the common factors together to find the HCF.

Example Problem:

Find the HCF of the polynomials 20(2x^3 + 3x^2 - 2x) and 48(x^4 + 8x).

Solution:

1. Factorize each polynomial into its prime factors:
20(2x^3 + 3x^2 - 2x) = 2^2 * 5 * x(2x^2 + 3x - 2)
48(x^4 + 8x) = 2^4 * 3 * x(x^3 + 8)

2. Identify the common factors in each polynomial:
The common factors in each polynomial are 2 and x.

3. Multiply the common factors together to find the HCF:
HCF = 2x

Therefore, the HCF of the polynomials 20(2x^3 + 3x^2 - 2x) and 48(x^4 + 8x) is 2x.