You can compute the highest common factor or the greatest common factor of any number of polynomials by reading this article. Here we are giving the step by step explanation to get the H.C.F of polynomials along with the solved examples. Go through the below sections to solve the questions easily.
Step By Step Process to get G.C.F of Polynomials
Students can check out the below sections to find the detailed procedure of calculating the greatest common factor of polynomials,
- First of all, find the factors of polynomials.
- Identify the expression which is occurring more times.
- Separate the common factors from given polynomials and multiply them.
Example Questions on H.C.F of Polynomials
Example 1:
Find the Highest Common Factor of the polynomials x² – 6x + 9 and x² – 9.
Solution:
Factorizing x² – 6x + 9 by using the identities (a – b)², we get
(x)² – 2(x)(3) + (3)²
= (x – 3)²
= (x – 3) (x – 3)
Also, factorizing x² – 9, we get
(x)² – (3)², by using the identities of a² – b².
= (x + 3) (x – 3)
Therefore, H.C.F. of x² – 6x + 9 and x² – 9 is (x – 3).
Example 2:
Find the H.C.F of (a + b)² and (a² – b²).
Solution:
Factors of (a + b)² = (a + b) (a + b)
Factors of (a² – b²) = (a + b) (a – b)
The common factor is (a + b)
Therefore, the highest common factor of (a + b)² and (a² – b²) is (a + b).
Example 3:
Find the highest common factor of polynomials x² + 15x + 56, x² + 5x – 24 and x² + 8x.
Solution:
Factorizing x² + 15x + 56 by splitting the middle term, we get
= x² + 8x + 7x + 56
= x(x + 8) + 7(x + 8)
= (x + 7) (x + 8)
Also, factorizing x² + 5x – 24, we get
= x² + 8x – 3x – 24
= x (x + 8) – 3 (x + 8)
= (x + 3) (x + 8)
Factoring x² + 8x by taking x common.
= x (x + 8)
In all three polynomials the common factor is (x + 8)
Therefore, H.C.F. of x² + 15x + 56, x² + 5x – 24 and x² + 8x is (x + 8).