H.C.F. of Polynomials by Factorization
Learn how to solve H.C.F. of polynomials by factorization splitting the middle term.
Solved examples on highest common factor of polynomials by factorization:
1. Find out the H.C.F. of x2 - 3x - 18 and x2 + 5x + 6 by factorization.Solution:
First expression = x2 - 3x - 18
= x2 - 6x + 3x - 18, by splitting the middle term - 3x = - 6x + 3x
= x(x - 6) + 3(x - 6)
= (x - 6) (x + 3)
Second expression = x2 + 5x + 6= x2 + 3x + 2x + 6, by splitting the middle term 5x = 3x + 2x
= x(x + 3) + 2(x + 3)
= (x + 3) (x + 2)
Therefore, in the two polynomials (x + 3) is the only common factors, so, the required H.C.F. = (x + 3).
Solution:
First expression = (2a2 - 8b2)
= 2(a2 - 4b2), by taking common 2
= 2[(a)2 - (2b)2], using the identity of a2 – b2
= 2(a + 2b) (a - 2b), we know a2 – b2 = (a + b) (a – b)
= 2 × (a + 2b) × (a - 2b)
Second expression = (4a2 + 4ab - 24b2)= 4(a2 + ab - 6b2), by taking common 4
= 4(a2 + 3ab - 2ab - 6b2), by splitting the middle term ab = 3ab - 2ab
= 4[a(a + 3b) - 2b(a + 3b)]
= 4(a + 3b) (a - 2b)
= 2 × 2 × (a + 3b) × (a - 2b)
Third expression = (2a2 - 12ab + 16b2)= 2(a2 - 6ab + 8b2), , by taking common 2
= 2(a2 - 4ab - 2ab + 8b2), by splitting the middle term - 6ab = - 4ab - 2ab
= 2[a(a - 4b) - 2b(a - 4b)]
= 2(a - 4b) (a - 2b)
= 2 × (a - 4b) × (a - 2b)
From the above three expressions ‘2’ and ‘(a - 2b)’ are the common factors of the expressions.
Therefore, the required H.C.F. is 2 × (a - 2b) = 2(a - 2b)
8th Grade Math Practice
From H.C.F. of Polynomials by Factorization to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Worksheet on Yesterday, Today and Tomorrow | Sequence of the Week-days
Nov 25, 24 01:18 AM
Practice the worksheet on yesterday, today and tomorrow, the questions are based on the sequence of the week-days, their names and order. We know, the present day is today, the day before today -
Yesterday, Today and Tomorrow | Name of each Day of the Week
Nov 25, 24 01:09 AM
We will learn the relation between yesterday, today and tomorrow. There are seven days in a week. We know the name of each day of the week. Sunday is known as the first day of the week. -
The Story about Seasons | Spring | Summer | Autumn | Winter
Nov 25, 24 12:48 AM
Kids let’s enjoy the story about seasons. Here we will discuss about the four seasons and the duration. Some months are too hot and some are too cold. The period of hot months is called the hot -
Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr
Nov 25, 24 12:17 AM
There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t… -
Time Duration |How to Calculate the Time Duration (in Hours & Minutes)
Nov 24, 24 11:01 PM
Time duration tells us how long it takes for an activity to complete. We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.