Mathematics Notes for 9th Class Exercise 6.1

“Math” a compulsory subject for 9th class Science students. and Mathematics Notes for 9th Class Exercise 6.1 or Math Notes Class 9 English Medium (Science Group) included in this book.

The Question is How to Finding H.C.F. ?
We can find H. C. F. of given expressions by the following two methods.
(i) By Factorization (ii) By Division
Sometimes it is difficult to find factors of given expressions. In that case, method of division can be used to find H. C. F. We consider some examples to explain these two methods.
(i) H.C.F. by Factorization
Example: Find the H. C. F. of the following polynomials. x2 – 4, x2 + 4x + 4, 2×2 + x – 6
Solution by factorization:

x2 – 4 = (x + 2) (x – 2)
x2 + 4x + 4 = (x + 2)2
2×2 + x – 6 = 2×2 + 4x – 3x – 6 = 2x(x + 2) – 3(x + 2)
= (x + 2) (2x – 3)
Hence, H. C. F. = x + 2

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Math Solution 9th Class (Science Group)

Mathematics Notes for 9th:

How to find L.C.M. by Factorization:

Working Rule to find L.C.M. of given Algebraic Expressions 
(i) Factorize the given expressions completely i.e., to simplest form.
(ii) Then the L.C.M. is obtained by taking the product of each factor appearing in any of the given expressions, raised to the highest power with which that factor appears.

Example: Find the L.C.M. of p(x) = 12(x3 – y3) and q(x) = 8(x3 – xy2)
Solution: By prime factorization of the given expressions, we have
p(x) = 12(x3 – y3) = 22 x 3 x (x – y) (x2 + xy + y2)
and q(x) = 8(x3 – xy2) = 8x(x2 – y2) = 23x(x + y) (x – y)
Hence L.C.M. of p(x) and q(x),
23 x 3 x x(x + y) (x – y) (x2 + xy + y2) = 24x (x + y) (x3 – y3)

There are Seventeen chapters in Mathematics 9th Class for Punjab Textbook Board, Lahore. Solutions of all the chapters are given below. Anyone can download the PDF file of the notes. Note that, you can view these notes only if you have PDF reader software/ App on your device. However online view of the notes is also available on eStudent.pk . You can find all solution along with 9th Class Math Notes in Urdu (Science Group), Math MCQs Class 9. 

Math Notes Class 9:

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