Class 9 Math Chapter 5 Question Answer
Handwritten and composed notes Class 9 Math Chapter 5 Question Answer Factorization of Chapter No.5: Factorization notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of Factorization for the students of Mathematics Science group of the (9 class) Matriculation and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Important notes of Class 9 Math Chapter 5 Question Answer for Matriculation part-I students.
- Complete Chapter test according to the paper patterns of all Punjab boards of Chapter No.5: Factorization 9th class Mathematics Science group in English medium.
- Complete Multiple Choice Questions (MCQs) of Chapter No.5: Factorization 9th class Mathematics Science group in English medium.
- Complete Chapter exercise wise solved questions of Chapter No.5: Factorization 9th class Mathematics Science group in English medium.
- Complete chapter review exercise questions of Chapter No.5: Factorization 9th class Mathematics Science group in English medium.
- Important definitions Asking in board question papers of Chapter No.5: Factorization 9th class Mathematics Science group in English medium.
- Here are the detailed 9th class math chapter 5 question answer pdf to help you prepare for your exams.
- FactorizationState and prove remainder theorem and explain through examples.
- Find Remainder (without dividing) when a polynomial is divided by a linear polynomial.
- Define zeros of a polynomial.
- State and prove Factor theorem.
- Use Factor theorem to factorize a cubic polynomial.
- Introduction: Factorization plays an important role in mathematics as it helps
to reduce the study of a complicated expression to the study of
simpler expressions. In this unit, we will deal with different types of
factorization of polynomials.
- Factorization: If a polynomial p(x) can be expressed as p(x) = g(x)h(x), then
each of the polynomials g(x) and h(x) is called a factor of p(x). For
instance, in the distributive property, ab + ac = a(b + c), a and (b + c) are factors of (ab + ac).
- When a polynomial has been written as a product consisting
only of prime factors, then it is said to be factored completely.
- You can also download the 9th class math chapter 5 question answer pdf download for free.
- (a) Factorization of the Expression of the type ka + kb + kc:
- Example 1: Factorize 5a − 5b + 5c, Solution
5a − 5b + 5c = 5(a − b + c)
- Example 2: Factorize 5a − 5b − 15c, Solution
5a − 5b − 15c = 5(a − b − 3c)
- (b) Factorization of the Expression of the type ac + ad + bc + bd:
- We can write ac + ad + bc + bd as,
- (ac + ad) + (bc + db) = a(c + d) + b(c + d)
- (ac + ad) + (bc + db)= (a + b)(c + d)
For explanation consider the following examples.
- Example 1: Factorize 3x − 3a + xy − ay, Solution
Regrouping the terms of given polynomia,
- 3x + xy − 3a − ay = x(3 + y) − a(3 + y) (monomial factors)
- 3x + xy − 3a − ay = (3 + y) (x − a) (3 + y) is common factor
- Zero of a Polynomial: Definition: If a specific number x = a is substituted for the variable x in a
polynomial p(x) so that the value p(a) is zero, then x = a is called a zero
of the polynomial p(x).
A very useful consequence of the remainder theorem is what is
known as the factor theorem.
- Factorization of a Cubic Polynomial: We can use Factor Theorem to factorize a cubic polynomial as explained below. This is a convenient method particularly for
factorization of a cubic polynomial. We state (without proof) a very
useful Theorem.
- Rational Root Theorem: Let a0
x^n + a1
x^n−1
+ … + an−1
x + an = 0, a0 ≠ 0
- be a polynomial equation of degree n with integral coefficients. If p / q
is a rational root (expressed in lowest terms) of the equation, then
p is a factor of the constant term an and q is a factor of the leading
coefficient a0.