factorise 6x+4, 3x^2-9x, 8x^2y^3+12xy^4z
Answers
Answer:
1. Factors of natural numbers
2. Factors of algebraic expressions
An irreducible factor is a factor that cannot be expressed further as a product of factors.
The chapter gives detail about the following topics:
What is Factorisation?
When we factorise an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions.
After this, the Method of Common Factors is explained.
A systematic way of factorising an expression is the common factor method. It contains three steps.
Another section deals with a method called Factorising by regrouping terms. To practice questions based on this method, unsolved exercise 14.1 is given.
Now the question arises What is Regrouping?
Rearranging the expression allows us to form groups leading to factorisation. This is called regrouping.
Factorisation using identities and factors in the form of (x +a) (x+b) are explained.
Division of Algebraic Expressions: This section is divided into the following sub-sections:
a. Division of a monomial by another monomial
b. Division of a polynomial by a monomial
Division of algebraic expressions continued ( Polynomial ÷ Polynomial)
Division is the inverse of multiplication.
Can You Find the Error?
Important statements mentioned in the section:
Remember to make use of brackets, while substituting a negative value.
Remember, when you multiply the expression enclosed in a bracket by a constant (or a variable) outside, each term of the expression has to be multiplied by the constant (or the variable).
Coefficient 1 of a term is usually not shown. But while adding like terms, we include it in the sum.
Remember, when you square a monomial, the numerical coefficient and each factor has to be squared.
While dividing a polynomial by a monomial, we divide each term of the polynomial in the numerator by the monomial in the denominator.