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About Factorization of Algebraic Expressions
Factorization of algebraic expressions is the process of finding the factors of an algebraic expression. This can be done by using the distributive property, the commutative property, or the associative property.
Methods for Factorisation of Algebraic Expressions
There are a number of methods that can be used to factorise algebraic expressions. The most common methods are the quadratic equation method, the grouping method, and the trial and error method.
The quadratic equation method can be used to factorise expressions that can be written in the form ax2 + bx + c. The grouping method can be used to factorise expressions that can be written in the form ax2 + bx + c = (ax + b) (x + c). The trial and error method can be used to factorise expressions that cannot be written in either of the above forms.
Factorization of Algebraic Expressions by Taking Out Common Factors
Factorization is the process of dividing an algebraic expression into simpler terms. This can be done by taking out common factors.
For example, the expression 6×2 – 9x + 3 can be factorized by taking out the common factor of 6.
6×2 – 9x + 3 = 6 (x2 – 3x + 1)
Factorization of Algebraic Expressions By Grouping of Terms
Factorization of algebraic expressions by grouping of terms is the process of grouping terms together and then factoring the group.
Grouping of terms is the process of combining like terms.
For example, the expression 9x + 6x can be grouped together as 9x and 6x.
The expression can then be factored as 9x(1 + 6x).
Difference of Two Squares
A difference of two squares is a polynomial equation in which the two squares of the two terms in the equation are subtracted. The coefficients of the equation are real numbers. The equation is usually written in the form:
ax2 − bx + c = 0
where a, b, and c are real numbers. The roots of the equation are the solutions to the equation.
Key Concepts Discussed in Factorization are-
1. Factorization of Polynomials
2. Prime Factorization
3. Greatest Common Factor
4. Least Common Multiple
Different Methods by Which Factorization of Algebraic Expressions Takes Place-
There are a few methods by which factorization of algebraic expressions can take place. One way is to use the distributive property to group like terms together. Another approach is to use the Zero Product Property to factor out any common factors. Lastly, factoring by grouping can be used to factor an expression into a product of two binomials.
