# Exercise 12.1 class 8 solution

### Exercise 12.1 class 8 solution-factors

In mathematics, factors are numbers that can be multiplied together to obtain a specific result. When you multiply two or more factors, you get a product.

For example, if you have the number 12, it has several factors, including 1, 2, 3, 4, 6, and 12, because these numbers can be multiplied to give 12:

1 x 12 = 12 2 x 6 = 12 3 x 4 = 12

In this case, 1, 2, 3, 4, 6, and 12 are all factors of 12. Factors are important in various mathematical concepts, including factorization, prime factorization, and finding common factors in problems involving fractions or equations.

### Exercise 12.1 class 8 solution- factors of algeric terms

The factors of an algebraic term are expressions that can be multiplied together to obtain the original term. To find the factors of an algebraic term, you need to break it down into its constituent parts. The factors of an algebraic term depend on its structure, but I’ll provide some examples to illustrate the concept.

1. Monomial (Single Term):
• The factors of a monomial are its constituent factors, which are often prime numbers and variables.
• For example, in the term 4x^2, the factors are 4, x, and x.
2. Polynomial (Sum of Monomials):
• To find the factors of a polynomial, you can factor it by looking for common factors among its monomials.
• For example, in the polynomial 2x^2 + 4x, common factors are 2 and x. So, it can be factored as 2x(x + 2).
• Quadratic expressions are often factored into the product of two binomials. For example, factoring the quadratic expression x^2 - 4, you get (x - 2)(x + 2) as the factors.
4. Other Algebraic Expressions:
• More complex algebraic expressions may require methods like long division, synthetic division, or grouping to identify their factors.

### Exercise 12.1 class 8 solution-factorization

Factorization is the process of breaking down a mathematical expression or number into a product of its constituent factors. The factors are the numbers or algebraic expressions that, when multiplied together, result in the original expression or number.

There are different types of factorization, including:

1. Prime Factorization: This involves breaking down a positive integer into a product of prime numbers. For example, the prime factorization of 12 is 2 × 2 × 3.
2. Algebraic Factorization: This is the process of breaking down algebraic expressions into simpler expressions. For e
3. xample, the quadratic factorization of x^2 – 5x + 6 is (x – 2)(x – 3).
4. Common Factor Factorization: This involves factoring out a common factor from all the terms of an expression. For example, in the expression 6x^3 + 9x^2, you can factor out 3x^2 to get 3x^2(2x + 3).
5. Difference of Squares Factorization: This applies when you have an expression in the form of a^2 – b^2, and it can be factored as (a + b)(a – b).
6. Sum or Difference of Cubes Factorization: Special factorization patterns for expressions of the form a^3 + b^3 or a^3 – b^3, which can be factored as (a + b)(a^2 – ab + b^2) and (a – b)(a^2 + ab + b^2), respectively.

Factorization is a fundamental concept in mathematics and is used in various areas, including simplifying expressions, solving equations, finding common factors, and breaking down numbers into their prime components. It’s a valuable tool for understanding and manipulating mathematical expressions.

### Exercise 12.1 class 8 solution- exercise preview

here the exercise preview is given below-

Example of factorization – factorize 2x+6

2.factorize 3d(x+y)-5c(x+y)

3.factorize ax-ay + bx – by.

### Exercise 12.1 class 8 solution – solution pdf

students can view or download the pdf from here.click at the bottom to scroll the pdf pages.we provide Exercise 12.1 class 8 solution, just to help student to achieve their efficiency.

12.1-1

Exercise 3.2 class 8 solution

Exercise 2.3 class 8 solution

Exercise 13.2 class 8 solution

https://nautiyalqueen.blogspot.com/2022/01/beauty.html