Learn Class 8 Math - Factorisation

What are the Factors?

Factorization is converting an expression into the product of its factors. These factors may be algebraic expressions, variables, and numbers also.

Division of a polynomial by a monomial

A polynomial 2x3 + 4x2 + 6xis divided by monomial 2x as shown below:

(2x3+4x2+6x)2x = 2x3 / 2x + 4x22x + 6x / 2x = x2+ 2x + 3

Factors of natural numbers

A top issue shape is a form of top factors, where every quantity is expressed.

Algebraic expressions

An algebraic expression is described because of the mathematical expression, which includes variables, numbers, and operations. The values of this expression are now no longer constant.For example: x + 1, p – q, 3x, 2x+3y, 5a/6b etc.

Factors of algebraic expressions and factorization

A fundamental element is an element that can not be expressed in addition as a made of factors. For example, algebraic expressions may be expressed in fundamental form.

Factorization by common factors

The best not unusual place elements are determined to factorize an algebraic expression.

Factorization using algebraic identities

Algebraic identities can be used for factorisation

Example: 9x2 + 12xy + 4y2

= ( 3x)2 + 2 x 3x x 2y+(2y)2

Factorisation Sample Questions for Class 8

Question 1

Factorize : 9y²- 18y -7

A. 9{(y+1/3)(y-7/3)}

B. 9{(y+3)(y-7)}

C. 9{(y-3)(y-7)}

D. 9{(y+3)(y+7)}

Question 2

Factorise: a²-2ac-b²+c²

A. (a-c)²-b²

B. (a-c-b)(a-c+b)

C. (a+c)²-b²

D. (a+c-b)(a-c+b)

Question 3

Factorize : -3(a - 2b) + 9(a -2b)²

A. 3(a-2b)(3a-6b-1)

B. -3(a-2b)(3a-6b-1)

C. -3(a-2b)(-3a+6b+1)

D. 3(a-2b)(-3a+6b+1)

Question 4

Factorize : 6x² + 3y² + 6x²y² + 3

A. (1 +y²)(6x² + 3)

B. 3(1+ y²)(1 + 2x²)

C. 3(1 +y²)(y²+1)(1+2x²)

D. 6x²(1+y²)+3(y²+1)

Question 5

Factorize : 1 - 81a⁴

A. (1+9a²)(1-9a²)

B. (1+9a)(1-9a)

C. (1+9a²)(1+3a)(1-3a)

D. (1+3a)(1-3a)