Question

x³+3/2x²+3/4x+1/8 factorise

Answer 1

Answer:

(x + 1/2)^3

Step-by-step explanation:

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Answer 2

Concept:

The process of breaking an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring.

Factors of a number mean a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder

Given:

We have given equation x³+3/2x²+3/4x+1/8

Find:

We have to factorize equation x³+3/2x²+3/4x+1/8

Solution:

Eq= x³+3/2x²+3/4x+1/8

take LCM of 2, 4, and 8 to make denominator 1

   = 8x³+ 12x²+ 6x + 1

   = 2x(4x²+ 6x + 3) +1

   = (2x + 1) ( 4x²+ 4x + 3x + 3 )

   = (2x + 1) (4x (x+ 1) + 3 (x+1))

   = (x+ 1) (2x + 1) ( 4x + 1)

Hence, the factors of the equation x³+3/2x²+3/4x+1/8 is (x+ 1) (2x + 1) ( 4x + 1).

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