x³+3/2x²+3/4x+1/8 factorise
Answers
Answer:
(x + 1/2)^3
Step-by-step explanation:
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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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