Question

Factorise : x 2 + x/4 - 1/8

Answer 1

Answer:

x²+x/4-1/8 = (x+1/2)(x-1/4)

Explanation:

Given quadratic polynomial:

x²+x/4-1/8

Splitting the middle term, we get

= x²+x/2-x/4 -1/8

= x(x+1/2)-1/4(x+1/2)

= (x+1/2)(x-1/4)

Therefore,

x²-x/4-1/8 = (x+1/2)(x-1/4)

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Answer 2

The value of $x^{2}+\frac{x}{4}-\frac{1}{8} \text { is } \bold{\left(x+\frac{1}{2}\right)\left(x-\frac{1}{4}\right)}$.  

To find:

Factorize: $x^{2}+\frac{x}{4}-\frac{1}{8}$

Solution:

$x^{2}+\frac{x}{4}-\frac{1}{8}$

$=x^{2}+\frac{x}{2}-\frac{x}{4}-\frac{1}{8}$

$=x(x)+x \times \frac{1}{2}-x \times \frac{1}{4}-\frac{1}{8}$

$=x\left(x+\frac{1}{2}\right)-\frac{1}{4}\left(x+\frac{1}{2}\right)$

$=\left(x+\frac{1}{2}\right)\left(x-\frac{1}{4}\right)$

A ‘polynomial’ is an expression consisting of ‘variables’ and ‘coefficients’ that involves the arithmetic operations like ‘addition’, ‘subtraction’, and ‘non-negative integer exponents’ of variables. “Polynomial equation” is an ‘equation that has multiple terms’ made up of ‘numbers and variables’.