Question

factorize (X+1)(2x-1)(4x²+3x-1)/(2x²+x-1)(x+1)​

Answer 1

Solution :

Let us factorize the terms

(4x² + 3x - 1) and (2x² + x - 1) first.

Now, 4x² + 3x - 1

 = 4x² + (4 - 1) x - 1

 = 4x² + 4x - x - 1

 = 4x (x + 1) - 1 (x + 1)

 = (x + 1) (4x - 1)

and 2x² + x - 1

 = 2x² + (2 - 1) x - 1

 = 2x² + 2x - x - 1

 = 2x (x + 1) - 1 (x + 1)

 = (x + 1) (2x - 1)

Thus, $\frac{(x+1)(2x-1)(4x^{2}+3x-1)}{(2x^{2}+x-1)(x+1)}$

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

Now, cancelling (x + 1), (2x - 1) and

(x + 1) from both the numerator and denominator, we get the value as continued below

= 4x - 1 ,

which is the required simplification.