Question

16. Factorize: 4x^2 - 5x + 1

a.(x - 1)(4x + 1)

b.(4x - 1)(x - 1)

c.(4x - 1)(x +1)

d.(x + 1 )(4x +1)

​

Answer 1

Question

Factorize:

$\sf\:4x{}^{2}-5x+1$

Theory ;

⇒Splitting the middle term method :

The middle term should be splitted in such a way that their sum gives the middle term while their multiplication gives the value equal to product of coefficient of x^2 and x^0.

Solution :

Splitting the middle term method :

we need to find two numbers whose ,

sum =-5

and product = 4

$\sf\:4x{}^{2}-5x+1$

Factorize using splitting the middle term method

$\implies\:\sf\:4x{}^{2}-4x-x+1$

$\implies\:\sf\:4x(x-1)+-1(x-1)$

$\implies\sf\:(4x-1)(x-1)$

Therefore, correct option is b)

Verification:

(4x-1)(x-1)

= 4x(x-1)-1(x-1)

= 4x² -4x -x +1

= 4x² -5x +1

Hence verified !

_________________________

More About Factorization method:

A factorization method called " grouping." .

Answer 2

Question :-

Factorize: 4x^2 - 5x + 1

a.(x - 1)(4x + 1)

b.(4x - 1)(x - 1)

c.(4x - 1)(x +1)

d.(x + 1 )(4x +1)

Solution :-

$4 {x}^{2} - 5x + 1 \\ \\By \: splitting \: middle \: term \: \implies \\ \\ = 4 {x}^{2} - 4x - x + 1 \\ \\ = 4x(x - 1) - 1(x - 1) \\ \\ =( 4x - 1)(x - 1)$

Option 'b' is correct ✓