Question

Factorize------ x^4-3x-2​

Answer 1

Step-by-step explanation:

Answer

Let x

2

=p, then the equation x

4

−3x

2

+2 becomes p

2

−3p+2

Consider the equation p

2

−3p+2 and factorise it as follows:

p

2

−3p+2=p

2

−2p−p+2=p(p−2)−1(p−2)=(p−1)(p−2)

Now, substitute the value of p as p=x

2

:

(p−1)(p−2)=(x

2

−1)(x

2

−2)=(x+1)(x−1)(x+2)(x−2) (Using identity a

2

−b

2

=(a+b)(a−b))

Hence, x

4

−3x

2

+2=(x

2

−1)(x

2

−2)=(x+1)(x−1)(x+

2

)(x−

2

)