Question

factorise x^4 + 3х^2 + 4​

Answer 1

Answer:

BRAINLEST!!

The given expression:

x^4 + 3x^2 + 4

We have to find, the factorisation of x^4 + 3x^2 + 4 is:

Solution:

∴ x^4 + 3x^2 + 4

Adding and subtracting x^2, we get

= x^4 + 3x^2 + 4 + x^2 - x^2

= x^4 + 4x^2 + 4 - x^2

= [(x^2)^2 + 2(x^2)(2) + 2^{2}] - x^2

Using the algebraic identity:

(a+b)^{2} =a^{2} +2ab+b^{2}

= (x^2+2)^{2}-

Using the algebraic identity:

a^{2} -b^{2} = (a + b)(a - b)

= (x^2 + 2 + x)(x^2 + 2 - x)

= (x^2 + x + 2 )(x^2 - x + 2)

∴ The factorisation of x^4 + 3x^2 + 4 = (x^2 + x + 2 )(x^2 - x + 2)

Thus, the factorisation of x^4 + 3x^2 + 4 is equal to "(x^2 + x + 2 )(x^2 - x + 2)".