Question

factorise x^4+3x^2+4

Answer 1

Hope this helps bud :) . I've used the formula for difference of two squares

Answer 2

The given expression:

$x^4$ + 3$x^2$ + 4

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

Solution:

∴ $x^4$ + 3$x^2$ + 4

Adding and subtracting $x^2$, we get

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

= $x^4$ + 4$x^2$ + 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 $x^4$ + 3$x^2$ + 4 = ($x^2$ + x + 2 )($x^2$ - x + 2)

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