Question

${x}^{4} + 5 {x}^{2} + 9$
factorise​

Answer 1

Since both terms are square, we factor the factor using the difference formula of two squares,

$a^{2} -b^{2} =(a+b)(a-b) ; a=x^{2} +3$ and $b=x$

so we have the answer is : $(x^{2} +x+3)(x^{2} -x-3)$

Answer 2

Step-by-step explanation:

We Have :-

$x^{4} + 5x^{2} + 9$

To Find :-

$factorise$

Solution :-

$x^{4} + 5x^{2} + 9 \\ \\ \\ it \: can \: be \: written \: as \: \\ \\ \\ x^{4} + 6x^{2} + 9 - x^{2} \\ \\ \\ (x^{2} )^{2} + 2(3)(x^{2} ) + (3)^{2} - x^{2} \\ \\ \\ (x^{2} + 3)^{2} - x^{2} \: \: \: \: \: \: \: \: ((a + b) ^{2} = a^{2} + b^{2} + 2ab) \\ \\ \\ (x^{2} + 3 - x)(x^{2} + 3 + x) \: \: \: \: \: \: \: \: (a ^{2} - b^{2} = (a + b)(a - b))$