Question

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FACTORISATION :-
${x}^{4} + {x}^{2} + 1 = 0$
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Answer 1

factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

The factors of any equation can be an integer, a variable or an algebraic expression itself.

Example :

24

24 = 4 × 6

4 & 6 are the factors of 24

9

9 = 3 × 3

3 is the factor of 9

Steps to factoring completely :-

Factor a GCF from the expression, if possible.

Factor a Trinomial, if it is possible.

Factor a Difference Between Two Squares as many times as it is possible.

Methods to factoring :-

Factoring out the GCF.

The sum-product pattern.

The grouping method.

The perfect square trinomial pattern.

The difference of squares pattern.

Answer 2

x⁴+x²+1

→ (x+1)²-x²

→ (x²+1-x) (x²+1+x)

→ (x²-x+1) (x²+x+1)

→ (x²+x+1) (x²-x+1)