Factorize : $x^{4} + x^{2} + 25.$

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Solution

$x^{4} + x^{2} + 25 \Rightarrow (x^{2})^{2} + (5)^{2} + 2 x^{2} \times 5 - 2 x^{2} \times 5 + x^{2} \Rightarrow (x^{2})^{2} + (5)^{2} + 10 x^{2} - 10 x^{2} + x^{2} = (x^{2})^{2} + (5)^{2} + 10 x^{2} - 9 x^{2} = (x^{2} + 5)^{2} - (3 x)^{2} {∵ a^{2} - b^{2} = (a + b) (a - b)} = (x^{2} + 5 - 3 x) (x^{2} + 5 + 3 x) = (x^{2} - 3 x + 5) (x^{2} + 3 x + 5)$

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Similar questions

The factors of $x^{4} + x^{2} + 25$ are

x^{4} - x^{3} - x^{2}

x^{4} + x^{2} + 1

Factorize

i) x⁴ - y⁴+ x²- y²

The factors of x⁴ + x² + 25 are

(a) (x² + 3x + 5) (x² − 3x + 5)

(b) (x²+ 3x + 5) (x² + 3x − 5)

(c) (x² + x +5) (x² − x + 5)

(d) none of these