The factors of $X^4 +x^2 +25 $ are :

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

The factors of $X^4 +x^2 +25 $ are :

Options:

$(x^2 +3x - 5)(x^2 -3x + 5)$

$(x^2 +3x + 5)(x^2 -3x + 5)$

$(x^2 -3x + 5)(x^2 -3x + 5)$

$(x^2 +3x + 5)(x^2 +3x + 5)$

Correct Answer:

$(x^2 +3x + 5)(x^2 -3x + 5)$

Explanation:

The factors of $X^4 +x^2 +25 $ =

we can write this equation as = (x²)² + 2 × x² × 5 + (5)² - (3x)²

= (x² + 5)² - (3x)²

= (x²+ 5 + 3x)(x² + 5 - 3x)