Is $x^{4} - a^{4}$ divisible by $x + a$ ?

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Solution

Divide $x^{4} - a^{4}$ by $x + a$ as shown:

From the division, we conclude that the remainder is $0$ .

Hence, $x^{4} - a^{4}$ is divisible by $x + a$ .

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Similar questions

p (x) = x^{4} - a^{4}

x - a

Factorise

(i) a⁴ − b⁴

(ii) p⁴ − 81

(iii) x⁴ − (y + z)⁴

(iv) x⁴ − (x − z)⁴

(v) a⁴ − 2a²b² + b⁴

\int \frac{x}{x^{4} - a^{4}}

a^{4} - b^{4}

p^{4} - 81

x^{4} - (y + z)^{4}

x^{4} - (x - z)^{4}

a^{4} - 2 a^{2} b^{2} + b^{4}

\frac{a^{4}}{x^{4}}

\to

\infty

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