Question

show that. 13^3-5^3is divided by 8 . whoever gives the right and first I will mark him/her brainlest ​

Answer 1

Topic: Polynomials

Hint

Polynomial identity $A^{3}-B^{3}=(A-B)(A^{2}-AB+B^{2})$.

The polynomial has two factors.

Solution

The given value is $13^{3}-5^{3}=(13-5)(13^{2}-13\cdot 5+5^{2})$ which is divisible by $8$.

Solve similar problems.

Question: Where $n$ is a natural number, show that $n^{4}+4$ is prime only when $n=1$.

Solution: If the given polynomial is factorized $n^{4}+4=(n^{4}+4n^2+4)-4n^{2}=(n^2+2)^{2}-(2n)^{2}=(n^{2}+2n+2)(n^{2}-2n+2)$ and $n^2-2n+2$ is the least factor. Hence, it should be $n^{2}-2n+2=1$ which leads to $n=1$.