Answer to Question #84616 in Algebra for Elizabeth Driver

Question

Are both x^2+16 and x^3+27 factorable? Why or why not (explain).

Answer 1

X^3+27 can be expressed as product of two factors:

X^3+27=x^3+3^3=(x+3)(x^2-3x+9).

Therefore x^3+27 is factorable.

But x^2+16 is not factorable,as x^2+16=x^2+4^2 can not be expressed as product of factors with non-negative integer powers.