Question

Factor the polynomial. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. x^3+216 this factors into:(Answer + Answer)(Answer - Answer+Answer)

Answer 1

`(x+6)(x^2-6x+36)`

Step-by-step explanation:

Given the expression

`x^3+216\text{ }`

This can also be written as:

`x^3+6^3`

Using the sum of cube identity

`a^3+b^3=\mleft(a+b\mright)\cdot\mleft(a^2-ab+b^2\mright)`

Comparing both expressions, we can see that:

a = x

b = 6

Substituting these parameters into the identity expression

`\begin{gathered} x^3+6^3=(x+6)\cdot\mleft(x^2-6x+6^2\mright) \\ x^3+216=(x+6)(x^2-6x+36) \end{gathered}`

This gives the required factor of the given expression