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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)

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 an class=

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Answer:

[tex](x+6)(x^2-6x+36)[/tex]

Explanation:

Given the expression

[tex]x^3+216\text{ }[/tex]

This can also be written as:

[tex]x^3+6^3[/tex]

Using the sum of cube identity

[tex]a^3+b^3=\mleft(a+b\mright)\cdot\mleft(a^2-ab+b^2\mright)[/tex]

Comparing both expressions, we can see that:

a = x

b = 6

Substituting these parameters into the identity expression

[tex]\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}[/tex]

This gives the required factor of the given expression

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