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## Polynomial Arithmetic

From profit/cost models to the flight of a baseball to approximating the motion of a wave, polynomials are a mathematical way to represent values which are sums of powers of variables.

# Applying the Perfect Cube Identity

If $$x^2=7$$, what is the value of $(x+3)^3-(x-3)^3?$

Simplify

$( 2 + \sqrt{3})^3 + ( 2 - \sqrt{3})^3.$

If $8x^3-512y^3=(2x-ay)(bx^2+cxy+dy^2),$ what is the value of $$a+b+c+d$$?

Simplify

$( 4 + \sqrt{19})^3 + ( 4 - \sqrt{19})^3.$

If $x^3+8=(x+a)(x^2+bx+c),$ what is the value of $$a+b+c$$?

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