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Use the Factor Theorem to determine if $x鈭�5$ is a factor of $f\left(x\right)=x^3鈭�125$.

Use the Factor Theorem to determine if$x鈭�6$ is a factor of $f\left(x\right)=x^3鈭�216$.

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.

$$\begin{gathered} \left(a\right)9y^3-10y^2+2y-6 \\ \left(b\right)-12p^{3}q \\ \left(c\right)a^2+9ab+18b^2 \\ \left(d\right)20x^2{y}^2-10a^2{b}^2+30 \\ \left(e\right)17 \end{gathered}$$

In the following exercises, add or subtract the polynomials.

$\left(a^3-2a^{2}b\right)+\left(a{b}^2+b^3\right)-\left(3a^{2}b+4a{b}^2\right)$

In the following exercises, add or subtract the polynomials.

$\left(x^3-x^{2}y\right)-\left(4x{y}^2-y^3\right)+\left(3x^{2}y-x{y}^2\right)$

In the following exercise, add or subtract the polynomials.

$\left(x^3-2x^{2}y\right)-\left(x{y}^2-3y^3\right)-\left(x^{2}y-4x{y}^2\right)$

For the function $f\left(x\right)=8x^2-3x+2$, find:

$\left(a\right)f\left(5\right)\left(b\right)f(-2)\left(c\right)f\left(0\right)$

For the function $g\left(x\right)=4鈭�36x$, find:

$鈸�g\left(3\right)鈸�g\left(0\right)鈸�g(鈭�1)$

For the function $g\left(x\right)=16鈭�36x^2$, find:

$鈸�g(鈭�1)鈸�g\left(0\right)鈸�g\left(2\right)$

A painter drops a brush from a platform $75$feet high. The polynomial function $h\left(t\right)=鈭�16t^2+75$gives the height of the brush $t$seconds after it was dropped. Find the height after$t=2$ seconds.