Polynomial Basics

Simplify  $\left(\frac{3a^3}{b^4}\right)^2$  

•  $\frac{9a^6}{b^8}$  

•  $\frac{3a^5}{b^6}$  

•  $\frac{9a^5}{b^6}$  

•  $\frac{9a^5}{b^2}$  

Simplify  $\frac{\left(x^{-2}y^{-3}\right)\left(x^{-3}y^5\right)}{z^{-2}}$  

•  $\frac{y^2z^2}{x^5}$  

•  $\frac{x^6z^2}{y^{15}}$  

•  $\frac{x^{-5}\left(xy\right)^{-10}\left(yx\right)^9y^{-15}}{z^{-2}}$  

• None of the above

Simplify  $2x\left(x^3+x-7\right)+\left(x+1\right)\left(x-2\right)$  

•  $2x^4+3x^2-15x-2$  

•  $2x^6-2x^5-2x^4-16x^3+10x^2+28x$  

•  $2x\left(x^3+x-7\right)$  , because  $\left(x+1\right)\ and\ \left(x-2\right)$  are roots and so equal 0.

•  $\left(x+1\right)\left(x-2\right)=x^2-x-2$  because these factors are roots and so the rest of the expression equals 0.

Expand $\left(2x-y\right)^3$  

•  $8x^3-12x^2y+6xy^2-y^3$  

•  $8x^3-y^3$  

•  $\left(4x^2-y^2\right)\left(2x-y\right)$  

•  $8x^3-2x^3y-2xy^3+y^3$  

If  $f\left(x\right)=2x^2-x-3$  , find  $f\left(h-1\right)$  .

•  $2h^2-5h$  

•  $2x^2h-2x^2-hx-x-3$  

•  $2h^2-h-5$  

•  $2x^2\left(h-1\right)^2-x\left(h-1\right)-3$  

If  $g\left(x\right)=\left(3x^4+2x^3-3x^2+x-12\right)\left(2x^2+x-3\right)$ , is g(x) a polynomial?

• Yes

• No

• Cannot be determined

If  $g\left(x\right)=\left(3x^4+2x^3-3x^2+x-12\right)\left(2x^2+x-3\right)$ , what is the first term of the polynomial in standard form?

•  $6x^6$  

•  $6x^8$  

•  $5x^8$  

•  $3x^4$  

If  $g\left(x\right)=\left(3x^4+2x^3-3x^2+x-12\right)\left(2x^2+x-3\right)$ , what is the y-intercept?

• 36

• -12

• -36

• 6

Let  $h\left(x\right)=-\frac{3}{4}x^7-3x^5+x^4-\frac{1}{2}x^3+6$  .  What is the leading coefficient of the polynomial?

•  $-\frac{3}{4}$  

•  $\frac{3}{4}$  

•  $3$  

•  $-3$  

•  $6$  

Let  $h\left(x\right)=-\frac{3}{4}x^7-3x^5+x^4-\frac{1}{2}x^3+6$  .  What does the degree tell us about the graph?

• The tails point in opposite directions

• The tails point in the same direction

• The graph is concave down

• The graph points down to the right