Graphs of Polynomials review

Consider the polynomial function

 $p\left(x\right)=4x^8-6x^7+3x^3-10$  .  What is the end behavior for the graph?

• As  $x\rightarrow\infty,p\left(x\right)\rightarrow\infty$  and as  $x\rightarrow-\infty,p\left(x\right)\rightarrow\infty$  

• As $x\rightarrow\infty,p\left(x\right)\rightarrow-\infty$   and as  $x\rightarrow-\infty,p\left(x\right)\rightarrow\infty$  

• As  $x\rightarrow\infty,p\left(x\right)\rightarrow-\infty$  and as  $x\rightarrow-\infty,p\left(x\right)\rightarrow-\infty$  

• As  $x\rightarrow\infty,p\left(x\right)\rightarrow\infty$  and as  $x\rightarrow-\infty,p\left(x\right)\rightarrow-\infty$  

What could be the equation of p?

• $p\left(x\right)=\left(x+1\right)^2\left(2x+5\right)^2\left(x-3\right)^2$

• $p\left(x\right)=\left(x+1\right)^2\left(2x+5\right)\left(x-3\right)$

• $p\left(x\right)=\left(x+1\right)^2\left(2x+5\right)\left(x-3\right)^2$

• $p\left(x\right)=\left(x+1\right)\left(2x+5\right)\left(x-3\right)^2$

Tags

CCSS.HSA.APR.B.3

Find all the zeros of

 $p\left(x\right)=x\left(2x+5\right)\left(x+1\right)$  

•  $-\frac{5}{2}$  

• -1

• 0

• 1

•  $\frac{5}{2}$  

Tags

CCSS.HSF-IF.C.7C

 $f\left(x\right)=\left(x-5\right)\left(2x+7\right)\left(7x-3\right)$  has zeros at x = -3.5,  $x=\frac{3}{7}$  , and x = 5.  What is the sign of f on the interval  $\frac{3}{7}<x<5$  ?  

• f is always positive on the interval

• f is always negative on the interval

• f is sometimes positive and sometimes negative on the interval

Tags

CCSS.HSA.APR.B.3

What could be the equation of p?

• $p\left(x\right)=\left(2x-1\right)^2\left(x-2\right)^2$

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

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

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

Tags

CCSS.HSA.APR.B.3

Find all of the zeros for $p\left(x\right)=2x^3-x^2-8x+4$  

• -4

• -2

•  $\frac{1}{2}$  

• 2

• 4

Find all of the zeros of $p\left(x\right)=3x^3-3x^2-18x$  

• -3

• -2

• 0

• 2

• 3