D6.U.05 - Polynomial Quiz Reviews

Long division was used to divide 

 $x^2-6x-16$  by  $x+2.$  Is this correct?

• This is correct

• This is incorrect

For long/synthetic division to work, what needs to be added to the problem

 $\left(2x^3+5x^2+9\right)\div\left(x+3\right)?$  

•  $0x^4$  

•  $0x^3$  

•  $0x^2$  

•  $0x$  

• 0

A student is using long division to divide 
 $3x^3-4x^2-x+1$  by  $x+1.$  

What value should go in the box next? (i.e. what should be the second term for the quotient?)

•  $-1x$  

•  $1x$  

•  $7x$  

•  $-7x$  

Use long division to divide
 $x^4+7x^3+17x^2+20x$  by  $x^2+4$  

•  $x^2+13x+7+\frac{-52}{x^2+4}$  

•  $x^2+7x+\frac{13x-8}{x^2+4}$  

•  $x^2+7x+13+\frac{-8x-52}{x^2+4}$  

•  $x^2+1+\frac{1}{x^2+4}$  

To use Synthetic Division, what should be the order of the polynomial coefficients if 

 $\left(3x-4x^3+6x^4+1\right)\div\left(x+3\right)$  

• 3   -4  6  1

• 6  -4  3  1 

• 6  -4  3  1

• 6  -4  0  3  1

What is the correct way to write the quotient after Synthetic Division?

•  $2x^3-x^2-25x-12$  

•  $2x^4-x^3-25x^2-12x+0$  

Which binomial is a factor of 

 $f\left(x\right)=x^3-6x^2+3x+10?$  

Hint: What is an efficient, algebraic way to check without performing division with each binomial?

•  $x+1$  

•  $x+2$  

•  $x+5$  

•  $x+10$  

What is the factored form of  $x^3-3x^2-4x+12$  if  $x=-2$  is a zero?

•  $\left(x-2\right)\left(x+2\right)\left(x+3\right)$  

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

•  $\left(x+2\right)^2\left(x+3\right)$  

•  $\left(x-2\right)\left(x+2\right)\left(x-3\right)$  

True or False: If  $\left(7x+4\right)$  is a factor of a polynomial, then $\left(\frac{4}{7},0\right)$  is a root of the function

• True

• False

 $f\left(x\right)=\left(x^2+9\right)\left(x-1\right)^3\left(2x+5\right)$  

State the zeros of the polynomial and their multiplicities for

•  $\left(-9,0\right),\left(1,0\right),\left(-5,0\right)$  

•  $\left(-9,0\right),\left(1,0\right)\ mult:\ 3,\left(-5,0\right)$  

•  $\left(\pm3i,0\right)\ mult:\ 2,\left(1,0\right)\ mult:\ 3,\left(-\frac{5}{2},0\right)$  

•  $\left(\pm3i,0\right),\left(1,0\right)\ mult:\ 3,\left(-\frac{5}{2},0\right)$