DIVISION of POLYNOMIALS f(x) by Linear Binomials (x+a).

Given that   $\frac{x^3+2x^2-5x-6}{x-3}=f\left(x\right)+\frac{24}{x-3}$  Determine the quotient function,  $f\left(x\right).$  

•  $x^2+6x+10.$  

•  $x^2+5x+10.$  

•  $x^2+12x+10.$  

•  $x^3+5x+10.$  

Tags

CCSS.HSA.APR.D.6

Given the identity  $\frac{4x^3-3x^2+x+7}{x-2}=4x^2+5x+11\ +\frac{Q}{x-2}.$  Determine the numerical value of Q.

• 30

• 33

• 29

• -29

Tags

CCSS.HSA.APR.D.6

Consider the identity function 
  $4x^3-3x^2+x+7=\left(x-2\right)\left(4x^2+5x+11\right)+R.$ Determine the numerical value of the constant  $R.$  

•  $R=26.$  

•  $R=27.$  

•  $R=29.$  

•  $R=28.$  

Tags

CCSS.HSA.APR.B.2

 If given a rational function such as  $\frac{x^4-26x^2+25}{x-5}\ OR\ \left(x^4-26x^2+24\right)\div\left(x-5\right)$  
According to the Remainder Theorem, instead of carrying out long division or synthetic division in order to obtain the remainder,  $R,$   $simply\ plug\ in\ the\ zero\ obtained\$ 

 $from\ the\ linear\ binomial\ divisor,\ x-5.$

 

 $for\ x\ in\ the\ Dividend\ Function\ x^4-26x^2+25.$  Determine the Remainder of the above rational function using the Remainder Theorem.

•  $10$  

•  $-12$  

•  $8$  

•  $0$  

Tags

CCSS.HSA.APR.B.2

According to the Factor Theorem, any linear  $divisor\ such\ as\ \left(x-a\right)$  will be a factor of the polynomial  $f\left(x\right)$  if and only if   $f\left(a\right)=0.$  Using the Factor Theorem, which of the following polynomials has  $x-5,$  as one of its linear factors?

•  $x^3+2x^2-5x-6$  

•  $x^3+2x^2-5x-20$  

•  $x^4-26x^2+25$  

•  $2x^5-3x^4+x^3-2x^2+x-8.$  

Tags

CCSS.HSA.APR.B.2