Lesson 15 The Remainder Theorem

Lesson 15 The Remainder Theorem

​

Multiple Choice

For the polynomial function

 $f\left(x\right)=x^3-2x^2-5x+6$  , we have f(0)=6, f(2)=-4, f(-2)=0, f(-1)=8, f(1)=0.  Rewrite f(x) as a product of linear factors.

•  $f\left(x\right)=\left(x-1\right)\left(x-3\right)\left(x+2\right)$  

•  $f\left(x\right)=\left(x+1\right)\left(x+3\right)\left(x-2\right)$  

•  $f\left(x\right)=\left(x+1\right)\left(x+3\right)\left(x+2\right)$  

•  $f\left(x\right)=\left(x+1\right)\left(x-3\right)\left(x-2\right)$  

Multiple Select

Select all the polynomials that have (x−4) as a factor.

• $x^3-13x-12$

• $x^3+8x^2+19x+12$

• $x^3-x^2-10x-8$

• $x^2-4$

Open Ended

Write a polynomial function, p(x), with degree 3 that has p(7)=0.

Fill in the Blank

Long division was used here to divide the polynomial function

 $p\left(x\right)=x^3+7x^2-20x-110$  by (x-5) and to divide is by (x+5).  What is p(-5)?

Fill in the Blank

Long division was used here to divide the polynomial function

 $p\left(x\right)=x^3+7x^2-20x-110$  by (x-5) and to divide is by (x+5).  What is p(5)?

Multiple Choice

Which polynomial function has zeros when

 $x=5,\ \frac{2}{3},\ -7$  ?

•  $f(x)=(x+5)(2x+3)(x−7)$  

•  $f(x)=(x+5)(3x+2)(x−7)$  

•  $f(x)=(x−5)(2x−3)(x+7)$  

•  $f(x)=(x−5)(3x−2)(x+7)$  

Multiple Choice

The polynomial function

 $q\left(x\right)=3x^4+8x^3-13x^2-22x+24$  has known factors (x+3) and (x+2).  Rewrite q(x) as the product of linear factors.

•  $q(x)=(x+3)\left(x+2\right)(x-1)\left(3x-4\right)$  

•  $q(x)=(x+3)\left(x+2\right)(x-1)\left(3x+4\right)$  

•  $q(x)=(x-3)\left(x-2\right)(x+1)\left(3x+4\right)$  

Open Ended

We know these things about a polynomial function f(x): it has degree 3, the leading coefficient is negative, and it has zeros at x=-5,-1,3. Sketch a graph of f(x) given this information.