question 1.

 

- For function f

 

-the graph of y=f(x) extends down into quadrant lll and down into quadrant IV

 

-the zeros of f are -2,3 and 5 

 

-the degree of f<5

 

 

 

1.what degrees is possible for f?

 

2.what are the maximum and minimum multiplicities possible for a zero of f?

 

3.two possible equations?

 

4.two possible graphs of y=f(x)

 

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question 2.

 

a.show that p(x)/x-a=Q(x)+R/x-a can be rearranged to p(x)=Q(x)(x-a)+R

 

b.evaluate p(a),showing it simplifies to R.

 

c.how does the answer in part b. relate to the remainder theorem?

 

d.using p(x)=Q(x)(x-a)+a to explain the factor theorem.(hint:what is the value of R if there is no remainder? substituted this value for R into Q(x)(x-a)+R to show x-ais a factor of p(x).

 

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quastion 3

 

a cube with side length x has been modified by adjusting its side length x has been modified by adjusting its length, width and height. A student determined a function of the form v(x)=(x+a)(x+b)(x+c) can be used to represent the volume of the new box for different values of x, and then she graphed the function.

 

a.based on the graph ,predict how the side lengths of the original cube changed.(hint:what do the zeros of the function represent?

 

b.determine a polynomial function of the form v(x)=(x+a)(x+b)(x+c) that's matches the function in the graph .

 

c.which parts of the graph are realistic?(hint:all sides must be positive.using two negative side lengths to give positive volume is not realistic.)

 

4 years ago

Answered By Safian Q

Q1a) 4 Q1b) maximum 2, minimum 1 Q1c) -((x+2)^2)(x-3)(x-5), -((x-3)^2)(x+2)(x-5)

Attached Graph:

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