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Write an equation for the polynomial graphed below

12345-1-2-3-4-512345-1-2-3-4-5 

 

Find a degree 33 polynomial that has zeros −44, 44 and 66 and in which the coefficient of x2x2 is −1818. 
The polynomial is

 
find The polynomial of degree 5, P(x)Px has leading coefficient 1, has roots of multiplicity 2 at x=3x3 and x=0x0, and a root of multiplicity 1 at x=−1x1 
Find a possible formula for P(x)Px. 
 
find thte polynomial of degree 33, P(x)Px, has a root of multiplicity 22 at x=1x1 and a root of multiplicity 11 at x=−2x2. The yy-intercept is  y=−1.2y1.2. 
Find a formula for P(x)Px. 
 
example 
 

Find the polynomial with zeroes at x=1,-2, and 4, where 1 and 4 have multiplicity 1, and -2 has multiplicity 2.  Also, the y-intercept of the polynomial is equal to 48.

Answer: the polynomial must look like     A(x-1)(x-4)(x+2)^2  

             note that I've multiplied the factors by a variable A which can be adjusted to match the y-intercept value

             y(0)=48   means   A(0-1)(0-4)(0+2)^2 = 48

                                       16A=48

                                        A=3

              the final polynomial is     3(x-1)(x-4)(x+2)^2

 

You'll need to use reasoning like this on a few of the problems.

 

 

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