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 4444 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 33P(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.