Question:
the equation of a polynomial to match the dotted graph
Points given (-3,0), (-2,0), (0,0), (3,0)
Solution:
Notice that if P is a polynomial and c is a real number, then the following are equivalent:
1. c is a zero of P.
2. x = c is a solution of the equation P(x) = 0.
3. x- c is a factor of P(x).
4. c is an x-intercept of the graph of P.
Then, due to the above, we can conclude that as -3, -2, 0, and 3 are zeroes of P, the P(x) can be written as:
[tex]P(x)\text{ = (x+3)}(x+2)(x+0)(x-3)[/tex]
this is equivalent to:
[tex]P(x)\text{ =x (x+3)}(x+2)(x-3)[/tex]
In expanded form, this is equivalent to:
[tex]P(x)\text{ = }x^4+2x^3-9x^2-18x[/tex]
then, the correct answer is:
[tex]P(x)\text{ = }x^4+2x^3-9x^2-18x[/tex]
