SOLUTION: Please help and show all work. Thanks Real Zeros of Polynomials 1. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicit

Question 1023621: Please help and show all work. Thanks

Real Zeros of Polynomials
1. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x=−2. It goes through the point (5,14).
Find a formula for P(x).
P(x)=

2. The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and root of multiplicity 1 at x=-1. The y-intercept is y=-12.5.
Find a formula for P(x).
P(x)=
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1. A polynomial with a root of multiplicity 2 at x=3 has as a factor.
A polynomial with roots of multiplicity 1 at x=0 and x=−2
has and as factors.
The factors listed make
, with a polynomial f degree 4.
If the graph of such polynomial goes through point (5,14), then ,and , so
-->-->--> .
So, is a formula for such a polynomial.

2. Similarly, the polynomial must be of the form
, with ,
ana if the y-intercept is ,
must be such that .
So, -->-->-->-->,
and is a formula for such a polynomial.
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