SOLUTION: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=−5.The y-intercept is y=−8 Find a formula for P(x). If a polynomial f(

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=−5.The y-intercept is y=−8 Find a formula for P(x). If a polynomial f(      Log On


   

Question 1137581: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=−5.The y-intercept is y=−8 Find a formula for P(x).
If a polynomial f(x)has a remainder of −6 when divided by x−3, what is f(3)?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
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If a polynomial f(x)has a remainder of −6 when divided by x−3, what is f(3)?
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f%28x%29=g%28x%29%28x-3%29%2B%28-6%29
f%283%29=g%283%29%283-3%29-6
f%283%29=0-6
highlight%28f%283%29=-6%29

Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=−5.The y-intercept is y=−8 Find a formula for P(x).

The polynomial in factored form is

P%28x%29+=+a%28x-2%29%5E2%28x%2B5%29

To find the coefficient a, use the fact that the y-intercept is -8 -- i.e., that f(0) = -8:

-8+=+a%28-2%29%5E2%285%29
-8+=+20a
a+=+-2%2F5

The equation in factored form is

P%28x%29+=+%28-2%2F5%29%28x-2%29%5E2%28x%2B5%29

graph%28400%2C400%2C-8%2C6%2C-24%2C12%2C%28-2%2F5%29%28x-2%29%5E2%28x%2B5%29%29