# Thread: Write a Function For This Polynomial

1. ## Write a Function For This Polynomial

Draw the graph and write a function for the polynomial that fits the following description.

p is a fourth-degree polynomial with x-intercepts -2, -1, and 5 and y-intercept -50; p(x) is positive only on the interval (-2 , -1 ).

P(X)= _____________________

2. Originally Posted by DesiKid89
Draw the graph and write a function for the polynomial that fits the following description.

p is a fourth-degree polynomial with x-intercepts -2, -1, and 5 and y-intercept -50; p(x) is positive only on the interval (-2 , -1 ).

P(X)= _____________________

try drawing axis with the intervals given. by marking the intervals where the graph is positive and/or negative (with say a tick for positive and an x for negative) you would realize that the zero x = 5 is a double root.

thus we have: $\displaystyle P(x) = (x + 2)(x + 1)(x - 5)^2$

now expand

3. Ok, I expanded it out and I ended up with:

P(X)= x^4 - 7x^3 - 5x^2 - 55x + 50

....and apparently that ended up being wrong, so can someone explain what I did wrong (and possibly what the correct answer may be)?

4. Originally Posted by DesiKid89
Ok, I expanded it out and I ended up with:

P(X)= x^4 - 7x^3 - 5x^2 - 55x + 50

....and apparently that ended up being wrong, so can someone explain what I did wrong (and possibly what the correct answer may be)?
it should be a +55x here. but there is something else wrong. we need a negative x^4 graph to fulfill the conditions. so multiply through by -1 (after you fix the sign on the 55x)

so in short, you must find $\displaystyle P(x) = -(x + 2)(x + 1)(x - 5)^2$

5. Yeah now I got:

P(X)= -x^4 + 7x^3 + 3x^2 -55x -50

...and that was right, thanks a lot man. Your like my new math idol, lol.

6. Originally Posted by DesiKid89
Yeah now I got:

P(X)= -x^4 + 7x^3 + 3x^2 -55x -50

...and that was right, thanks a lot man. Your like my new math idol, lol.
you're welcome... you had a math idol??