# Math Help - Finding a degree 3 polynomial w/ specified zeros...

1. ## Finding a degree 3 polynomial w/ specified zeros...

Find a degree 3 polynomial with zeros -2, 1, and 5 going through the point [0, -3].

This is what I have so far:

y=ax^3 + bx^2 + cx + d

0=-8a + 4b - 2c + d
0= a + b + c + d
0= 125a + 25b + 5c + d
-3= 0a + 0b + 0c + d

d= -3

So how do I solve this system now?

Any help is greatly appreciated.

2. Another approach:

$p(x)=a(x+2)(x-1)(x-5)$

$p(0)=-3\Rightarrow 10a=-3\Rightarrow a=-\frac{3}{10}$

Now you can expand the polynomial.

3. How did you get 10a = -3?

Nevermind. Thank you for your help