# How do you write a polynomial in expanded form (multiply it out) if its a 3rd degree leading coefficient, -3 and zero's are 5, -2 and 0?

Jul 6, 2016

$P \left(x\right) = - 3 {x}^{3} + 9 {x}^{2} + 30 x .$

#### Explanation:

Reqd. Poly., say P9x) is cubic , having its zeroes, 5,-2,&0.

$\therefore \left(x - 5\right) , \left(x + 2\right) ,$ and, $\left(x - 0\right) = x$ are its factors and no more.

Given that the leading co-eff. is $- 3.$ Hence,

$P \left(x\right) = - 3 x \left(x - 5\right) \left(x + 2\right) = - 3 x \left\{{x}^{2} + \left(2 - 5\right) x + 10\right\} = - 3 x \left({x}^{2} - 3 x - 10\right\} = - 3 {x}^{3} + 9 {x}^{2} + 30 x .$#