Question

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?

Answer 1

`P(x)=-3x^3+9x^2+30x.`

Explanation:

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

`:. (x-5), (x+2),` and, `(x-0)=x` are its factors and no more.

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

`P(x)=-3x(x-5)(x+2) = -3x{x^2+(2-5)x+10}=-3x(x^2-3x-10}=-3x^3+9x^2+30x.`#