Question

Write the standard form of the simplest polynomial with the roots 2, 3, and -3

Answer 1

$\text{If}\ x_1,\ x_2\ \text{and}\ x_3\ \text{are roots of a polynomial, then we can write that polynomial}\\\text{in form}\ (x-x_1)(x-x_2)(x-x_3).\\\\\text{We have\ the\ roots:}\ 2,\ 3\ \text{and}\ -3.\\\\w(x)=(x-2)(x-3)(x-(-3))=(x-2)\underbrace{(x-3)(x+3)}_{use\ a^2-b^2=(a-b)(a+b)}\\\\=(x-2)(x^2-9^2)=(x-2)(x^2-9)=(x)(x^2)+(x)(-9)+(-2)(x^2)+(-2)(-9)\\\\=x^3-9x-2x^2+18=\boxed{x^3-2x^2-9x+18}$