Polynomial Factorizations

Question

Find the zeros of this function:

$f(x) = x^2 - 3x - 40.$

My homework tells me to use a graphing calculator but I don't have one. How can I solve this w/o one?

• Thank you everyone for your help. I understand factoring a bit better now :)

Answer 1

$$ (x-8)(x+5) = x^2-3x-40 $$ because $$ (x+a)(x+b) = x^2+(a+b)x + ab $$

Answer 2

There is a quite well known "quadratic formula", that given a polynomial $f(x)=ax^2+bx+c$, the roots of the polynomial are given by $$x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ The roots of the polynomial are the zeros of $f(x)$. Can you continue from here?

Answer 3

$4f(x)=4x^2-12x-160=(2x-3)^2-\text{what?}$