Question

describe how you would verify the zeros of a function. Use your description to verify f(x) = x3 – 3x2 – 16x + 48

Answer 1

i figured it out thanks anyway

Answer 2

i would try likely values, after a few guesses f(4) = 0

factor theorem says if f(p) = 0 then (x-p) is a factor

so factor out (x-4)

Answer 3

\[f(x) = x^3 – 3x^2 – 16x + 48=x^2(x-3)-16(x-3)=(x+4)(x-4)(x-3)=0\]\[\implies x=-4,~x=4,~or~x=3\]To confirm these zeros, substitute them into f(x) to confirm that it actually results in a zero output.