Question

Use the Factor Theorem to find ALL zeros of f(x) = x^3 - x^2 - 11x + 15, given that 3 is a zero. Show all work and express zeros in exact form (no decimals).

Answer 1

Explanation:

by synthetic division

3) 1 -1 -11 15

| 3 6 -15 (add)

____________

1 2 -5 |0

x²+2x-5=0

`x=\frac{-2 \pm\sqrt{2^(2) -4*1*-5} }{2*1} \\or~x=(-2 \pm√(4+20) )/(2) \\or~x=(-2 \pm2√(6) )/(2) \\or ~x=-1 \pm √(6)`