Question

given that x=3 is a zero of P(x) =x^3-5x^2-2x+24 find all other zeros of p(x)

Answer 1

idea is to factor out
\[x^3-5x^2-2x+24=(x-3)\times q(x)\]

Answer 2

q(x) will be a polynomial of degree 2 and you find the zeros either by factoring or using quadratic formula. you find q(x) by dividing. synthetic division is easiest

Answer 3

but really easiest is using a calculator.
http://www.wolframalpha.com/input/?i=P%28x%29+%3Dx^3-5x^2-2x%2B24

Answer 4

synthetic division :)

coeffs of ploy
addends
-----------
x | new polys

Answer 5

1 -5 -2 24
0 3 -6 -24
------------
3 | 1 -2 -8 0 ; the zero at the end tells us its a zero of the poly

x^2 -x -8 is whats left to get zeros for, and quadratics thed to be easier to deal with;

Answer 6

opps... i dropped out the 2, this is better

x^2 -2x -8

Answer 7

we can either factor this, or use the quadratic formula to determine the zeros; the quad form will always provide results whereas factoring depends on luck

Answer 8

(1/2) (2+-sqrt(4-4(1)(-8)))

(1/2) (2+-sqrt(4+32))

(1/2) (2+-sqrt(36))

(1/2) (2+- 6)

(1/2) (-4 or 8) means x = -2 or 4