Question

If x=3 is a zero of the polynomial function f(x) = x3 - 5x2 - 2x + 24, find another zero of f(x) by division or factoring

Answer 1

we have the function

f(x)=x^3-5x^2-2x+24

Remember that

If x=3 is a zero of the given function

then

(x-3) is a factor of the given function

so

Divide the given function f(x) by the factor

x^3-5x^2-2x+24 : (x-3)

x^2-2x-8

-x^3+3x^2

--------------------------

-2x^2-2x+24

2x^2-6x

----------------------

-8x+24

8x-24

------------

0

therefore

x^3-5x^2-2x+24=(x-3)( x^2-2x-8)

Solve the quadratic equation

x^2-2x-8=0

using the formula

a=1

b=-2

c=-8

substitute

$x=\frac{-(-2)\pm\sqrt{-2^2-4(1)(-8)}}{2(1)}$$x=\frac{2\pm6}{2}$

The values of x are

x=4 and x=-2

therefore

x^3-5x^2-2x+24=(x-3)(x+2)(x-4)

The zeros of the function f(x) are

x=3

x=4

x=-2