Use long divisions to show that x^2+16 is a factor of f(x)=3x^3-2x^2+48x-32. Then find all zeros of f(x).

Answer 1

_________3x - 2__

x²+0x+16 | 3x³-2x²+48x-32

- 3x³+0x²+48x

-2x² -32

-2x² -32

0

The remainder of 0 shows this is a factor

To find the zeros, set each factor equal to zero and solve

x²+16=0 Subtract 16 from both sides

x²=-16 Square root of both sides

x=±4i

3x-2=0 Add 2 to both sides

3x=2 Divide both sides by 3

x=2/3

Answer 2