Use synthetic division to find the zeros of the function (must show process)

Question

Use synthetic division to find the zeros of the function (must show process)

 

f(x)= x^3-12x^2+12x+80

Answer 1

f(x) = x³ -12x² + 12x + 80

 

OK, Katheryn.

There are 2 or 0 positive real zeros, and 1 negative real zeros, according to Descartes' Rule of Sign.

Also, the possible rational zeros are ±{1, 2, 4, 5, 8, 10, 16, 20, 40, 80}

 

Try ±1 and 2,  these 3 won't work.

 

 -2| 1     -12    12    80

    |_____-2__ 28   -80

      1      -14   40  | 0

 

Therefore, x= -2, and x² - 14x + 40 = 0

 

And x² - 8x -20 = 0,   (x - 10)(x - 4) = 0.

 

So, x = -2, 4, and 10.

 

I hope this helps.