Question

Given the polynomial equation: x^3-7x^2-x+7=0

1. Make a list of possible rational roots

2. Test the possible roots until you find one that produces a reminder of 0. Show your work.

3. Write the resulting quadratic function.

4. Factor or use the quadratic formula to find the final 2 roots.

Answer 1

( - 1 )³ - 7 · ( - 1 )² - ( - 1 ) + 7 = - 1 - 7 + 1 + 7 = 0
The first possible root is x 1 = - 1 and ( x + 1 ) is a factor:
x³ - 7 x² - x + 7 = ( x + 1 ) ( x² - 8 x + 7 ) = 0
x² - 8 x + 7 = x² - 7 x - x + 7 = x ( x - 7 ) - ( x - 7 ) = ( x - 7 ) ( x - 1 ) = 0
Final 2 roots are: x 2 = 1, x 3 = 7.