Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.

Question

f(x)=x^3-8x^2-31x-22

Find the real zeros of f.

Use the real zeros to factor f.

in factored form

Answer 1

x^3 - 8x^2 - 31x - 22 = 0

possible solutions are +or- {1,2,11,22}

(-1)^3 - 8(-1)^2 - 31(-1) - 22 =

-1 - 8 + 31 - 22 =

-9 + 31 - 22 =

22-22 = 0

so -1 is a solution

-1 | 1 -8 -31 -22

-1 9 22

___________________________

1 -9 -22 0

x^2 - 9x -22 = 0

( x - 11 )( x + 2 ) = 0

x = 11 or x = -2

notice that 11 and -2 are in the list

solution {-1, -2, 11}