Question

y=x^3+x^2-9x-9, list the intercepts and test for symmetry

Answer 1

use the factor theorem

P(-1) = 0 so (x + 1) is a factor

then by polynomial division the factors are

(x + 1)(x^2 - 9) or (x +1)(x-3)(x+3)

then the x-intercepts are x = -3, -1, 3

the y intercept is when x = 0 or y = -9

test to see if the function is odd, even of neither

P(-x) = -x^3 + x^2 + 9x - 9

the function is neither odd nor even so does not have symmetry