Question

Use the rational zero theorem to find all possible rational zeros for the polynomial function P(x)=2x^3+9x^2+12x-8

Answer 1

Look at all of the factors of the leading coefficient, 2: (1,2)
Look at all of the factors of the trailing coefficient, 8: (1,2,4,8)
Then the possible rational roots can formed using the factors,

{1/1,2/1,4/1,8/1,1/2,2/2,4/2,8/2}
Ordering and removing duplicates, the possible rational roots are,
{1/2,1,2,4,8} and their negative counterparts,
{-1/2,-1,-2,-4,-8}

Answer 2

determine whether the equation defines y as a function of x: y=-5x+2