Question

Find all the zeroes of the polynomial p(x) =2x^4+x^3 -14x^2-19 x-6 If two of its zeroes are -2 and -1.

Answer 1

As 2 zeroes are 2 and 1 the polynomial is divisible by (x + 2) and (x + 1)

and by x^2 + 3x + 2

if we do long division the quotient is 2x^2 - 5x - 3

this factors to (2x + 1)(x - 3)

so the other zeroes are -1/2 and 3.