The factors of the polynomial equation P(x) = 4x3+x2+5x+8 is
(x + 1), (4x2 – 3x + 8)
The constant term in the given polynomial is 8. But the given polynomial 4x3+x2+5x+8 can also be written as x3+14x2+54x+2.
So one of the zeros of the polynomial can be obtained by finding the values of given polynomial at the factors of 2 i.e, 1,-1,-2,2.
Here we see that P(-1) = 0, which means that (x+1) is a factor of the polynomial P(x).
The quotient obtained by dividing P(x) by (x+1) is the other factor.