If -1 is a zero of the polynomial f(x)=-4x^3-9x^2+x+6 and find all other zeros
If -1 is a zero of the polynomial f(x)=-4x^3-9x^2+x+6, then we know that (x+1) is a factor of the polynomial.
Using polynomial division or synthetic division, we can divide the polynomial f(x) by (x+1) to find the other factors and zeros.
Dividing -4x^3-9x^2+x+6 by (x+1), we get:
-4x^2 - 13x + 6
Now we need to factorize the quadratic polynomial -4x^2 - 13x + 6.
The factors of -24 that add up to -13 are -16 and -1.
So, we get: -4x^2 - 16x + 3x + 6
= -4x(x + 4) + 3(x + 2)
= (x + 2)(-4x + 3)
Therefore, the zeros are x = -1, -2, and 3/4.