Answer:
3
Explanation:
You want to know the number of roots of x^3+4x^2-9x-36.
Degree
The degree of the given polynomial is the highest exponent of x: 3. That is the number of roots the polynomial has.
There are 3 roots.
DesCartes' rule of signs
The number of sign changes among the coefficients tells you the number of positive real roots. The signs go from + to - one time, so there is one positive real root.
When the signs of odd-degree terms are switched, the signs become ...
- + + -
There are two sign changes here, meaning that there may be 2 or 0 negative real roots. (If there are 0 real roots, the two roots are complex.)
Factors
You can see that successive pairs of terms have coefficients with the same ratio. That means you can factor this by grouping terms:
x^3+4x^2-9x-36
= (x^3+4x^2) -(9x+36)
= x^2(x +4) -9(x +4)
= (x^2 -9)(x +4)
= (x -3)(x +3)(x +4) . . . . . roots -4, -3, and +3
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Additional comment
The graph shows you the polynomial has 3 real roots.