# How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^3+7x^2+7x-15#?

##### 1 Answer

Use Descartes' Rule of Signs to find that

Further find all (rational) zeros:

#### Explanation:

Given:

#f(x) = x^3+7x^2+7x-15#

**Descartes' Rule of Signs**

The pattern of signs of the coefficients is

The pattern of signs of coefficients of

**Rational Roots Theorem**

Since *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1, +-3, +-5, +-15#

**Sum of coefficients shortcut**

The sum of the coefficients of

#1+7+7-15 = 0#

Hence

#x^3+7x^2+7x-15 = (x-1)(x^2+8x+15)#

Note that

#x^2+8x+15 = (x+3)(x+5)#

So the remaining two zeros are