Find the Maximum Number of Real Roots f(x)=6x^3-3x^2+5x+9

$f (x) = 6 x^{3} - 3 x^{2} + 5 x + 9$

Step 1

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$6 x^{3} \to 3$

$- 3 x^{2} \to 2$

$5 x \to 1$

$9 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$3$

Step 3

The maximum number of possible roots is the degree of $6 x^{3} - 3 x^{2} + 5 x + 9$ .

$3$