Find the Maximum Number of Real Roots f(x)=3x^6+2x^5+x^4-2x^3

$f (x) = 3 x^{6} + 2 x^{5} + x^{4} - 2 x^{3}$

Step 1

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

$3 x^{6} \to 6$

$2 x^{5} \to 5$

$x^{4} \to 4$

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

Step 2

The largest exponent is the degree of the polynomial.

$6$

Step 3

The maximum number of possible roots is the degree of $3 x^{6} + 2 x^{5} + x^{4} - 2 x^{3}$ .

$6$