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

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

Step 1

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

$3 x^{4} \to 4$

$5 x^{3} \to 3$

$- 4 x^{2} \to 2$

$- 5 x \to 1$

$- 2 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$4$