Find the Maximum Number of Real Roots n(t)=4t^3-2t^2+8t+5

$n (t) = 4 t^{3} - 2 t^{2} + 8 t + 5$

Step 1

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

$4 t^{3} \to 3$

$- 2 t^{2} \to 2$

$8 t \to 1$

$5 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$3$

Step 3

The maximum number of possible roots is the degree of $4 t^{3} - 2 t^{2} + 8 t + 5$ .

$3$