Find the Maximum Number of Real Roots H(x)=x^3-7x^2-x+7

$H (x) = x^{3} - 7 x^{2} - x + 7$

Step 1

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

$x^{3} \to 3$

$- 7 x^{2} \to 2$

$- x \to 1$

$7 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$3$

Step 3

The maximum number of possible roots is the degree of $x^{3} - 7 x^{2} - x + 7$ .

$3$