Finite Math Examples

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

Step 1

Apply the distributive property.

$f (x) = 6 x^{4} + 6 (- 2 x^{2}) + 6 (2 x) + 6 \cdot - 4$

Step 2

Simplify.

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Step 2.1

Multiply $- 2$ by $6$ .

$f (x) = 6 x^{4} - 12 x^{2} + 6 (2 x) + 6 \cdot - 4$

Step 2.2

Multiply $2$ by $6$ .

$f (x) = 6 x^{4} - 12 x^{2} + 12 x + 6 \cdot - 4$

Step 2.3

Multiply $6$ by $- 4$ .

$f (x) = 6 x^{4} - 12 x^{2} + 12 x - 24$

Step 3

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

$6 x^{4} \to 4$

$- 12 x^{2} \to 2$

$12 x \to 1$

$- 24 \to 0$

Step 4

The largest exponent is the degree of the polynomial.

$4$

Step 5

The maximum number of possible roots is the degree of $6 x^{4} - 12 x^{2} + 12 x - 24$ .

$4$