Finite Math Examples

$f (x) = 2 {(x - 3)}^{2} + 1$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$f (x) = 2 ((x - 3) (x - 3)) + 1$

Step 1.2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$f (x) = 2 (x (x - 3) - 3 (x - 3)) + 1$

Step 1.2.2

Apply the distributive property.

$f (x) = 2 (x \cdot x + x \cdot - 3 - 3 (x - 3)) + 1$

Step 1.2.3

Apply the distributive property.

$f (x) = 2 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3) + 1$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $x$ by $x$ .

$f (x) = 2 (x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3) + 1$

Step 1.3.1.2

Move $- 3$ to the left of $x$ .

$f (x) = 2 (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3) + 1$

Step 1.3.1.3

Multiply $- 3$ by $- 3$ .

$f (x) = 2 (x^{2} - 3 x - 3 x + 9) + 1$

Step 1.3.2

Subtract $3 x$ from $- 3 x$ .

$f (x) = 2 (x^{2} - 6 x + 9) + 1$

Step 1.4

Apply the distributive property.

$f (x) = 2 x^{2} + 2 (- 6 x) + 2 \cdot 9 + 1$

Step 1.5

Simplify.

Tap for more steps...

Step 1.5.1

Multiply $- 6$ by $2$ .

$f (x) = 2 x^{2} - 12 x + 2 \cdot 9 + 1$

Step 1.5.2

Multiply $2$ by $9$ .

$f (x) = 2 x^{2} - 12 x + 18 + 1$

Step 2

Add $18$ and $1$ .

$f (x) = 2 x^{2} - 12 x + 19$

Step 3

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

$2 x^{2} \to 2$

$- 12 x \to 1$

$19 \to 0$

Step 4

The largest exponent is the degree of the polynomial.

$2$

Step 5

The maximum number of possible roots is the degree of $2 x^{2} - 12 x + 19$ .

$2$