Algebra Examples

$p (x) = (x^{3} - 8) (x - 2)$

Step 1

Expand $(x^{3} - 8) (x - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$p (x) = x^{3} (x - 2) - 8 (x - 2)$

Step 1.2

Apply the distributive property.

$p (x) = x^{3} x + x^{3} \cdot - 2 - 8 (x - 2)$

Step 1.3

Apply the distributive property.

$p (x) = x^{3} x + x^{3} \cdot - 2 - 8 x - 8 \cdot - 2$

Step 2

Simplify each term.

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Step 2.1

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 2.1.1

Multiply $x^{3}$ by $x$ .

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Step 2.1.1.1

Raise $x$ to the power of $1$ .

$p (x) = x^{3} x + x^{3} \cdot - 2 - 8 x - 8 \cdot - 2$

Step 2.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$p (x) = x^{3 + 1} + x^{3} \cdot - 2 - 8 x - 8 \cdot - 2$

Step 2.1.2

Add $3$ and $1$ .

$p (x) = x^{4} + x^{3} \cdot - 2 - 8 x - 8 \cdot - 2$

Step 2.2

Move $- 2$ to the left of $x^{3}$ .

$p (x) = x^{4} - 2 \cdot x^{3} - 8 x - 8 \cdot - 2$

Step 2.3

Multiply $- 8$ by $- 2$ .

$p (x) = x^{4} - 2 x^{3} - 8 x + 16$

Step 3

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

$x^{4} \to 4$

$- 2 x^{3} \to 3$

$- 8 x \to 1$

$16 \to 0$

Step 4

The largest exponent is the degree of the polynomial.

$4$

Step 5

The maximum number of possible roots is the degree of $x^{4} - 2 x^{3} - 8 x + 16$ .

$4$