Algebra Examples

$f (x) = x^{4} (2 - x^{3}) + 1$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x^{4} \cdot 2 + x^{4} (- x^{3}) + 1$

Step 1.2

Move $2$ to the left of $x^{4}$ .

$2 \cdot x^{4} + x^{4} (- x^{3}) + 1$

Step 1.3

Rewrite using the commutative property of multiplication.

$2 \cdot x^{4} - x^{4} x^{3} + 1$

Step 1.4

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Step 1.4.1

Move $x^{3}$ .

$2 x^{4} - (x^{3} x^{4}) + 1$

Step 1.4.2

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

$2 x^{4} - x^{3 + 4} + 1$

Step 1.4.3

Add $3$ and $4$ .

$2 x^{4} - x^{7} + 1$

Step 2

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

$2 x^{4} \to 4$

$- x^{7} \to 7$

$1 \to 0$

Step 3

The largest exponent is the degree of the polynomial.

$7$