Algebra Examples

${(x + 3)}^{5}$

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Step 1.1

Use the Binomial Theorem.

$x^{5} + 5 x^{4} \cdot 3 + 10 x^{3} \cdot 3^{2} + 10 x^{2} \cdot 3^{3} + 5 x \cdot 3^{4} + 3^{5}$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $3$ by $5$ .

$x^{5} + 15 x^{4} + 10 x^{3} \cdot 3^{2} + 10 x^{2} \cdot 3^{3} + 5 x \cdot 3^{4} + 3^{5}$

Step 1.2.2

Raise $3$ to the power of $2$ .

$x^{5} + 15 x^{4} + 10 x^{3} \cdot 9 + 10 x^{2} \cdot 3^{3} + 5 x \cdot 3^{4} + 3^{5}$

Step 1.2.3

Multiply $9$ by $10$ .

$x^{5} + 15 x^{4} + 90 x^{3} + 10 x^{2} \cdot 3^{3} + 5 x \cdot 3^{4} + 3^{5}$

Step 1.2.4

Raise $3$ to the power of $3$ .

$x^{5} + 15 x^{4} + 90 x^{3} + 10 x^{2} \cdot 27 + 5 x \cdot 3^{4} + 3^{5}$

Step 1.2.5

Multiply $27$ by $10$ .

$x^{5} + 15 x^{4} + 90 x^{3} + 270 x^{2} + 5 x \cdot 3^{4} + 3^{5}$

Step 1.2.6

Raise $3$ to the power of $4$ .

$x^{5} + 15 x^{4} + 90 x^{3} + 270 x^{2} + 5 x \cdot 81 + 3^{5}$

Step 1.2.7

Multiply $81$ by $5$ .

$x^{5} + 15 x^{4} + 90 x^{3} + 270 x^{2} + 405 x + 3^{5}$

Step 1.2.8

Raise $3$ to the power of $5$ .

$x^{5} + 15 x^{4} + 90 x^{3} + 270 x^{2} + 405 x + 243$

Step 2

The degree of a polynomial is the highest degree of its terms.

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Step 2.1

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

$x^{5} \to 5$

$15 x^{4} \to 4$

$90 x^{3} \to 3$

$270 x^{2} \to 2$

$405 x \to 1$

$243 \to 0$

Step 2.2

The largest exponent is the degree of the polynomial.

$5$

Step 3

The leading term in a polynomial is the term with the highest degree.

$x^{5}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

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Step 4.1

The leading term in a polynomial is the term with the highest degree.

$x^{5}$

Step 4.2

The leading coefficient in a polynomial is the coefficient of the leading term.

$1$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $x^{5}$

Leading Coefficient: $1$