Algebra Examples

9 x^{3} + 3 x^{8} + 6 x^{7} + 5 x^{6} - 7 x^{5}

$9 x^{3} + 3 x^{8} + 6 x^{7} + 5 x^{6} - 7 x^{5}$

Step 1

Move

$9 x^{3}$ .

$3 x^{8} + 6 x^{7} + 5 x^{6} - 7 x^{5} + 9 x^{3}$

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.

$3 x^{8} \to 8$

$6 x^{7} \to 7$

$5 x^{6} \to 6$

$- 7 x^{5} \to 5$

$9 x^{3} \to 3$

Step 2.2

The largest exponent is the degree of the polynomial.

$8$

Step 3

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

$3 x^{8}$

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.

$3 x^{8}$

Step 4.2

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

$3$

Step 5

List the results.

Polynomial Degree:

$8$

Leading Term:

$3 x^{8}$

Leading Coefficient:

$3$

$9 x^{3} + 3 x^{8} + 6 x^{7} + 5 x^{6} - 7 x^{5}$

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