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Algebra 1 : How to find the degree of a polynomial

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Example Question #1 : How To Find The Degree Of A Polynomial

Give the degree of the polynomial.

$6x^{5}+5x^{4}-3x^{2}+x^{7}$ $\displaystyle 6x^{5}+5x^{4}-3x^{2}+x^{7}$

Possible Answers:

$\displaystyle 6$

$\displaystyle 18$

$\displaystyle 9$

$\displaystyle 5$

$\displaystyle 7$

Correct answer:

$\displaystyle 7$

Explanation:

$6x^{5}+5x^{4}-3x^{2}+x^{7}$ $\displaystyle 6x^{5}+5x^{4}-3x^{2}+x^{7}$

The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7.

The degree of the polynomial is the highest degree of any of the terms; in this case, it is 7.

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of the polynomial?

$ab^{2}+a^{2}b^{3}-a^{3}b^{1}$ $\displaystyle ab^{2}+a^{2}b^{3}-a^{3}b^{1}$

Possible Answers:

$\displaystyle 2$

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 5$

Correct answer:

$\displaystyle 5$

Explanation:

$ab^{2}+a^{2}b^{3}-a^{3}b^{1}$ $\displaystyle ab^{2}+a^{2}b^{3}-a^{3}b^{1}$

To find the degree of the polynomial, you first have to identify each term [term is for example $ab^{2}$ $\displaystyle ab^{2}$], so to find the degree of each term you add the exponents.

EX: $ab^{2}$ $\displaystyle ab^{2}$ $= a^{1}b^{2} = 1+2= 3$ $\displaystyle = a^{1}b^{2} = 1+2= 3$ - Degree of 3

Highest degree is $5\rightarrow$ $\displaystyle 5\rightarrow$ $a^{2}b^{3}= 2+3= 5$ $\displaystyle a^{2}b^{3}= 2+3= 5$

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of the polynomial?

$\displaystyle 12x^2y^3+6xy^4z-2xz+1$

Possible Answers:

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 1$

$\displaystyle 12$

$\displaystyle 0$

Correct answer:

$\displaystyle 6$

Explanation:

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

12x²y³: 2 + 3 = 5

6xy⁴z: 1 + 4 + 1 = 6

2xz: 1 + 1 = 2

The degree is therefore 6.

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Example Question #1 : How To Find The Degree Of A Polynomial

$\displaystyle x^5+x^3+x^2+x+1$

What is the degree of the polynomial?

Possible Answers:

$\displaystyle 5$

$\displaystyle 4$

$\displaystyle 11$

$\displaystyle 3$

$\displaystyle 2$

Correct answer:

$\displaystyle 5$

Explanation:

The degree is the highest exponent value of the variables in the polynomial.

Here, the highest exponent is x⁵, so the degree is 5.

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Example Question #2 : How To Find The Degree Of A Polynomial

Simplify:

$\frac{2x-5}{5-2x}$ $\displaystyle \frac{2x-5}{5-2x}$

Possible Answers:

-1

None of the above

Correct answer:

-1

Explanation:

The given expression can be re-written as:

$\frac{2x-5}{\left -(2x-5 \right )}$ $\displaystyle \frac{2x-5}{\left -(2x-5 \right )}$

Cancel (2x - 5):

$\frac{1}{-1} = -1$ $\displaystyle \frac{1}{-1} = -1$

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Example Question #1 : How To Find The Degree Of A Polynomial

Find the degree of the polynomial: $y=\frac{1}{x}-\frac{1}{x^2}$ $\displaystyle y=\frac{1}{x}-\frac{1}{x^2}$

Possible Answers:

$\displaystyle -1$

$\displaystyle 1$

$\textup{These are not polynomial terms.}$ $\displaystyle \textup{These are not polynomial terms.}$

$\displaystyle -2$

$\displaystyle 2$

Correct answer:

$\textup{These are not polynomial terms.}$ $\displaystyle \textup{These are not polynomial terms.}$

Explanation:

The polynomial terms may only have variables raised to positive integer exponents. No square roots, fraction powers, and variables in the denominator are allowed.

The correct answer is:

$\textup{These are not polynomial terms.}$ $\displaystyle \textup{These are not polynomial terms.}$

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of the following polynomial? $\displaystyle y=6x^5-2x^2+3x^6+x-3x^4$

Possible Answers:

$\displaystyle 5$

$\displaystyle 6$

$\displaystyle 2$

$\displaystyle 3$

$\displaystyle 1$

Correct answer:

$\displaystyle 6$

Explanation:

The degree of the polynomial is the highest power in the polynomial.

The highest power given is the term: 3x^6 $\displaystyle 3x^6$

Therefore, the degree of the polynomial is $\displaystyle 6$.

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of following polynomial?

$400z^{4} + 3z^{7} - 25z + 312$ $\displaystyle 400z^{4} + 3z^{7} - 25z + 312$

Possible Answers:

$\displaystyle 1$

$\displaystyle 7$

$\displaystyle 25$

400 $\displaystyle 400$

$\displaystyle 4$

Correct answer:

$\displaystyle 7$

Explanation:

The degree of a polynomial with a single variable (in our case, $\displaystyle z$), simply find the largest exponent of that variable within the expression. The term $3z^{7}$ $\displaystyle 3z^{7}$ shows $\displaystyle z$ being raised to the seventh power, and no other $\displaystyle z$ in this expression is raised to anything larger than seven. Therefore, the degree of this expression is $\displaystyle 7$.

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Example Question #3 : How To Find The Degree Of A Polynomial

What is the degree of the following polynomial? $\displaystyle y=-x^3y^2 + 2x^4$

Possible Answers:

$\displaystyle 5$

$\displaystyle 3$

$\displaystyle 4$

$\displaystyle 2$

$\displaystyle 1$

Correct answer:

$\displaystyle 5$

Explanation:

The polynomial has more than one variable. The degree of the polynomial is the largest sum of the exponents of ALL variables in a term.

The first term is $-x^{3}y^{2}$ $\displaystyle -x^{3}y^{2}$.

The degree of this term is 3+2=5 $\displaystyle 3+2=5$

The second term is $2x^{4}$ $\displaystyle 2x^{4}$.

The degree of this term is $\displaystyle 4$.

The degree of the polynomial is the largest of these two values, or $\displaystyle 5$.

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of the following polynomial?

$x^{2} + 3x^{7} - 5$ $\displaystyle x^{2} + 3x^{7} - 5$

Possible Answers:

$\displaystyle 7$

$\displaystyle 2$

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 1$

Correct answer:

$\displaystyle 7$

Explanation:

To find the degree of a polynomial, simply find the highest exponent in the expression. As seven is the highest exponent above, it is also the degree of the polynomial.

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Algebra 1 : How to find the degree of a polynomial

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #2 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #3 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

All Algebra 1 Resources

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