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SAT Math : How to find the degree of a polynomial

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Example Questions

Example Question #1 : Polynomials

Find the degree of the polynomial:

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

Possible Answers:

$\displaystyle 3$

$\displaystyle 1$

$\displaystyle 5$

$\displaystyle 2$

$\displaystyle 8$

Correct answer:

$\displaystyle 5$

Explanation:

To find the degree of a polynomial we must find the largest exponent in the function.

The degree of the polynomial $x^{3}-3x^{5}+7$ $\displaystyle x^{3}-3x^{5}+7$ is 5, as the largest exponent of $\displaystyle x$ is 5 in the second term.

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Example Question #2 : Polynomials

What is the degree of the polynomial $5x^{2}y^{2}+4y^{3}+3x+10$ $\displaystyle 5x^{2}y^{2}+4y^{3}+3x+10$?

Possible Answers:

$\displaystyle 3$

$\displaystyle 2$

$\displaystyle 5$

$\displaystyle 4$

$\displaystyle 8$

Correct answer:

$\displaystyle 4$

Explanation:

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

$5x^{2}y^{2}$ $\displaystyle 5x^{2}y^{2}$ has a degree of 4 (since both exponents add up to 4), so the polynomial has a degree of 4 as this term has the highest degree.

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Example Question #3 : Polynomials

Find the degree of the following polynomial:

$7xy^{2}z^{3}+8y^{5}-3x^{4}+4$ $\displaystyle 7xy^{2}z^{3}+8y^{5}-3x^{4}+4$

Possible Answers:

$\displaystyle 6$

$\displaystyle 4$

$\displaystyle 5$

$\displaystyle 2$

$\displaystyle 1$

Correct answer:

$\displaystyle 6$

Explanation:

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Even though $8y^{5}$ $\displaystyle 8y^{5}$ has a degree of 5, it is not the highest degree in the polynomial -

$7xy^{2}z^{3}$ $\displaystyle 7xy^{2}z^{3}$ has a degree of 6 (with exponents 1, 2, and 3). Therefore, the degree of the polynomial is 6.

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

Solve each problem and decide which is the best of the choices given.

What is the degree of the following polynomial?

$\displaystyle 3x^4-9x^2+12x^7-9x$

Possible Answers:

$\displaystyle 2$

$\displaystyle 4$

$\displaystyle 1$

$\displaystyle 12$

$\displaystyle 7$

Correct answer:

$\displaystyle 7$

Explanation:

The degree is defined as the largest exponent in the polynomial. In this case, it is $\displaystyle 7$.

$3x^4-9x^2+12x^{\color{Red} 7}-9x$ $\displaystyle 3x^4-9x^2+12x^{\color{Red} 7}-9x$

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Example Question #1 : Polynomials

What is the degree of this polynomial?

$\displaystyle x^2(x^3)^2$

Possible Answers:

Degree 10

Degree 8

Degree 6

Degree 12

Degree 7

Correct answer:

Degree 8

Explanation:

$\displaystyle x^2(x^3)^2$

When an exponent with a power is raised to another power, the value of the power are multiplied.

$x^2(x^{2*3})=x^2(x^6)$ $\displaystyle x^2(x^{2*3})=x^2(x^6)$

When multiplying exponents you add the powers together

$x^{6+2}=x^8$ $\displaystyle x^{6+2}=x^8$

The degree of a polynomial is the determined by the highest power. In this problem the highest power is 8.

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Example Question #2 : Polynomials

Find the degree of the following polynomial: $\displaystyle 12-x^5+18x^3-100x^2+3x^6$

Possible Answers:

$\displaystyle 12$

$\displaystyle 16$

$\displaystyle 0$

$\displaystyle 6$

$\displaystyle 5$

Correct answer:

$\displaystyle 6$

Explanation:

The degree of a polynomial is the largest exponent on one of its variables (for a single variable), or the largest sum of exponents on variables in a single term (for multiple variables).

Here, the term with the largest exponent is 3x^6 $\displaystyle 3x^6$, so the degree of the whole polynomial is 6.

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SAT Math : How to find the degree of a polynomial

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Polynomials

Example Question #2 : Polynomials

Example Question #3 : Polynomials

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

Example Question #1 : Polynomials

Example Question #2 : Polynomials

All SAT Math Resources

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