The degree of a polynomial is the value of the largest exponent of the variable.
For example, consider the polynomial The degree of the polynomial is since this is the value of the largest exponent.
What are the degrees of the following polynomials?
Let's look at each polynomial, one by one.
The polynomial can be written as The two exponents are and and the larger is so the degree of the polynomial is
The polynomial can be written as The only exponent is so the degree of the polynomial is
The polynomial can be written as The exponents are and and the largest is so the degree of the polynomial is
What is the degree of the polynomial $x^7 - 10x^2 - 16?$
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a
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$-10$ |
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b
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$1$ |
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c
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$16$ |
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d
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$10$ |
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e
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$7$ |
The degree of the polynomial $11p^5 - 7p^8 + 3p^2 - 9$ is
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a
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b
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c
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d
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e
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What is the degree of the polynomial $3-6z^6 - 5.5z^5 + \dfrac{z^9}{7} - z?$
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a
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$2$ |
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b
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$9$ |
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c
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$5$ |
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d
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$6$ |
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e
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$7$ |
Let's go back to our polynomial
Note the following definitions:
The term with the largest power of , which is is called the leading term.
The coefficient of the leading term, is called the leading coefficient.
The term is called the constant term because it has no variable.
For some polynomials, the constant term is zero. For example:
What are the leading term, the leading coefficient, and the constant term of the polynomial
The leading term is the term with the largest power of Here, this is
The leading coefficient is the coefficient of the leading term. Here, the leading term is which is equivalent to so the leading coefficient is
The constant term is because it has no variable.
What is the constant term of the polynomial $4x^{6}+2x^3-5x - 10?$
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a
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$2$ |
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b
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$-5$ |
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c
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$4$ |
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d
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$10$ |
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e
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$-10$ |
The leading term of the polynomial $8x^2 - 4x^8 + 3x^5 + 3x - 1$ is
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a
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b
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c
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d
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e
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What is the leading coefficient of the polynomial $3-6t+2t^{4}?$
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a
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$2$ |
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b
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$-6$ |
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c
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$6$ |
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d
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$3$ |
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e
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$4$ |
Each type of polynomial of degree between and has a specific name:
| Degree | Name | Example |
|---|---|---|
| Constant | ||
| Linear | ||
| Quadratic | ||
| Cubic | ||
| Quartic | ||
| Quintic |
Classify the following polynomials according to their respective degrees.
Let's analyze each polynomial individually.
For polynomial I, the degree is Therefore, it is a quadratic polynomial.
For polynomial II, the degree is Therefore, it is a cubic polynomial.
For polynomial III, the degree is Therefore, it is a quartic polynomial.
Classify the polynomial $3x^2-1$ according to its degree.
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a
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Cubic |
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b
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Linear |
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c
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Quintic |
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d
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Quartic |
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e
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Quadratic |
Classify the polynomial $6x^4-2x^2+1$ according to its degree.
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a
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Quintic |
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b
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Cubic |
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c
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Quartic |
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d
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Quadratic |
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e
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Linear |
Which of the following are true regarding the polynomial $2t-12+4t^{3}?$
- It is linear
- Its leading coefficient is $4$
- Its constant term is $12$
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a
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I only |
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b
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II and III only |
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c
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III only |
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d
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II only |
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e
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I and II only |