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Questions and Answers
What is the degree of the polynomial $3x^4 - 2x^3 + 5x^2 - 7x + 1$?
What is the degree of the polynomial $3x^4 - 2x^3 + 5x^2 - 7x + 1$?
- 6
- 3
- 4 (correct)
- 5
Which term has the highest degree in the polynomial $-2x^6 + 4x^3 - 6x^5 + 9x - 1$?
Which term has the highest degree in the polynomial $-2x^6 + 4x^3 - 6x^5 + 9x - 1$?
- $4x^3$
- $9x$
- $-2x^6$ (correct)
- $-6x^5$
What is the leading coefficient of the polynomial $-7x^3 + 4x^2 - 9x + 2$?
What is the leading coefficient of the polynomial $-7x^3 + 4x^2 - 9x + 2$?
- -7 (correct)
- -9
- 4
- 2
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Study Notes
Polynomial Degrees and Leading Coefficients
- The degree of a polynomial is the highest power of the variable (usually x) in the polynomial.
- To find the degree of a polynomial, identify the term with the highest power of the variable.
- The degree of the polynomial $3x^4 - 2x^3 + 5x^2 - 7x + 1$ is 4, because the highest power of x is 4.
Identifying Terms with Highest Degrees
- In the polynomial $-2x^6 + 4x^3 - 6x^5 + 9x - 1$, the term with the highest degree is $-2x^6$, which has a degree of 6.
- The term with the highest degree is the term with the highest power of the variable.
Leading Coefficients of Polynomials
- The leading coefficient of a polynomial is the coefficient of the term with the highest degree.
- The leading coefficient of the polynomial $-7x^3 + 4x^2 - 9x + 2$ is -7, because the term with the highest degree is $-7x^3$.
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