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Questions and Answers
What is the degree of the polynomial $3x^2 + 2x - 1$?
What is the degree of the polynomial $3x^2 + 2x - 1$?
- 1
- Not defined
- 3
- 2 (correct)
Which of the following is not a polynomial?
Which of the following is not a polynomial?
- $\frac{1}{x}$ (correct)
- $4x^3 + 2x^2 - x + 5$
- $5x^2 - 3x + 2$
- $2x^{0.5} + 3$
Which of the following is a binomial?
Which of the following is a binomial?
- $4x^2 - 3x + 1$ (correct)
- $6x^4 - 4x^2 + 3$
- $2x^3 - 5x^2 + x - 7$
- $7x^6 + 2x^5 - x^3 + 9$
What is the sum of the degrees of the monomials in the polynomial $3x^2 + 4x - 5$?
What is the sum of the degrees of the monomials in the polynomial $3x^2 + 4x - 5$?
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Study Notes
Degree of a Polynomial
- The degree of a polynomial is the highest power of the variable in the expression.
- For the polynomial (3x^2 + 2x - 1), the highest power is (2), making its degree 2.
Identifying Non-Polynomials
- A polynomial consists of terms with non-negative integer exponents.
- Any expression that includes negative exponents, fractional exponents, or variables in the denominator is not a polynomial.
Definition of a Binomial
- A binomial is a polynomial with exactly two terms.
- Examples of binomials include expressions like (4x + 3) or (x^2 - 5x).
Sum of Degrees of Monomials
- Monomials are terms in a polynomial, which can be single variables or products of variables with coefficients.
- In the polynomial (3x^2 + 4x - 5), the monomials are (3x^2), (4x), and (-5).
- The degrees of these monomials are (2), (1), and (0) respectively.
- The sum of the degrees is (2 + 1 + 0 = 3).
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