Podcast
Questions and Answers
What is a polynomial?
What is a polynomial?
A polynomial is an expression consisting of one term or the sum of terms, whose variables have whole-number exponents.
Which of the following is not a polynomial?
Which of the following is not a polynomial?
Polynomials can have a square root in the power of the variable.
Polynomials can have a square root in the power of the variable.
False (B)
What is a term in a polynomial?
What is a term in a polynomial?
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What is the constant term in the polynomial 5x² - 6x - 2?
What is the constant term in the polynomial 5x² - 6x - 2?
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What is the numerical coefficient of the term -5x³?
What is the numerical coefficient of the term -5x³?
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What is the degree of the polynomial -6x⁴ - 2x³ + 7?
What is the degree of the polynomial -6x⁴ - 2x³ + 7?
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Which of the following is a binomial?
Which of the following is a binomial?
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What are equivalent polynomials?
What are equivalent polynomials?
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Study Notes
Polynomials
- Polynomials are expressions consisting of variables and coefficients.
- A polynomial is one term or the sum of terms.
- Variables in polynomials have whole-number exponents.
- Examples include: 3x, 5x²-2x+7, 10, -17x¹⁰
Terms
- A term is a number, variable, or a product of numbers and variables.
- Examples include: 3x, 5x-3, 6x²+7x+3.
- 3x = 1 term, 5x-3 = 2 terms, 6x²+7x+3 = 3 terms.
Constants
- A constant is a term without a variable.
- Examples include: 5, -2, 0
Numerical Coefficient
- The numerical coefficient is the number multiplied by the variable.
- Examples include: in 3x, the coefficient is 3; in -5x²+6x, the coefficients are -5 and 6; in -7x²+4, the coefficient is -7.
Degree
- The degree of a polynomial is the highest power of the variable.
- Examples include: in 3x, the degree is 1; in 5x²-6x, the degree is 2; in -6x⁴-2x³, the degree is 4.
Types of Polynomials
- Monomial: 1 term (e.g., 3x)
- Binomial: 2 terms (e.g., 5x-6)
- Trinomial: 3 terms (e.g., 6x²-4x+7)
Equivalent Polynomials
- Equivalent polynomials have the same value, even if the terms are in a different order.
- Examples are 3x²-5x+7 and -5x+3x²+7 or 5x-4x+6 and x+6.
Polynomial Modelling with Tiles
- Tiles represent parts of terms in expressions.
- Square tiles = x²
- Rectangle tiles = x
- Small Square tiles = -1 or constant term.
- Negative tiles are represented by black color.
- Positive tiles are represented by white color
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Description
This quiz covers the fundamentals of polynomials, including definitions of terms, constants, numerical coefficients, and degrees. You will also learn about different types of polynomials such as monomials and binomials. Test your knowledge and understanding of these essential algebraic concepts.
