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?
- 3x
- 10
- 3/x (correct)
- -17x¹⁰
- √x (correct)
- 5x² - 2x + 7
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?
What is the constant term in the polynomial 5x² - 6x - 2?
What is the constant term in the polynomial 5x² - 6x - 2?
What is the numerical coefficient of the term -5x³?
What is the numerical coefficient of the term -5x³?
What is the degree of the polynomial -6x⁴ - 2x³ + 7?
What is the degree of the polynomial -6x⁴ - 2x³ + 7?
Which of the following is a binomial?
Which of the following is a binomial?
What are equivalent polynomials?
What are equivalent polynomials?
Flashcards
Polynomial
Polynomial
A mathematical expression consisting of one or more terms, where each term is a product of constants, variables, and whole-number exponents.
Constant term
Constant term
A term in a polynomial without any variables.
Numerical Coefficient
Numerical Coefficient
The numerical factor that multiplies the variable in a term.
Degree of a polynomial
Degree of a polynomial
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Term in a polynomial
Term in a polynomial
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Equivalent polynomials
Equivalent polynomials
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Modeling polynomials with tiles
Modeling polynomials with tiles
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X squared tile (x²)
X squared tile (x²)
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X tile (x)
X tile (x)
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Unit tile (1)
Unit tile (1)
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Model a polynomial using tiles
Model a polynomial using tiles
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Name the polynomial represented by tiles
Name the polynomial represented by tiles
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Represent a polynomial with tiles using zero pairs
Represent a polynomial with tiles using zero pairs
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Standard form of a polynomial
Standard form of a polynomial
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Constant term of a polynomial
Constant term of a polynomial
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Degree of a term
Degree of a term
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Coefficient of a polynomial
Coefficient of a polynomial
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Degree of a polynomial
Degree of a polynomial
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Monomial
Monomial
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Binomial
Binomial
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Trinomial
Trinomial
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Linear polynomial
Linear polynomial
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Quadratic polynomial
Quadratic polynomial
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Cubic polynomial
Cubic polynomial
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Constant polynomial
Constant polynomial
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Zero polynomial
Zero polynomial
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Adding polynomials
Adding polynomials
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Subtracting polynomials
Subtracting polynomials
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Multiplying polynomials
Multiplying 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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