Polynomials and Like Terms Quiz

Polynomials

• A variable is a letter representing an unknown real number (e.g., a, b, c, x, y, z).

• A term is a number or a product of a number and variable(s) raised to a power. (e.g., 5, 2x, 3x², 2xy).

• The coefficient of a term is its numerical factor (e.g., in 5x, the coefficient is 5; in 3x², the coefficient is 3) .

• A constant term is a number on its own (e.g., 5, -1.3).

• A monomial is an algebraic expression with one term (e.g., 3x², 7).

• A binomial is an algebraic expression with two terms (e.g., 2x - 1, x²-2xy).

• A trinomial is an algebraic expression with three terms (e.g., x² - 3x + 4).

• A polynomial is one term or a combination of sums or differences of monomials. (e.g., 3x, 2x - 1, 4x² + y + 2).

• The degree of a term is the sum of the exponents of its variables (e.g., in 5x², the degree is 2).

• The leading term of a polynomial is the term with the highest degree.

• The degree of a polynomial is the same as the degree of its leading term.

Like Terms

• Terms with the same variable raised to exactly the same powers are called like terms.
• Like terms can be added or subtracted.
• Unlike terms cannot be added or subtracted.

Simplifying Polynomials

• Combine like terms to simplify a polynomial.

Adding and Subtracting Polynomials

• Horizontally: Add or subtract like terms.
• Vertically: Arrange like terms in columns and add or subtract.
• Algebra tiles can be used as a visual aid to represent polynomials and their operations.

Multiplying Polynomials

• Multiply monomials by multiplying numerical factors and variables factors.
• Use the distributive property to multiply a polynomial by a monomial.
• Use algebra tiles to multiply polynomials visually.

Dividing Polynomials

• Dividing a polynomial by a constant: divide each term by the constant.
• Dividing a polynomial by a monomial: divide each term of the polynomial by the monomial.
• Use algebra tiles to visualize the division process.