Factoring and Classifying Polynomials

The video tutorial covers the basics of polynomials, including definitions, classifications, and operations such as addition, subtraction, multiplication, and factoring. It explains how to write polynomials in standard form, identify degrees and leading coefficients, and classify them by the number of terms. The tutorial also demonstrates techniques for adding, subtracting, and multiplying polynomials using methods like FOIL and the box method, as well as factoring using the greatest common factor and grouping.

What is a term in the context of polynomials?

• A variable with a negative exponent

• A constant number only

• A variable number or product of variables and numbers with whole number exponents

• A number or variable with a fractional exponent

Which of the following is a coefficient?

• The variable in a term

• The exponent in a term

• The sum of the exponents in a term

• The number in front of a variable

How is the degree of a monomial determined?

• By the number of variables in the term

• By the sum of the exponents of the variables

• By the coefficient of the term

• By the constant term

What is the standard form of a polynomial?

• When terms are arranged in alphabetical order

• When terms are arranged from least to greatest exponent

• When terms are arranged from greatest to least exponent

• When terms are arranged by the size of their coefficients

What do you call a polynomial with a degree of 2?

• Quadratic polynomial

• Constant polynomial

• Linear polynomial

• Cubic polynomial

How do you classify a polynomial with three terms?

• Binomial

• Quadrinomial

• Trinomial

• Monomial

What is the leading coefficient of a polynomial in standard form?

• The sum of all coefficients

• The smallest coefficient in the polynomial

• The coefficient of the term with the lowest degree

• The coefficient of the first term when arranged in standard form

When adding polynomials, what must be true for terms to be combined?

• They must be in standard form

• They must have the same variable and exponent

• They must have the same coefficient

• They must have the same degree

What is the result of subtracting 5x² + 2x - 11 from 3x² + 8x - 7?

• 2x² + 6x - 18

• -8x² - 10x + 18

• -2x² + 6x + 4

• 8x² + 10x - 18

Which method is NOT used for multiplying polynomials?

• Subtraction method

• Distributive property

• Box method

• FOIL method