Exploring Algebraic Expressions and Polynomials

This video tutorial covers algebraic expressions, focusing on radicals and polynomials. It begins with an introduction to algebraic expressions, emphasizing the absence of equal signs. The tutorial then explains how to simplify radicals using prime factorization, specifically the 'birthday cake' method. It demonstrates operations with radicals, including addition, subtraction, and multiplication, ensuring like terms are used. The video transitions to polynomials, detailing their classification by degree and number of terms. It covers operations such as addition, subtraction, and multiplication of polynomials, using examples to illustrate each concept.

What distinguishes an algebraic expression from an equation?

• An expression contains an equal sign.

• An expression cannot contain variables.

• An expression does not contain an equal sign.

• An expression must contain an inequality symbol.

What is the first step in simplifying a radical using the 'birthday cake' method?

• Multiply the number by itself.

• Divide the number by its smallest prime factor.

• Perform prime factorization of the number.

• Find the square root of the number.

How do you simplify the square root of 40 using prime factorization?

• 5 square roots of 8

• 10 square roots of 4

• 2 square roots of 10

• 4 square roots of 5

What is necessary to add or subtract radicals?

• They must have the same radicand.

• They must have the same coefficient.

• They must have different radicands.

• They must be cube roots.

How do you multiply the square root of 10 by the square root of 2?

• Square root of 12

• 5 square roots of 4

• Square root of 20

• 2 square roots of 5

What is the degree of a polynomial that classifies it as quadratic?

• Degree 1

• Degree 2

• Degree 4

• Degree 3

What do you call a polynomial with three terms?

• Trinomial

• Monomial

• Polynomial

• Binomial

How do you classify a polynomial with a highest variable exponent of 1?

• Quadratic

• Cubic

• Linear

• Quartic

What is the result of subtracting polynomials 5x^2 - 6 and -5x - 6?

• 10x^2 - 12

• x^2 - 11x

• x^2 + 2x - 12

• 9x^2 + 2x - 12

When multiplying binomials using the area model, what is the first step?

• Combine like terms

• Multiply the coefficients by the variables

• Write one binomial down the side and the other across the top

• Add the coefficients