Factoring and Distributing Polynomials

The video tutorial introduces the concept of factoring polynomials, explaining it as the process of breaking down polynomials into the product of smaller factors. It contrasts this with multiplication, using the distributive principle and examples of multiplying binomials. The focus then shifts to factoring, with a promise of examples to follow.

What is the primary goal of factoring polynomials?

• To add polynomials together

• To break down polynomials into smaller factors

• To divide polynomials by constants

• To convert polynomials into equations

Which mathematical principle is used to multiply expressions like 3xy(x + 7y - 5)?

• Distributive Principle

• Identity Principle

• Associative Principle

• Commutative Principle

What is the result of distributing 3xy across the expression (x + 7y - 5)?

• 3x^2y + 21xy - 15xy^2

• 3x^2y + 21xy^2 - 15xy

• 3x^2y + 21xy^2 + 15xy

• 3xy + 21xy - 15xy

When distributing pairs of binomials, what is the result of x times x?

• x

• x^2

• 2x

• x^3

What is the simplified form of the trinomial x^2 + 7x + 12?

• (x + 3)(x + 4)

• (x + 2)(x + 6)

• (x + 1)(x + 12)

• (x + 5)(x + 2)

What is the reverse process of multiplying polynomials?

• Adding

• Subtracting

• Factoring

• Dividing