Factoring Trinomials and Polynomials: A Comprehensive Overview

This video tutorial covers various factoring techniques in algebra, including factoring the greatest common factor (GCF), factoring by grouping, factoring trinomials, perfect square trinomials, difference of squares, and sums and differences of cubes. It also demonstrates how to solve equations by factoring. Each section provides examples to illustrate the concepts and methods discussed.

What is the greatest common factor (GCF) of the expression 3x + 15?

• 15

• x

• 5

• 3

What is the GCF of 7x and -28?

• x

• 28

• 7x

• 7

When factoring by grouping, what should the common factor of the first two terms also be a factor of?

• The middle term

• None of the above

• The first term

• The last two terms

What is the result of factoring the expression 4x^2 + 8x?

• 2x(x + 4)

• 4x(x + 2)

• 4(x + 2)

• 8x

In a trinomial where the leading coefficient is 1, what must the two numbers found multiply to?

• None of the above

• The leading coefficient

• The coefficient of the x term

• The constant term

Which of the following is a perfect square trinomial?

• x^2 - x - 1

• x^2 + 6x + 9

• x^2 + 5x + 6

• x^2 + x + 1

What is the factored form of x^2 - 25?

• (x - 5)^2

• (x + 5)(x - 5)

• x + 5

• x - 5

How do you factor the difference of squares, a^2 - b^2?

• (a - b)^2

• (a + b)(a - b)

• a^2 - 2ab + b^2

• (a + b)^2

What is the formula for factoring the sum of cubes, a^3 + b^3?

• a + b (a^2 - ab + b^2)

• a - b (a^2 + ab + b^2)

• a + b (a^2 + ab + b^2)

• (a + b)^3

What is the factored form of x^3 + 8?

• x + 2

• (x + 2)(x^2 - 2x + 4)

• x^3 + 2^3

• (x + 2)^3