Factoring Quadratic Expressions and Trinomials

The video tutorial covers various techniques for factoring quadratic expressions. It begins with an introduction to the importance of identifying the right technique for factoring. The instructor provides three examples: factoring 6x^2 + 3x by finding common factors, factoring 4x^2 - 4x - 48 using the sum-product method, and recognizing perfect squares in 3x^2 + 10x + 25. The video emphasizes the importance of checking for common factors first and using the sum-product method for quadratics with a leading coefficient of one.

What is the first step in factoring the quadratic expression 6x^2 + 3x?

• Identify the sum-product pair

• Complete the square

• Use the quadratic formula

• Factor out the common factor

When factoring 4x^2 - 4x - 48, what common factor is first identified?

• x

• 8

• 4

• 2

In the expression x^2 - x - 2, what two numbers add up to -1 and multiply to -2?

• 1 and -2

• 2 and -1

• -1 and 2

• -3 and 1

Which method is used to factor x^2 - x - 2 after factoring out the common factor?

• Graphing

• Completing the square

• Sum-product method

• Quadratic formula

What is the result of factoring 3x^2 + 10x + 25 using the sum-product method?

• (x + 4)(x + 6)

• (x + 2)(x + 8)

• (x + 3)(x + 7)

• (x + 5)(x + 5)

Which of the following is a perfect square trinomial?

• x^2 + 5x + 6

• x^2 + 4x + 4

• x^2 + 3x + 2

• x^2 + 2x + 1

What is the common factor in the expression 3x^2 + 30x + 75?

• 3

• 5

• 10

• 15

How can you recognize a perfect square trinomial?

• All terms are even numbers

• The first term is a perfect square

• The middle term is twice the product of the square roots of the first and last terms

• The constant term is a perfect square

What is the sum of the numbers that factor the expression x^2 + 10x + 25?

• 20

• 5

• 10

• 15

What is the product of the numbers that factor the expression x^2 + 10x + 25?

• 100

• 50

• 25

• 10