Factoring and Integer Operations

The video tutorial explains how to factor two trinomials using the shortcut method for trinomials in the form x^2 + bx + c. It emphasizes the importance of factoring out the greatest common factor first. The first example involves factoring a trinomial with a positive leading coefficient, while the second example deals with a trinomial where the leading coefficient is negative. The tutorial provides a detailed walkthrough of finding integers whose product and sum match the constant and linear coefficients, respectively, to achieve the factored form.

What is the first step in any factoring problem?

• List all possible integer pairs

• Identify the leading coefficient

• Factor out the greatest common factor

• Find the product of the constant term

What is the greatest common factor of the first trinomial?

• 4

• 6

• 2

• 8

Which pair of integers has a product of 48 and a sum of 14?

• 3 and 16

• 6 and 8

• 2 and 24

• 4 and 12

What is the factored form of x^2 + 14x + 48?

• (x + 2)(x + 24)

• (x + 6)(x + 8)

• (x + 4)(x + 12)

• (x + 3)(x + 16)

Why do we factor out negative y instead of positive y in the second trinomial?

• To change the sign of the middle term

• To ensure the leading coefficient is positive

• To make the constant term positive

• To simplify the trinomial

What is the greatest common factor of the second trinomial?

• y

• -y^2

• -y

• y^2

Which pair of integers has a product of 30 and a sum of -17?

• -5 and -6

• -1 and -30

• -2 and -15

• -3 and -10

What is the factored form of y^2 - 17y + 30?

• (y - 1)(y - 30)

• (y - 5)(y - 6)

• (y - 2)(y - 15)

• (y - 3)(y - 10)

What is the product of the integers -2 and -15?

• -17

• 17

• -30

• 30

What is the sum of the integers -2 and -15?

• -17

• 17

• -30

• 30