Factor a Trinomial by First Factoring Out a Negative

The video tutorial explains how to factor a trinomial into its component factors. It begins by introducing the concept of factoring and demonstrates factoring out a negative one from the terms. The instructor then uses the diamond method to find two numbers that multiply to the constant term and add to the linear coefficient. The process involves identifying factor pairs and ensuring one factor is negative to achieve the correct sum. The tutorial concludes by verifying the factors and writing the trinomial as a product of its factors.

What is the first step in factoring a trinomial when the leading coefficient is negative?

• Divide all terms by the leading coefficient

• Multiply all terms by two

• Factor out a negative one from all terms

• Add a positive constant to all terms

In the diamond method, what do you need to find two numbers that do what?

• Multiply to give the constant term and add to give the linear coefficient

• Multiply to give the linear coefficient and add to give the constant term

• Add to give the constant term and subtract to give the linear coefficient

• Multiply to give the leading coefficient and add to give the constant term

Which pair of numbers correctly multiplies to -20 and adds to -1?

• -5 and 4

• 5 and -4

• -10 and 2

• 10 and -2

What is the final factored form of the trinomial x^2 - x - 20?

• (x - 5)(x + 4)

• (x + 5)(x - 4)

• (x + 4)(x - 5)

• (x - 4)(x + 5)

Why is it necessary to check the multiplication and addition of the chosen factors?

• To ensure they are both positive

• To verify they satisfy the original trinomial conditions

• To confirm they are the smallest possible numbers

• To make sure they are both negative