Simplifying a rational expression with a trinomial

The video tutorial covers advanced factoring techniques for trinomials, focusing on simplifying expressions by factoring the numerator and denominator separately. The instructor provides two examples, one detailed and one quicker, to demonstrate the process. Key concepts include identifying factors, understanding restrictions, and simplifying expressions. The tutorial emphasizes the importance of practice in mastering these techniques.

What is the first step in simplifying a fraction with trinomials in the numerator and denominator?

• Combine the numerator and denominator

• Factor the numerator and denominator separately

• Add the coefficients of the trinomials

• Multiply the trinomials together

When factoring a trinomial using mental math, what should you consider about the numbers?

• They should be prime numbers

• They should multiply to give the constant term and add to give the middle term

• They should be even numbers

• They should be greater than zero

In the example discussed, what are the factors of the trinomial that multiply to give -6 and add to give 5?

• X - 6 and X + 1

• X - 2 and X + 3

• X + 6 and X - 1

• X + 2 and X - 3

What is a restriction in the context of a factored polynomial?

• A value that makes the polynomial greater than one

• A value that makes the polynomial equal to zero

• A value that makes the polynomial negative

• A value that makes the polynomial positive

Which terms can be divided out in the final expression of the example?

• X - 2

• X - 1

• X + 6

• X + 1