Rational Expressions and Factoring Concepts

The video tutorial explains how to add and subtract rational expressions by ensuring a common denominator. It demonstrates the process of adding numerators while keeping the denominator constant, and emphasizes the importance of simplifying expressions by factoring. The tutorial also covers subtracting rational expressions, rearranging terms, and factoring trinomials. The video concludes with a summary of the methods and simplification techniques discussed.

What is necessary to add or subtract rational expressions?

• Different denominators

• Different numerators

• Common numerators

• Common denominators

When adding rational expressions with like denominators, what do you do with the numerators?

• Add them

• Multiply them

• Subtract them

• Divide them

Why can't you simplify across addition or subtraction in rational expressions?

• Because it violates the rules of arithmetic

• Because it changes the numerator

• Because it requires factoring first

• Because it changes the denominator

What is the first step in factoring a polynomial?

• Multiply the terms

• Divide by the smallest term

• Find the greatest common factor

• Add the terms

What is the result of factoring out the greatest common factor from 8x + 4?

• 4x + 1

• 8x + 4

• 2x + 1

• 4x + 2

When subtracting rational expressions, why is it easier to factor with a positive leading coefficient?

• It simplifies the denominator

• It changes the expression to addition

• It makes the expression longer

• It simplifies the factoring process

What are the factors of x^2 - 3x - 28?

• (x + 7)(x - 4)

• (x - 4)(x + 7)

• (x - 7)(x + 4)

• (x + 4)(x + 7)

What happens when you divide a common factor from both the numerator and denominator?

• The expression becomes undefined

• The expression remains the same

• The expression doubles

• The common factor cancels out

How can the expression -1(x - 7) be rewritten?

• x + 7

• -x + 7

• -x - 7

• x - 7

Which of the following is equivalent to -x + 7?

• -7 + x

• 7 - x

• -7 - x

• 7 + x