Simplifying Rational Expressions with Desmos

What is the first step in simplifying a fraction through factoring?

• Combine like terms

• Simplify the constants

• Factor the numerator and denominator

• Identify the LCD

Which of the following is not a step in simplifying fractions?

• Factoring the numerator and denominator

• Canceling out common factors

• Applying the quadratic formula

• Identifying the LCD

Which of the following is true when factoring out the greatest common factors?

• None of the above

• The denominator remains unchanged

• Both the numerator and denominator are factored

• Only the numerator is factored

What is the result of factoring out the greatest common factor in the expression 3x^2 + 21x + 30?

• x(3x + 21 + 30)

• 3(x + 7)(x + 3)

• None of the above

• 3(x^2 + 7x + 10)

What common mistake might occur when using the formula for factoring differences of squares?

• Incorrectly applying the distributive property

• All of the above

• Misidentifying the terms that form perfect squares

• Forgetting to apply the formula

What error is commonly made when factoring the expression x^2 - 25?

• None of the above

• Treating it as a prime expression

• Applying the difference of squares incorrectly

• Factoring it as (x + 5)^2

In factoring by grouping, what should you do after grouping the terms?

• None of the above

• Cancel out all common terms

• Combine all like terms

• Factor out the greatest common factor from each group

When factoring by grouping, what is a crucial step after factoring out from each group?

• Apply the quadratic formula

• Simplify the constants

• Identify the common binomial factor

• Re-group the terms

What should you always do after factoring an expression to ensure accuracy?

• Simplify the constants

• Apply the quadratic formula

• Check your work by re-multiplying the factors

• Combine like terms

What is the importance of double-checking your factored expressions?

• Both A and B

• To practice more problems

• To verify the original expression can be reconstructed

• To ensure all terms are factored correctly