Simplify a rational expression

The video tutorial explains the process of factoring rational expressions. It begins with identifying the greatest common factor (GCF) in the denominator and extracting common factors from the numerator. The instructor demonstrates factoring by inspection, focusing on finding values that multiply and add to specific numbers. The tutorial continues with factoring the denominator and simplifying the expression by canceling out common terms, resulting in a simplified rational expression.

What is the first step in factoring a polynomial expression?

• Multiply all terms by 2

• Divide the expression by the highest degree term

• Add all coefficients together

• Identify the greatest common factor (GCF) and factor it out

When factoring by inspection, what should you look for in the terms of a trinomial?

• Two numbers that multiply to the constant term and add to the linear coefficient

• Two numbers that add to the constant term and multiply to the linear coefficient

• Two numbers that add to the quadratic coefficient and multiply to the constant term

• Two numbers that multiply to the linear coefficient and add to the constant term

Which of the following is the factored form of X^2 + X - 2?

• (X + 2)(X - 1)

• (X - 1)(X + 2)

• (X - 2)(X + 1)

• (X + 1)(X - 2)

What is the factored form of X^2 - 5X - 14?

• (X - 7)(X + 2)

• (X + 7)(X - 2)

• (X - 2)(X + 7)

• (X + 2)(X - 7)

After canceling out common factors, what is the simplified form of the expression 2(X - 1) / (X - 7)?

• 2(X - 1) / (X - 7)

• 2(X + 1) / (X - 7)

• 2(X + 1) / (X + 7)

• 2(X - 1) / (X + 7)