Factoring and Simplifying Expressions

This video tutorial teaches how to simplify rational expressions, which are fractions made up of polynomials. It begins with a basic example of simplifying an integer fraction using prime factorization. The lesson then progresses to simplifying rational expressions by identifying and canceling common factors in the numerator and denominator. The tutorial concludes with advanced techniques for simplifying more complex expressions, emphasizing the importance of factoring.

What is a rational expression?

• A fraction made up of integers

• A fraction or expression with a fraction made up of polynomials

• An integer divided by a polynomial

• A polynomial with no fractions

What is the prime factorization of 42?

• 2 x 3 x 7

• 3 x 14

• 2 x 21

• 6 x 7

Why does 7 divide into 42 to give 6?

• Because 42 is a multiple of 6

• Because 7 is a divisor of 6

• Because 7 is a factor of 42

• Because 42 is a prime number

What is the first step in simplifying a rational expression?

• Factor the numerator and denominator

• Multiply the numerator and denominator

• Add the numerator and denominator

• Subtract the numerator from the denominator

How do you know an expression is factored?

• It has addition and subtraction

• It is written as a product of terms

• It is a single term

• It has no parentheses

What is a common factor in the expression X + 1?

• X - 1

• X

• 1

• X + 1

What happens when you divide a factor by itself?

• You get the numerator

• You get the factor

• You get one

• You get zero

What is the result of simplifying 42/7?

• 8

• 7

• 6

• 5

What is the common factor in the expression X - 5?

• X + 5

• X

• X - 5

• 5

What is the simplified form of 2x + 3 times 1 times 1?

• 2x + 3

• 2x + 6

• 3x + 2

• x + 3