The video tutorial explains how to rewrite rational expressions when there is no common factor, using long division and remainders. It introduces the concept of a + b/c form, emphasizing its importance in understanding fractions and rational expressions. The tutorial provides a detailed example of solving a rational expression with variables using long division, highlighting the process of distributing, subtracting, and identifying remainders. The video concludes with rewriting the expression in a + b/c form, ensuring a comprehensive understanding of the topic.

What is the primary method taught in this lesson for rewriting rational expressions?

• Using substitution

• Using synthetic division

• Using long division

• Using factoring

In the a + b/c form, what does 'a' represent?

• The remainder

• The original denominator

• A whole or complete number

• An unknown variable

How can the fraction 2 and 1/8 be rewritten?

• 8/8 + 8/8 + 1/8

• 2 + 1/8

• 1 + 1 + 1/8

• All of the above

When dealing with rational expressions, what should you remember about the variable 'x'?

• It is always equal to zero

• It represents a known number

• It represents an unknown number

• It is the remainder

What is the first step in rewriting the expression 3x^2 - 4x + 15 over x + 7?

• Multiply by the denominator

• Rewrite the expression

• Add the numerator and denominator

• Factor the expression

What do you multiply 'x' by to get 3x^2 in the example provided?

• 7

• 3x

• x

• 3

Why can't x + 7 equal zero in the example?

• It would make the expression zero

• It would make the expression positive

• It would make the expression undefined

• It would make the expression negative

What is the remainder when dividing 3x^2 - 4x + 15 by x + 7?

• 25

• 190

• 15

• 90

How is the final expression written after completing the long division?

• As a single fraction

• In a + b/c form

• As a product of factors

• As a sum of terms

What is the role of 'b' in the a + b/c form?

• The variable

• The remainder

• The whole number

• The original denominator