Exploring Operations with Rational Expressions

What is the initial algebraic expression given in the problem?

• 6x^2 + 5x / 3x + 1

• 3x^2 + 5x / 6x + 1

• 5x^2 + 6x / 1x + 3

• 1x^2 + 3x / 5x + 6

What is the first step in algebraic long division?

• Determine how many times the divisor goes into the leading term of the dividend

• Divide the constant term by the leading coefficient

• Multiply the divisor by the quotient

• Subtract the product from the dividend

What is the result of multiplying 2x by (3x + 1)?

• 5x^2 + 2x

• 6x^2 + 2x

• 5x^2 + 3x

• 6x^2 + 3x

After subtracting, what is the new term in the dividend?

• 1x

• 2x

• 3x

• 4x

What is the remainder after completing the division?

• 0

• 1

• -1

• -2

What is the final expression obtained after algebraic long division?

• 2x + 1 - 1/(3x + 1)

• 2x - 1/(3x + 1)

• 2x + 1/(3x + 1)

• 2x - 1 + 1/(3x + 1)

Which value is used for substitution to check the expressions?

• 1

• 3

• 0

• 2

What is the result of the expression when x=2?

• 24/7

• 27/7

• 35/7

• 34/7

Which expression matches the value 34/7 when x=2?

• 2x - 1/(3x + 1)

• 2x - 1 + 1/(3x + 1)

• 2x + 1/(3x + 1)

• 2x + 1 - 1/(3x + 1)

Why is it useful to use algebraic long division in this context?

• To calculate the discriminant of the polynomial

• To find the exact quotient and remainder

• To simplify the expression for graphing

• To determine the degree of the polynomial