Exploring Adding and Subtracting Rational Expressions

What is the first step in adding polynomials?

• Combine unlike terms

• Distribute the negative sign

• Combine like terms

• Write the polynomial in expanded form

What is the result of combining like terms in the polynomial 3x^2 + 11x + 4 - 5x + x^2 - 13?

• 3x^2 + 5x - 8

• 3x^2 + 6x - 9

• 4x^2 + 6x - 9

• 4x^2 + 5x - 9

What does the term 'standard form' imply in polynomial operations?

• Polynomials are expanded completely

• Terms are arranged from highest to lowest degree

• All variables are isolated on one side

• Coefficients are simplified

When subtracting polynomials, what must you distribute across the terms?

• The coefficient

• The highest degree term

• The negative sign

• The constant term

In the expression 8b^2 + ab - 2a^2 - (-10ab + 7a^2 - b^2), what is the correct process for simplification?

• Combine like terms directly without changing signs

• Multiply each term by -1

• Subtract each term directly

• Change the signs of the second polynomial and combine like terms

What is the final step in multiplying polynomials?

• Combine unlike terms

• Distribute each term

• Simplify the constants

• Write the answer in standard form

How do you handle the cubing of the binomial (2c + 5d)?

• Add the binomial to itself three times

• Multiply the binomial by itself three times

• Square the first term and multiply by the second

• None of the above

When multiplying (2x + 1)(4 - 9x - 2x), what method is used?

• Synthetic division

• Long division

• FOIL method

• Factoring

What rule is applied when dividing terms in a polynomial by a monomial?

• Chain rule

• Power rule

• Quotient rule

• Product rule

How do you simplify the division of 20x^3 - 4x^2 - 8x by 4x?

• 5x^2 + x - 2

• 5x^3 - x^2 - 2x

• 5x^2 - x + 2

• 5x^2 - x - 2