Dividing Polynomials Using Long Division

What is the initial polynomial given in the problem statement?

• 3x^4 - 12x + 5

• 3x^3 - 12x + 5

• 3x^4 - 12x^2 + 5

• 3x^4 - 12x + 10

Why do we add zero coefficients for missing terms in the polynomial?

• To simplify the division process

• To make the polynomial look longer

• To ensure all terms are accounted for in descending order

• To confuse the students

What is the first step in the long division process?

• Multiply

• Bring down

• Divide

• Subtract

After dividing the leading term, what is the next step in the long division process?

• Multiply

• Subtract

• Bring down

• Add

What happens to the signs of the terms when you subtract in polynomial long division?

• They become positive

• They remain the same

• They become negative

• They switch to the opposite sign

What is the purpose of enclosing terms in parentheses during subtraction?

• To ensure correct sign changes

• To separate terms

• To make it look neat

• To add complexity

What is the result of dividing -15x by x?

• 15

• -1

• -15

• 0

What is the remainder when 3x^4 - 12x + 5 is divided by X + 1?

• 0

• 5

• 20

• 15

What is the quotient obtained from the division of 3x^4 - 12x + 5 by X + 1?

• 3x^3 + 3x^2 - 3x - 15

• 3x^3 - 3x^2 + 3x - 15

• 3x^3 - 3x^2 + 3x + 15

• 3x^3 - 3x^2 - 3x + 15

What is the final step in the long division process?

• Check the remainder

• Divide

• Multiply

• Subtract