Dividing Polynomials

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Multiple Choice

Which law of exponents is used to simplify the expression y^{12} ÷ y^{7}?

• Product rule

• Power rule

• Quotient rule

• Zero exponent rule

Open Ended

Explain how the quotient rule for exponents is applied when dividing monomials, using the example b^5 / b^2.

Multiple Choice

Which of the following is the correct simplification of 20x^{10} ÷ 2x^{5}?

• 10x^{15}

• 10x^{5}

• 18x^{5}

• 22x^{2}

Fill in the Blank

Fill in the blank: When dividing polynomials, you should divide both numerical coefficients and apply the laws of ___ to simplify the literal coefficients.

Multiple Select

Which of the following are correct steps when dividing each term of a polynomial by a monomial?

• Divide the coefficients of each term by the monomial's coefficient

• Subtract the exponents of like variables

• Multiply the exponents of like variables

• Add the coefficients of each term to the monomial's coefficient

Multiple Choice

When dividing the polynomial (20x^3 + 10x^2 + 8x - 12) by 2, what is the first term of the quotient?

• 10x^3

• +5x^2

• +4x

• -6

Open Ended

Explain how the process of long division for whole numbers (as shown in the first image) is similar to the process for dividing polynomials (as shown in the later images).

Multiple Choice

What is the correct order of steps when performing long division, as shown in the examples?

• Divide, Multiply, Subtract, Bring down, Repeat

• Multiply, Divide, Subtract, Bring down, Repeat

• Divide, Subtract, Multiply, Bring down, Repeat

• Divide, Multiply, Bring down, Subtract, Repeat

Multiple Select

Which of the following are true about the result of dividing (x^2 + 5x + 6) by (x + 2)?

• The quotient is x + 3

• There is no remainder

• The divisor is x + 3

• The dividend is x^2 + 5x + 6

Open Ended

Describe how you would handle a remainder when dividing polynomials, as shown in the example (2x^2 - 6x - 10) ÷ (x + 2).

Fill in the Blank

When a term is missing in a polynomial during division, we use ___ as a coefficient for the missing term.