Notes: Dividing Polynomials

Open Ended

What is the significance of being able to divide polynomials by monomials in algebra?

Multiple Choice

Which of the following is a prerequisite concept needed to divide a polynomial by a monomial?

• Understanding how to add polynomials

• Knowing how to multiply exponents

• Factoring quadratic equations

• Solving linear equations

Multiple Choice

Which of the following is the correct first step when dividing polynomials using long division?

• Write the dividend in standard form, including terms with a coefficient of 0.

• Divide as you would with numbers.

• Write the final answer.

• Multiply the divisor by the first term of the dividend.

Multiple Select

Which of the following are necessary steps when performing synthetic division?

• Write the coefficients of the dividend.

• Multiply the first coefficient by the divisor and add to the next coefficient.

• Write the remainder as the boxed number.

• Divide the divisor into each term of the dividend.

Open Ended

Explain the difference between long division and synthetic division when dividing polynomials.

Fill in the Blanks

Fill in the blank: In synthetic division, the value written in the upper left corner is the value of

for the divisor (x - a).

Multiple Choice

What must be true about the divisor for synthetic division to be used?

• It must be a linear binomial in the form (x - a).

• It must be a quadratic binomial.

• It must have a leading coefficient of 1.

• It must be a constant.

Multiple Choice

Given the polynomial (5x^3 - 13x^2 + 10x - 8) and the divisor (x - 2), what is the degree of the first term in the quotient when using synthetic division?

• 2

• 3

• 1

• 0

Fill in the Blanks

Dividing polynomials by a monomial can be simplified by

each term of the polynomial by the monomial.

Open Ended

What is one thing you learned today about dividing polynomials by a monomial?

Open Ended

Divide (3x^4 - x^3 + 5x - 1) by (x + 2) using synthetic division.