Synthetic Division of Polynomials

Mrs. Fry explains how to use placeholders in polynomial division, specifically when dividing a larger polynomial by a binomial. She demonstrates setting up a synthetic division problem by inserting zeros for missing terms and follows a pattern of multiplying and adding to find the remainder. The final answer is written with one less degree than the original polynomial, and the remainder is expressed as a fraction.

Why is it necessary to use placeholders when dividing polynomials?

• To avoid using synthetic division

• To make the division faster

• To ensure all terms are accounted for

• To simplify the polynomial

What is the polynomial structure of x^4 + 9 when placeholders are used?

• x^4 + x^3 + x^2 + x + 9

• x^4 + 9

• x^4 + 9x^3 + 9x^2 + 9x + 9

• x^4 + 0x^3 + 0x^2 + 0x + 9

What is the first step in setting up a synthetic division problem?

• Identify the divisor and set it equal to zero

• Write the polynomial in descending order

• Add all coefficients

• Multiply all terms by the divisor

What value is placed outside the synthetic division box for the divisor x + 3?

• 3

• -3

• 0

• 1

In synthetic division, what operation is performed after multiplying the outside number with the first coefficient?

• Square

• Add

• Divide

• Subtract

What is the result of multiplying -3 by 1 in the synthetic division process?

• -3

• 1

• 3

• 0

What is the next step after writing the result of the multiplication under the first zero in synthetic division?

• Multiply again

• Add the result to the zero

• Subtract the result from the zero

• Divide the result by the zero

What is the final remainder when dividing x^4 + 9 by x + 3 using synthetic division?

• 27

• 92

• 90

• 81

How is the remainder expressed in the final answer of a synthetic division problem?

• As a fraction over the divisor

• As a decimal

• As a percentage

• As a whole number

What is the degree of the resulting polynomial after dividing x^4 + 9 by x + 3?

• 4

• 3

• 2

• 1