This document provides instructions for dividing polynomials using synthetic division. It explains the steps to arrange the coefficients of the polynomials being divided and to systematically multiply and add the terms. The key steps are to arrange the coefficients in descending order, multiply the divisor by the leading coefficient and add it to the next term, and repeat until the remainder is obtained. Examples are provided to demonstrate the process. The document also discusses the remainder theorem and factor theorem.

1. Division of
Polynomials
using
Synthetic
Division
MATHEMATICS 10 –
QUARTER 1

2. ‘Writing Persuasive Essays’
Write a persuasive essay using
effective arguments and
supporting evidence.

3. Write each polynomial in descending order of x
and give its degree.
1. x3 + x2 – 22x - 25x5 + 2
2. 4x2 + 21x5 - 26x3 + 28x - 10 + 5x4
3. 6 – 31x + 3x3 – 2x4
4. x3 + 7x2 + 5x4 – 25x +5
5. x3 + 7x2 + 5 – 25x + 5x5

4. Give the numerical coefficient of each
polynomial in descending order of x.
1. x3 + x2 – 22x - 25x5 + 2
2. 4x2 + 21x5 - 26x3 + 28x - 10 + 5x4
3. 6 – 31x + 3x3 – 2x4
4. x3 + 7x2 + 5x4 – 25x +5
5. x3 + 7x2 + 5 – 25x + 5x5

5. Think about
this.
1. What are the steps to divide polynomial by
another polynomial using synthetic division?
2. Why do you have to change the sign of the
constant of the divisor?
3. Which is easier to perform, long division or
synthetic division? Explain briefly your answer.

6. To divide polynomial P(x) by another
polynomial D(x) in the form (x – a) using
synthetic division
1. Arrange on the line the coefficients of the polynomial
(order is in descending powers). Insert a zero for the
coefficient of the missing power of x.
2. Write a, the divisor, on the left.
3. Bring down the first coefficient on the third line.
Multiply the first coefficient by a. Write the product
on the second line below the second coefficient.

7. To divide polynomial P(x) by another
polynomial D(x) in the form (x – a) using
synthetic division
4. Find the sum of the product and the second coefficient then write the
sum on the third line below the product.
5. Multiply this sum by a, add the product to the next coefficient and
write again the new sum on the third line, and so on.
6. Do the same process until a product has been added to the final
coefficient.
7. The last sum in the third line is the remainder. The preceding
numbers are the numerical coefficient of the quotient. The quotient is
a polynomial of degree one less than the degree of P(x).

8. Do the following with a partner!
1.(x3 + 7x2 + 15x + 14) ÷ (x + 3)
2.(3x3 - 7x2 + x - 7) ÷ (x - 3)
3.(x3 + 8x2 – 5x - 84) ÷ (x + 5)
4.(2x4 + x3 - 9x2 - x + 6) ÷ (x + 2)

9. Guess
Who?
• Divide using synthetic division.
• Each problem was given a corresponding box below. The remainder of these
problems are found in column B. Write the corresponding letter in the box provided
for the question

10. Study:
Remainder Theorem and Factor
theorem.
1. What is the remainder
theorem?
2. What is the factor theorem?