TLP 4 Division of Polynomials Using Long Division



Dapdap Street, Poblacion 3 Carcar City, Cebu
Telephone Number: 487-8927
A Teaching- Learning Package in Mathematics 10
Teacher: Maryland V. Pasilan

Method: Deductive Method
TLP 4: Division of Polynomials using long division

Objectives: Through the discussion and examples, the student will be able to:
1. perform division of polynomial using long division.
A. ACTIVATION
Looking Back
From the given statement below, check all appropriate sentences that can be deducted.
The expression 5x2 + 3x – 1 is a polynomial.
____ A polynomial is an algebraic expression.
____ A polynomial contains specific number of terms.
____ Each term of a polynomial is of the form axn where a is a real number, and n is a whole number.
____ Every term of a polynomial has a variable.
____ All the terms of a polynomial contains an exponent.
From the checked sentences, formulate a working definition for the word polynomial.
Based on the given definition, determine whether each algebraic expression is a polynomial or not.
a. 3 x 2+ x −1 (1) _________________________________ b. −10+ x−3 x 2−x 5 (2)
__________________________
c. √ 3 x7 + x 4 −3 x 2+ 4 (3) _________________________
1
d. 2 x 2+ x 2−3 x +5 x 2 (4) _________________________
Now, polynomials has different types, what are the different types of polynomials?
As you recall the in your previous lesson about polynomials, do you remember how to add, subtract or
multiply?
So, let us try these few examples.(In your notebook, try to perform the following)
a. Find the sum : ( 3 x 3+ 2 x 2−5 x +1 )+( 4 x 3−5 x 2−3 ) =
b. Find the difference: ( z 3−2 z 2+ 3 z−7 )−(2 z 3+5 z 2−4 z+ 3) =
c. Find the products: (3 x−5)(2 x+3) =
How was answering it?

Did it help you to recall how to perform operations of polynomials?
B. BUILDING – UP
It is easy to divide a monomial (has _________ term) by monomial or polynomial by a monomial. But how
about a polynomial by binomial (has ______ term(s) or a polynomial by polynomial. In dividing a polynomial
by polynomial, we can use a long division or synthetic division.
Let us have some examples
Example 1:
5
36 x 36 5−2
a. 2 =
x =4 x 3
9x 9
3 5 6 3 5 6
6 y −12 y −10 y 6 y 12 y 10 y 2 4
b. 2 = 2
− 2
− 2
=3 y−6 y −5 y
2y 2y 2y 2y
c. (-2x+3x2-4) ÷ (x-3)
Solution:
The process to be illustrated is referred to as long division.
Step 1.
Rewrite the given division problem in the form
With the terms of the divisor and dividend arranged according to the
descending powers of the variable.
Note: If there is no value for the next term according to the powers, just write zero. For example ,
3x5+2x2+x+2, as you can see there is no variables for x3 and x4 just write 0 (zero) for these two. So, if we
will arrange it, it will be 3x5+0x4+0x3+2x2+x+2.
Step 2.
Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
Step 3.
Multiply the quotients in step 2 by the divisor.
Step 4.
Subtract the product in step 3 from the dividend.
Step 5.
Repeat steps 1-4 with the difference obtained in step 4 as the new dividend, until the degree of the
remainder is less than the degree of the divisor.
Step 6.
Write the result in the form
P(x) = Q(x) • D(x) + R(x).
-2x+3x2-4 = (3x+7)(x-3) + 17
Example 2
Divide 3x2-4x+5 by x+2.
Solution:
Dividing polynomials is like dividing integers. Recall that the dividend is equal to the product of the
quotient and divisor, plus the remainder. In symbols:
Example 3
(2x4+3x3-4x-16) ÷ (x+2)
Solution:
Insert 0 for the missing term.
Thus, 2x4+3x3-4x-16 = (2x3-x2+2x-8)(x+2)
Example 4
Divide 2x3+4x-10 by x-1. Express your answer in the form P(x) = Q(x) • D(x) + R(x).
Solution:
Thus, 2x3+4x-10 = (2x2+2x+6) (x-1) – 4
Dividing a polynomial by another polynomial is just the same as you divide polynomial by a linear
polynomial. The dividend and the divisor must be arranged in descending order of terms.
Example 5
Divide P(x) = 3x5-8x4-x3-3x2-10x+3 by D(x) = x2-2x-3
Solution:
The quotient is 3x3-2x2+4x-1and no remainder.
Practice!
Students will be grouped into two groups. The teacher will have post a two sets of questions. Each
group must solve the questions.
Try This #1!
Using the long division, find the quotient and the remainder. Write your answer on in the form P(x) =
Q(x) • D(x) +R.
1. (2x3+x2-5x+3)÷(x+2) 2. (x2-5x+3)÷(x+2)
3. (3x3 + x2 – 8x – 4) ÷ (x- 2) 4. (2x3 – 7x2 – 5x + 4) ÷ (x-4)
C. CULMINATION
CHECKING- UP!
After the activity, each group must make a diagram to explain the steps in long division. They should
also need to give a one example. They will choose a representative to report it.
Evaluation
Students will choose their to answer the following.
A. Using the long division divide each polynomial by x-2. Write your answers in the form P(x) = Q(x) • D(x)
+R. Show your solutions.
1. 3x4-2x2-18 2. 5x4+3x3-5x2+8
3. (x4+25x-3) ÷ (x+3) 4. (2x3+3x2+2x+4) ÷ x+2
A short quiz will be followed.

TLP 4 Division of Polynomials Using Long Division

Uploaded by

Copyright:

Available Formats

TLP 4 Division of Polynomials Using Long Division

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

TLP 4 Division of Polynomials Using Long Division

Uploaded by

Copyright:

Available Formats



A Teaching- Learning Package in Mathematics 10

Teacher: Maryland V. Pasilan

TLP 4: Division of Polynomials using long division

How was answering it?

Rewrite the given division problem in the form

Thus, 2x3+4x-10 = (2x2+2x+6) (x-1) – 4

The quotient is 3x3-2x2+4x-1and no remainder.

3. (x4+25x-3) ÷ (x+3) 4. (2x3+3x2+2x+4) ÷ x+2

A short quiz will be followed.

You might also like