Polynomials
Essential Question:
How do you add or subtract polynomials?
Polynomials
• Polynomial
– A monomial, or a sum or difference of monomials
• Degree
– The degree of a polynomial in one variable is
determined by the exponent with the greatest value
within the polynomial
– Highest exponent within the polynomial
• Standard Form
– The terms of a polynomial are ordered from left to
right in decreasing order.
Naming a Polynomial According
to Degree
• Linear – if the degree is 1
• Quadratic – if the degree is 2
• Cubic – if the degree is 3
• 4th Degree –if the degree is 4
• 5th Degree– if the degree is 5
Write in standard form then identify the degree of
the polynomial.
1. 9 + x – 4x2
-4x2 + x + 9
degree: quadratic
2. X + 3x3 – 2
3x3 + x – 2
degree: cubic
3. 15 + 2x – 3x2
-3x2 + 2x + 15
degree: quadratic
4. 3x4 + 23 – 2x + 2x3
3x4 + 2x3 – 2x + 23
degree: quartic
5. 3 + z
z+3
degree: linear
Classifying Polynomials according to
number of terms.
• Terms
–it is a basic unit in a polynomial
including the sign.
–separated by + or –
• Types:
Monomial – one term (no + or – in between)
Binomial – polynomial with two terms
Trinomial – polynomial with three terms
Classify according to number of
terms.
1. 2x2 – 5x + 2
trinomial
2. -5x + 5
binomial
3. 7x3 + 10x – 2xy
trinomial
4. -10x3yz
monomial
5. -xy + 3y
binomial
Rules in Adding Polynomials
1. Arrange each polynomial in standard
form.
2. Write the terms that are similar in only
one column.
3. Add only the coefficients.
4. Do not add the exponents. Copy as it is.
Adding Polynomials
• Find the sum of
(2x2 – 3x + 5) + (4x2 + 7x – 2)
Solution:
2x2 – 3x + 5
+ 4x2 + 7x – 2
6x2 + 4x+ 3
The sum is 6x2 + 4x + 3.
Find the sum of
(3x2 + 4x4 – x + 1) + (3x4 + x2 – 6)
Solution:
4x4 + 3x2 – x + 1
+ 3x4 + x2
–6
7x4 + 4x2 – x – 5
The sum is 7x4 + 4x2 – x – 5.
Do this…
Find the sum of each of the following. Make
sure to write first in standard form.
1. (4x4 + x3 – 6) + (x3 + x2)
2. (2y3 + y2 + 1) + (3y3 – y2 + 2)
3. (2c – 3) + (c2 + c + 4)
4. (3d2 + 7d – 6) + (d3 + d2 – d – 1)
5. (4x2 – 7x3 + 2x – 3) + (5x3 – 3x – 4x2 + 6)
Write a polynomial expression for
the perimeter of each polygon.
1.
x2 + x
2x2
2x2
x2 + x
2.
3.
2x – 3
2x – 3
a3 + 2a
3x2 + 2
a+1
3x2 + 2
2a3 + a + 3
2x2 + x + 1
Rules in Subtracting Polynomials
1. Arrange in standard Form
2. Write in only one column those that are
similar terms.
3. Apply “Keep-Change-Change”
4. Proceed to addition.
Subtracting Polynomials
Find the difference of
(3x2 – 2x + 8) – (x2 – 4)
Solution:
3x2 – 2x + 8
–+ - x2
–+ 4
2x2 – 2x + 12
The difference is 2x2 – 2x + 12.
Subtract: (4x2 + 2 + 3x) – (3x – 2x2 + 7)
Solution:
–
+
4x2 + 3x + 2
-2x2 –
+ 3x –+ 7
+
6x2 + 0x – 5
The difference is 6x2 – 5.
Do this…
Find the difference of each of the following
polynomials.
1. (12x2 + 5x + 11) – (10x2 + 3x + 2)
2. (3x4 + 2x2 ) – (2x4 + 3)
3. (x3 + x2 + 7) – (x2 + x )
4. (3x2 + 3 – 5x) – (–x – 4 + 2x2)
5. (4y2 – y + 6) – (3y – 2)