This foldable organizes notes & examples for perfect square trinomials as well as the difference of two squares. PERFECT for interactive math notebooks. Works great during whole group/ guided instruction, as a centers activity, class work assignment,
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The beauty of a living thing is not the atoms that go into it, but the way those atoms are put together.
Idea Transcript
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.
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.