Adding

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Adding Subtracting Polynomials

• Lesson 10.1

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Learning Goal 1 (HS.N-RN.B3 and
HS.A-SSE.A.1) The student will be able to use
properties of rational and irrational numbers to
write, simplify, and interpret expressions based
on contextual situations.
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In addition to level 3.0 and above and beyond what was taught in class,  the student may         Make connection with other concepts in math         Make connection with other content areas. The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations. - justify the  sums and products of rational and irrational numbers -interpret expressions within the context of a problem The student will be able to use properties of rational and irrational numbers to write and simplify  expressions based on contextual situations. -identify parts of an expression  as related to the context and to each part With help from the teacher, the student has partial success with real number expressions. Even with help, the student has no success with real number expressions.
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Polynomial Poly Many nomial terms
Form axk
Where k is a non-negative integer.
This is a polynomial in one variable.
k is the degree of ax.
ax alone has a degree of 1
The constant a has a degree of 0.
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Degree the degree of a polynomial is the
largest degree of its terms.
Standard form terms are written in descending
order from the largest to the smallest degree.
Coefficient the integer in front of the
variable. How many you have of each variable.
If no number, you have one.
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Put this in standard form. -4x2 3x3 2
3x3 4x2 2
Name the coefficients and degree. 2x3 (-1)x2 5
Coefficients 2, -1 Degree 3
Coefficients -5, 10 Degree 2
-5x2 10x - 3
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Classifying Polynomials
Polynomial Polynomial Degree Classify Degree of Polynomial Classify Polynomial Terms
6 0 Constant Mononomial
-2x 1 Linear Mononomial
3x1 1 Linear Binomial
-x22x-5 2 Quadratic Trinomial
4x3-8x 3 Cubic Binomial
2x4-7x3-5x1 4 Quartic Polynomial
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Adding Polynomials add like terms! You add the
coefficients, not the variables!
Horizontal format
(2x2x-5) (x2x6) remove ( )
2x2x2xx-56 3x22x1
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Vertical format line up like terms and add.
(2x2x-5) (x2x6) remove ( ) and line up like
terms. 2x2x-5 x2x6 3x22x1
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Subtracting polynomials use either vertical or
horizontal format. Remember to change the
signs of every term in the second polynomial when
you remove the ( )!
Vertical format (8x4-3x2-11x-3)
(-13x4-3x22x-17) 8x4 - 3x2- 11x - 3
13x43x2-2x17 (combine after changing
signs) 21x4 -13x14
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Horizontal format (8x4-3x2-11x-3)
(-13x4-3x22x-17) Remove ( ) changing the signs
in the second polynomial. You are adding the
opposites!
8x4-3x2-11x-3 13x43x2-2x17 (now combine like
terms) 21x4-13x14
Classify this by degree and terms.
Quartic, trinomial
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Find the area of the shaded region.
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A bh-bh x ? 2x 4 ? 2x2 2x