warm-up: copy these notes polynomialdegreename using degree number of terms name using number of...
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Warm-Up: Copy these notesPolynomial Degree Name using
degreeNumber of terms
Name using number of terms
6 0 constant 1 Monomial
5x+9 11 linear 2 Binomial
2 quadratic 3 Trinomial
3 cubic 1 monomial
4 Fourth degree 3 Trinomial
32x
374 2 xx
xxx 328 34
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Examples of Monomials
18 z 24x 35.2 xy3
a
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ObjectivesThe student will be able to:
1. find the degree of a polynomial.
2. arrange the terms of a polynomial in ascending or descending order.
SOL: A.2.b
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Why am I learning this1. You can model real life situations
(sports statistics, money, interest, stocks, chemistry, physics, psychology) with polynomials.
2. Projectile Motion- Angry Birds
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What does each prefix mean?mono
one
bi
two
tri
three
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What about poly?one or more
A polynomial is a monomial or a sum/difference of monomials.
Important Note!!An expression is not a polynomial if there is a variable in the denominator.
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State whether each expression is a polynomial. If it is, identify it.
1) 7y - 3x + 4
trinomial
2) 10x3yz2
monomial
3)
not a polynomial2
57
2y
y
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Which polynomial is represented by
X2
1
1
X
X
X
1. x2 + x + 1
2. x2 + x + 2
3. x2 + 2x + 2
4. x2 + 3x + 2
5. I’ve got no idea!
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The degree of a monomial is the sum of the exponents of the variables.
Find the degree of each monomial.1) 5x2
2
2) 4a4b3c
8
3) -3
0
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To find the degree of a polynomial, find the largest degree of the terms.
1) 8x2 - 2x + 7
Degrees: 2 1 0
Which is biggest? 2 is the degree!
2) y7 + 6y4 + 3x4m4
Degrees: 7 4 8
8 is the degree!
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Find the degree of x5 – x3y2 + 4
1. 0
2. 2
3. 3
4. 5
5. 10
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A polynomial is normally put in ascending or descending order.
What is ascending order?
Going from small to big exponents.
What is descending order?
Going from big to small exponents.
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Put in descending order:
1) 8x - 3x2 + x4 - 4
x4 - 3x2 + 8x - 4
2) Put in descending order in terms of x:
12x2y3 - 6x3y2 + 3y - 2x
-6x3y2 + 12x2y3 - 2x + 3y
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3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x
-2x + 3y - 6x3y2 + 12x2y3
4) Put in ascending order:5a3 - 3 + 2a - a2
-3 + 2a - a2 + 5a3
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Write in ascending order in terms of y:x4 – x3y2 + 4xy – 2x2y3
1. x4 + 4xy – x3y2– 2x2y3
2. – 2x2y3 – x3y2 + 4xy + x4
3. x4 – x3y2– 2x2y3 + 4xy
4. 4xy – 2x2y3 – x3y2 + x4
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Standard form of a polynomial
Is when the polynomial is in descending order.
1753 24 xxx