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ObjectivesThe student will be able to:
LEARN ABOUT EXPONENTS AND ADD AND SUBTRACT POLYNOMIALS
MATH 8A
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Rule: For all numbers x and all integers m and n ,
SO,
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EXAMPLES
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PRACTICE
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MORE EXAMPLES
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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.
Remember, 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) 5/2y2 + 7y
not a polynomial
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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) 4a4b3c
3) -3
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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!
2) y7 + 6y4 + 3x4m4
Degrees: 7 4 8
8 is the degree!
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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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1. Add the following polynomials:(9y - 7x + 15a) + (-3y + 8x - 8a)
Group your like terms.
9y - 3y - 7x + 8x + 15a - 8a
6y + x + 7a
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Group your like terms.
3a2 + 3ab + 4ab - b2 + 6b2
3a2 + 7ab + 5b2
2. Add the following polynomials:(3a2 + 3ab - b2) + (4ab + 6b2)
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Line up your like terms. 4x2 - 2xy + 3y2
+ -3x2 - xy + 2y2
_________________________
x2 - 3xy + 5y2
3. Add the following polynomials using column form:
(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)
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Rewrite subtraction as adding the opposite.
(9y - 7x + 15a) + (+ 3y - 8x + 8a)
Group the like terms.
9y + 3y - 7x - 8x + 15a + 8a
12y - 15x + 23a
4. Subtract the following polynomials:(9y - 7x + 15a) - (-3y + 8x - 8a)
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Rewrite subtraction as adding the opposite.
(7a - 10b) + (- 3a - 4b)Group the like terms.
7a - 3a - 10b - 4b4a - 14b
5. Subtract the following polynomials:(7a - 10b) - (3a + 4b)
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Line up your like terms and add the opposite.
4x2 - 2xy + 3y2
+ (+ 3x2 + xy - 2y2)--------------------------------------
7x2 - xy + y2
6. Subtract the following polynomials using column form:
(4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2)
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PRACTICE
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PRACTICE
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PRACTICE
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