Adding polynomials 8r angi ariunzaya
Transcript of Adding polynomials 8r angi ariunzaya
Bellwork
2.) : .
Any Monomial is also a polynomial
a-b, 7-x, -2x2 +xy-3,
1/8x - xy2, r + 9, 6
5x + 7 8 2x
(5x + 7)
(-2x + 8)
3x + 15
+
=
5x + 7 8 2x
5x + 7
-2x + 8
3x + 15
+
3a + b 7a + 5b
(3a + b)
(7a + 5b)
4a + 4b
-
=
7a + 5b -3a - b
=
7a -3a + 5b - b
3a + b 7a + 5b
(3a + b)
(7a + 5b)
4a + 4b
-
Add c2 + 5c + 4 and 3c - 7
+
=
c2 + 5c + 4
3c - 7
c2 + 8c - 3
c2 + 5c + 3c + 4 - 7
c2 + 5c + 4 3c 7
+
c2 + 5c + 4
3c - 7
c2 + 8c - 3
Monomials
Have one term such as:
6, 7a, 5x2, -4m3n2
Why is
-4m3n2
a monomial?
Binomials
Have two terms such as
5x + 3, 6y2 - 2,
a - b, 2x2y - 3xy2
Notice:
The terms are separated by one operation sign (+ or -)
Trinomials
Have three terms such as:
3x2 + 5x - 6
-3m + m3 -2
Notice:
The terms are separated by two operation signs (+ or -)
Which of these are monomials?
1.) x2 y2, x2 /y2, 1/7, ax2 + bx + c, 1/x + y
Why aren't the othersMonomials?
Which of these are Polynomials?
1.) x2 + y2, x3, x2 - 1/3, ax2 + bx + c, 1/x + y
Why isn't 1/x + ya polynomial?
Clssifying Polynomial
Polynomials are Classified by degree.
The Degree is determined by the exponents of the terms.
For example:
The degree of a Monomial
Is the sum of the exponents of the variables of the monomial.
x3 3
x3 y2 5
MonomialDegree
3x3 y2 5
32x3 y2 5
The degree of a Monomial
Is the sum of the exponents of the variables of the monomial.
MonomialDegree
x 1
x y 2
9 0
The degree of a Polynomial
Is the highest degree of any of its terms after the poly has been simplified.
Polynomial Degree
3x2 + 5x + 7 2
The degree of a Polynomial
Polynomial Degree
3x2+ 5x + 7 2
3x2 -9xyz +y+z 3
x + y + 7 1
2x2 +7x -3y-2x2 1
ascending
going up
the stairs
descending
going down
the stairs
Descending order of Polynomials
From the highest degree to the lowest degree of the terms.
3x2 + 5x + 7
3x3 + 5x2 - 2x + 7
2
1
0
3
2
1
0
Ascending order of Polynomials
From the lowest degree to the highest degree of the terms.
7 + 5x + 3x2
7 - 2x + 5x2 + 3x3
2
1
0
3
2
1
0