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What do these prefixes mean?Can you give a word that starts with them?
MONOBITRIPOLY
Term
A number, a variable, or the product/quotient of
numbers/variables.Examples?
Degree of a Term
The exponent of the variable.
We will find them only for one-variable terms.
Term
3
4x
-5x2
18x5
Degree of Term
0
1
2
5
PolynomialA term or the
sum/difference of terms which contain only 1
variable. The variable cannot be in the
denominator of a term.
Degree of a Polynomial
The degree of the term with the highest degree.
Polynomial
6x2 - 3x + 2
15 - 4x + 5x4
x + 10 + x
x3 + x2 + x + 1
Degree ofPolynomial
2
4
1
3
Standard Form of a Polynomial
A polynomial written so that the degree of the
terms decreases from left to right and no terms have
the same degree.
Not Standard
6x + 3x2 - 2
15 - 4x + 5x4
x + 10 + x
1 + x2 + x + x3
Standard
3x2 + 6x - 2
5x4 - 4x + 15
2x + 10
x3 + x2 + x + 1
Naming Polynomials
Polynomials are named or classified by their
degree and the number of terms they
have.
Polynomial
7
5x + 2
4x2 + 3x - 4
6x3 - 18
Degree
0
1
2
3
Degree Name
constant
linear
quadratic
cubicFor degrees higher than 3 say:
“nth degree”
x5 + 3x2 + 3 “5th degree”x8 + 4 “8th degree”
Polynomial
7
5x + 2
4x2 + 3x - 4
6x3 - 18
# Terms
1
2
3
2
# Terms Name
monomial
binomial
trinomial
binomialFor more than 3 terms say:
“a polynomial with n terms” or “an n-term polynomial”
11x8 + x5 + x4 - 3x3 + 5x2 - 3“a polynomial with 6 terms” – or – “a 6-term
polynomial”
Polynomial
-14x3
-1.2x2
-1
7x - 2
3x3+ 2x - 8
2x2 - 4x + 8
x4 + 3
Name
cubic monomial
quadratic monomial
constant monomial
linear binomial
cubic trinomial
quadratic trinomial
4th degree binomial
Adding Polynomials
= 4x2+ 3x + 17
9.1 Adding and Subtracting Polynomials
(x2 + 2x + 5) + (3x2 + x + 12)in horizontal form:
x2+ 2x + 53x2 + x + 12+
= 4x2+ 3x + 17
in vertical form:
Simplify: The classify the polynomial by number of terms and degree
x2 + x + 1+ 2x2 + 3x + 2
3x2+ 4x + 3
(4b2 + 2b + 1)
+ (7b2 + b – 3)
11b2 + 3b – 2
9.1 Adding and Subtracting Polynomials
3x2 – 4x + 8+ 2x2 – 7x – 5
5x2 – 11x + 3
a2 + 8a – 5
+ 3a2 + 2a – 7
4a2 + 10a – 12
Simplify: The classify the polynomial by number of terms and degree
7d2 + 7d+ 2d2 + 3d
9d2+ 10d
(2x2 – 3x + 5)
+ (4x2 + 7x – 2)
6x2+ 4x + 3
9.1 Adding and Subtracting Polynomials
z2 + 5z + 4+ 2z2 - 5
3z2 + 5z – 1
(a2 + 6a – 4)
+ (8a2 – 8a)
9a2 – 2a – 4
Simplify: The classify the polynomial by number of terms and degree
3d2 + 5d – 1 + (–4d2 – 5d + 2)
–d2+ 1
(3x2 + 5x)
+ (4 – 6x – 2x2)
x2 – x + 4
9.1 Adding and Subtracting Polynomials
7p2 + 5+ (–5p2 – 2p + 3)
2p2 – 2p + 8
(x3 + x2 + 7)
+ (2x2 + 3x – 8)
x3 + 3x2 + 3x – 1
Simplify:
2x3 + x2 – 4+ 3x2 – 9x + 7
2x3 + 4x2 – 9x + 3
5y2 – 3y + 8
+ 4y3 – 9
4y3 + 5y2 – 3y – 1
9.1 Adding and Subtracting Polynomials
4p2 + 5p+ (-2p + p + 7)
4p2 + 4p + 7
(8cd – 3d + 4c)
+ (-6 + 2cd – 4d)
4c – 7d + 10cd – 6
Simplify:
(12y3 + y2 – 8y + 3) + (6y3 – 13y + 5)
(7y3 + 2y2 – 5y + 9) + (y3 – y2 + y – 6)
(6x5 + 3x3 – 7x – 8) + (4x4 – 2x2 + 9)
= 18y3 + y2 – 21y + 8
9.1 Adding and Subtracting Polynomials
= 8y3 + y2 – 4y + 3
= 6x5+ 4x4 + 3x3 – 2x2 – 7x + 1
Subtracting Polynomials ubtraction is adding the opposite)
(5x2 + 10x + 2) – (x2 – 3x + 12)
(5x2 + 10x + 2) + (–x2) + (3x) + (–12)
5x2 + 10x + 2
4x2+ 13x – 10
–(x2 – 3x + 12)
= 4x2+ 13x – 10
= 5x2 + 10x + 2 = –x2 + 3x – 12
Simplify:9.1 Adding and Subtracting Polynomials
= 2x2 – 2x + 12
(3x2 – 2x + 8) – (x2 – 4)
3x2 – 2x + 8 + (–x2) + 4
(10z2 + 6z + 5) – (z2 – 8z + 7)
10z2 + 6z + 5 + (–z2) + 8z + (–7)
= 9z2 + 14z – 2
Simplify:
7a2 – 2a
2a2 – 5a
– (5a2 + 3a)
9.1 Adding and Subtracting Polynomials
4x2 + 3x + 2
2x2 + 6x + 9 – (2x2 – 3x – 7)
3x2 – 7x + 5
2x2 – 11x – 2
– (x2 + 4x + 7)
7x2 – x + 3
4x2 + 10
– (3x2 – x – 7)
Simplify:
3x2 – 2x + 10
x2 – 6x + 16
– (2x2 + 4x – 6)
9.1 Adding and Subtracting Polynomials
3x2 – 5x + 3
x2 – 4x + 7 – (2x2 – x – 4)
2x2 + 5x
x2 + 5x + 3
– (x2 – 3)
4x2 – x + 6
x2 – x + 10
– (3x2 – 4)
Simplify:(4x5 + 3x3 – 3x – 5) – (– 2x3 + 3x2 + x + 5)
= 4x5 + 5x3 – 3x2 – 4x – 10
9.1 Adding and Subtracting Polynomials
(4d4 – 2d2 + 2d + 8) – (5d3 + 7d2 – 3d – 9)
= 4d4 – 5d3 – 9d2 + 5d + 17
(a2 + ab – 3b2) – (b2 + 4a2 – ab)
= –3a2 + 2ab – 4b2
Simplify by finding the perimeter:
x2 + x
2x2 B6c + 3
4c2 + 2c + 5
c2 + 1
B = 6x2 + 2x
A = 5c2 + 8c + 9
A
9.1 Adding and Subtracting Polynomials
2x2
x2 + x
3x2 – 5 x
x2 + 7 C D
2d2 + d – 4
d2 + 7
3d2 – 5d
C = 8x2 – 10x + 14
D = 9d2 – 9d + 3
3d2 – 5d
9.1 Adding and Subtracting PolynomialsSimplify by finding the perimeter:
x2 + 3 Fa + 1
2a3 + a + 3
a3 + 2a
F = 8x2 – 10x + 6
E = 3a3 + 4a + 4
E
9.1 Adding and Subtracting Polynomials
3x2 – 5x
Simplify by finding the perimeter:
HW: Section 9.1 Page 459 (2-26 even)
