6.1 polynomial functions. polynomials a polynomial is a sum of terms whose exponents are whole...
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6.1 Polynomial Functions
Polynomials
A polynomial is a sum of terms whose exponents are whole numbers (not fractions or negative numbers).
Polynomials:
y = x3 + 4x2 – 2x + 1
y = x
y = 10
257
2
3xxxy
Not Polynomials:
12 xxy
61
31
15 xxy
xxy
315
Classifying Polynomials
A polynomial is said to be in standard form when the terms are in descending order by degree.
y = x3 + 4x2 – 2x + 1
257
2
3xxxy
What is the degree of the polynomial? What is the leading coefficient?
Adding Polynomials
To add polynomials, just combine like terms:
(8x3 – 3x2 – 2x + 9) + (2x3 + 6x2 – x + 1) =
10x3 + 3x2 – 3x + 10
(12x4 – 5x2 + x + 7) + (2x3 + 6x2 – x + 2) =
12x4 + 2x3 + x2 + 9
Subtracting Polynomials To subtract polynomials, combine like terms. (Just be careful with the signs.)
(8x3 – 3x2 – 2x + 9) - (2x3 + 6x2 – x + 1) =
6x3 - 9x2 – x + 8
(12x4 – 5x2 + x + 7) - (2x3 + 6x2 – x + 2) =
12x4 - 2x3 - 11x2 + 2x + 5
Comparing ModelsUsing a graphing calculator, determine whether a linear model, a quadratic model, or a cubic model
best fits the values in the table.
X 0 5 10 15 20
Y 10.1 2.8 8.1 16.0 17.8
X 0 2 4 6 8
Y 2.8 5 6 5.5 4
Comparing ModelsThe table shows data on the number of employees that a small company had from 1975 to 2000. Find
a cubic function to model the data. Use it to estimate the number of employees in 1998.
Year Number of Employees
1975 60
1980 65
1985 70
1990 60
1995 55
2000 64
Multiplying PolynomialsMultiply:
2312 xx This is just FOIL
2346 2 xxx
26 2 xx
961 2 xxx This is just like FOIL
96
962
23
xx
xxx9157 23 xxx
Multiplying PolynomialsMultiply:
2312 22 xxxx
234 23 xxx 2795 234 xxxx
45232 23 xxxx
xxxx 81042 234
xxx 462 23
232 xx
121563 23 xxx127472 234 xxxx
Multiplying PolynomialsMultiply:
2435 22 xxxx
234 10205 xxx 61417215 234 xxxx
27354 23 xxxx
xxxx 828124 234
xxx 24 23
6123 2 xx
1035155 23 xxx104343174 234 xxxx
Multiplying PolynomialsMultiply:
41x 22 11 xx
1212 22 xxxx
234 2 xxx
xxx 242 23
122 xx
1464 234 xxxx