| Graphing Polynomials | Add, Subtract, Mult, & Divide Polynomials | Factoring Polynomials | Solving Polynomials | Fundamental Thm of Algebra |
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a function where all exponents are whole numbers and positive ... it is written in standard form when its terms are written in descending order of exponents
What is a polynomial function?
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20x^4 - 3x^3 - 6x - 2
Find the sum of:
(9x^4 - 3x^3 + 4x^2 + 5x +7)+ (11x^4 - 4x^2 - 11x -9) |
Box Method or Find GCF
If you are given a function with four terms to factor, what is your first step?
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a = -3, 3 and 4
Solve: a^3 - 4a^2 - 9a = -36
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False; they come in pairs
True or False:
Imaginary solutions do not come in pairs |
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No because it has a negative exponent
Is f(x) = 5x^3 - 7x^(-2) + x - 1 a polynomial function? Why or why not?
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9m^2 - 6m + 1
Find the product of:
(3m-1)^2 |
5(v-4)(v-2)
Factor: 5v^2 - 30v + 40
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Its multiplicity
How can you determine whether a polynomial equation has a repeated solution?
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x = =1 , -2 , 1+ isqrt(3) , 1 - isqrt(3)
Find all the zeros of:
x^4 + x^3 + 8x + 8 = 0 |
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TRUE!
degree: 3 (odd) rising left --> negative coefficient
True or False:
When the graph or a cubic polynomial function rises to the left, it falls to the right. |
3x^5 - 6x^4 - 6x^3 + 25x^2 - 23x +7
Find the product of:
(3x^3 - 9x +7)(x^2 - 2x +1) |
(3a - 4)(9a^2 +12a +16)
Factor: 27a^3 - 64
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18 possible zeros
How many possible zeros do we have for
f(x) = 3x^4 - 11x^3 - 42x^2 + 7x + 12 |
3,-3, 2i, -2i
find all solutions for:
x^4 - 5x^2 - 36 = 0 |
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degree = 4 (even)
Leading coefficient: 6 (positive) both ends go up
Describe the end behavior of :
f(x) = 6x^4 - 3x^3 +12x^2 + 8x + 2 |
2x^2 - 6x + 17 + -58/(x+3)
What is (2x^3 - x -7) / (x+3)
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(x-7y)(4x - 7y)
Factor: 4x^2 - 35xy + 49y^2
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c = 0, 3, sqrt(6), - sqrt(6)
Solve: 2c^4 - 6c^3 = 12c^2 - 36c
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f(x) = x^3 - 8x^2 + 22x - 20
Write a polynomial function f of at least degree that has rational coefficients, a leading coefficient of 1 and the given zeros:
2, 3+i |
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x = 3, -3, 4 Multiplicity = 1 for all
coefficient 1(positive) and exponent 3 (odd) left end goes down and right end goes up
Find the zeros, the multiplicity and describe the end behavior of:
f(x) = x^3 - 4x^2 - 9x + 36 |
80
Use the given value of n to find the coefficient of x^n in the expansion:
(2x+1)^5 , n=3 |
Synthetic division with x=2
f(x) = 2(x-2)(x+3)(3x+1)
Show that the binomial is a factor of f(x), then factor completely.
f(x) = 6x^3 + 8x^2 - 34x - 12; x- 2 |
x = -5 , 3, and -2
Solve: x^3 + 4x^2 -11x -30
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1 positive zero
1 negative real zero 2 imaginary solutions
Determine the possible numbers of positive zeros, negative zeros, and imaginary zeros for the function.
g(x) = x^4 + x^2 - 10 |
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