Elements of Polynomials
Write the polynomial in standard form:
9x3-5x2+6x4+10x+2
6x4+9x3-5x2+10x+2
What is an even graph? What kind of symmetry does it have?
All exponents are even and the graph has reflectional symmetry across the x-axis.
Simplify:
(-2x2-3x+12) + (5x2+7X+8)
3x2+4x+20
(8x+9)(9x2+6x-7)
72x3+129x2-2x-63
5x2+7x-6
(5x-3)(x+2)
What is the leading coefficient (1st term) and constant of this polynomial:
6x4+9x3-5x2+10x+2
LC: 6x4 and C: 2
What is an odd graph? Symmetry?
All exponents are odd. It has rotational symmetry across the x-axis.
Simplify:
(3x3+7x-19)-(5x3-3x+7)
-2x3+10x-26
(9x2+4)(2x2+7x-3)
18x4+63x3-19x2+28x-12
4x4-7x3+16x2-28x
(x3+4x)(4x-7)
Put in standard form: 1+3x-2x3
-2x3+3x+1
What is odd multiplicity?
Leading Expo is odd and the graph will CROSS the x-axis at that zero.
(14x3+5x2-8x)+(-6x3+3x2+15)
8x3+8x2-8x+15
(x4+4x3-2x2+12x-18)/(x2+3)
x2+4x-5 + -3/x2+3
27x3+64
(3x+4)(9x2-12x+16)
Identify and Classify the polynomial by degree and terms: -2x3+3x+1
Number of terms: 3
Degree: 3
Classify: Cubic Trinomial
What is Even multiplicity?
Leading expo is even and the graph will Touch the graph at that zero.
(12x2-7x+15)-(10x2-14x+5)
2x2+7x+10
(2x4-11x3+11x2+6x-10)/(x-4)
2x3-3x2-x+2+ -2/x-4
factor and find the roots:
2x3-5x2+6x-15
(x2+3)(2x-5)
x=5/2
x= +/- i [3]
Identify and Classify the polynomial by degree and terms: 6x4+9x3-5x2+10x+2
Number of terms: 5
Degree: 4
Classify: Quartic 5 term Polynomial
(x-3)(x-2)2=0
What is the multiplicity and what are the zeros.
Odd, crosses @ x=3
Even, touches @ x=2
(24x2+12x-9)-(18x2-34x+16)
6x2+46x-25
(3x6-2x5-11x4+5x3-16x2+25x-23)/(x2-5)
3x4-2x3+4x2-5x+4+ -3/x2-5
determine the number of possible zeros and solve for the zeros:
x4+3x3-9x2+3x-10
4 zeros
1 positive, 1 negative, 2 imaginary
x=2 x=-5 x= +/- i