Graphing Polynomials
Polynomial Division
Rational Root Theorem
100
Is this polynomial even or odd? Positive or negative?
Odd Negative
100
Synthetically Divide.
3x^4+2x^2-6x+4
divided by (x+2)
3x^3-4x^2+8x-22+48/(x+2)
100
State the number of complex zeroes.
y= 8x^5-3x^3+2x^2-7
5
200
What degree is this polynomial?
6x^5-4x^4+7x+10
5
200
Synthetically divide.
2x^4-x^3-20x^2-13x+30
divided by a root of -2
2x^3-5x^2-10x+7+16/(x+2)
200
State the possible rational zeroes.
y=3x^4+5x^2-x+6
+-1 +-1/3 +-2 +-2/3 +- 3 +-6
300
What is the end behavior for the polynomial?
x^3+3x^2+x-4
x->-oo, f(x)->-oo
x->oo, f(x)->oo
300
Long Divide.
4x^3+6x^2+6
divided by 2x+1
2x^2+2x-1+7/(2x+1)
400
What degree is this polynomial?
2x(x-3)(x+4)^2(2x-1)^3
7
400
State the possible rational zeros, FACTOR completely, and find all zeros (real, rational, and complex).
f(x)=x^4+5x^3-27x^2+9x
Possible Rational zeros:
0, +-1, +-3, +-9
Factors to:
f(x)=x(x-3)(x^2+8x-3)
Zeros:
0, 3, -4+-sqrt19
500
Write the equation of this polynomial in factored form.
f(x)=1/4(x+2)^2(x-1)^3(x-2)
500
Long Divide.
8x^5-20x^4-12x^3+2x^2-8x-3
divided by 2x-6
4x^4+2x^3+x-1-9/(2x-6)
500
State the possible rational zeros, FACTOR completely, and find all zeros (real, rational, and complex).
f(x)=3x^4+x^2-4
Possible rational zeros:
+-1,+-2,+-4,+-1/3,+-2/3,+-4/3
Factors to:
f(x)=(3x^2+4)(x-1)(x+1)
Zeros:
(+-2isqrt3)/3, +-1