Alternate Factoring Methods &Sum and Difference of Squares and Cubes
Creating Equations from Roots
Possible Roots, Remainder Theorem & Descartes Rule of Signs
Finding all Roots
Polynomial Characteristics
100
8r^3 − 64r^2 + r − 8
(8r^2 + 1)(r − 8)?
100
Write the polynomial function of the least degree with integral coefficients that has the given roots.
5,-3
What is
x^2-2x-15 ?
100
What are the possible roots of
x^4 -3x^3+2x^2-3x+9
+-1, +-3,+-9?
100
Find all real and rational roots of: x^2 - 2x-35
What is 7 and -2?
100
Graph the equation below and determine the x and y intercepts and give the domain and range.
f(x) = x^3+6x^2+9x.
What is the x-intercepts are -3 and 0. The y-intercept is 0. The domain and range are all real numbers.
200
7xy − 3n − x + 21ny
What is
(x + 3n)(7y − 1)?
200
Write the polynomial function of the least degree with integral coefficients that has the given roots.
0, -4 and 5
What is
x^3-x^2-20x
200
Find the possible roots
2x^4 - 3x^3-6x-12
What is
+-1/2,+-1,+-3/2,+-2,+-3,+-4,+-6,+-12 ?
200
Using the rational root theorem, find the zeros (the roots) of each of the following polynomial function:
x^3−2x^2−5x+6
What is
-2, 1, 3
200
Find the function f (in factored form) whose graph is given below.
f(x) = (x-2)^2(x-1)x(x+1)
300
16m^2 -225
(4m+15)(4m-15)?
300
Write the polynomial function of the least degree with integral coefficients that has the given roots.
3, sqrt3
What is
x^3-3x^2-3x+9
300
Determine if 3 is a factor of
(x^4+x^3-7x^2-x+6).
What is yes
300
Using the rational root theorem, find the zeros (the roots) of each of the following polynomial function:
3x^3+x^2−12x−4
What is
-2, 1/3, 2
300
The degree and lead coefficient of
f(x)=-x+5x^2-6x^3+10
What is degree 3 and lead coeffcient of -6?
500
y^2 +9
(y+3i)(y-3i)?
500
Write the polynomial function of the least degree with integral coefficients that has the given roots.
1, -2, 2i
What is
x^4+x^3+2x^2+4x-8 ?
500
Determine how many possible positive roots there are of:
x^4 - 3x^2 +5x +9
what is 2 or 0?
500
Using the rational root theorem, find the zeros (the roots) of each of the following polynomial function:
5x^3+8x^2−79x+30
What is
-5,2/5,3
500
f(x) = x^3-6x^2+32?
600
216a^3 − 125b^3
What is
(6a-5b)(36a^2+30ab+25b^2)
600
Find the factors that has the given roots.
4,4/5,2/5
What is
(x-4)(5x-4)(2x-5)
600
Determine how many possible negative roots there are of:
x^6 + 3x^5+5x^4+3x^3+3x^2-2x-15
What is 5, 3, or 1?
600
Using the rational root theorem, find the zeros (the roots) of each of the following polynomial function:
x^4-x^3-19x^2-11x+30
What is
x= -3,-2,1,5
600
Find the absolute maximum and minimum of the graph below:
What is maximum (0, -2,) and minimum (-2, -6)?
800
108 − 4x^3
What is
4(3 − x)(9 + 3x + x^2)
800
Find the equation of a function with the roots 3 and -1. Both roots have a multiplicity of 2.
x^4-4x^3-2x^2+12x+9?
800
Find the remainder when the equation below is divided by: x-2
2x^3+3x^2-17x-30
-36?
800
Using the rational root theorem, find the zeros (the roots) of each of the following polynomial function:
2x^4−x^3−9x^2+4x+4
What is
x=-2,-1/2,1,2
800
determine the intervals of increase and decrease
What is increasing (-1, 1) and decreasing
(- oo, -1)and(1,oo)
1000
(x-3)^2-y^2
What is
(X-3+y)(x-3-y)
1000
Write the polynomial function of the least degree with integral coefficients that has the given roots.
4, 4/5, 5/2
What is
10x^3-73x^2+152x-80 ?
1000
State the possible rational zeros for
-2x^4-15x^2 +50x+4x^5-25+30x^3
+-1/4,+-1/2,+-1,+-5/4,+-5/2,+-5,+-25/4,+-25/2,+-25?
1000
Using the rational root theorem, find the zeros (the roots) of each of the following polynomial function:
6x^4−5x^3−14x^2−x+2
What is
x = -1,-1/2,1/3,2
1000
Which equation is a quartic function with zeros at -4, -1, 2, 3?
x^5-2x^4-5x^3+10x^2+4x-8