Divide the following polynomial using Long Division.
x^3 + x^2 - 36x + 42 divided by (x + 7)
What is "x^2 - 6x + 6"
100
Using the Conjugate Root Theorem, find two additional roots of P(x) = 0 given the following roots of P(x).
14 - 5i, - 25i
What is "14 + 5i and 25i"
100
Find all roots of the following polynomial:
x^3 + 4x^2 + x - 6
What is " -3, -2, and 1"
100
The following is the 5th row of Pascal's Triangle, find the 10th row.
1 5 10 10 5 1
What is "1 10 45 120 210 252 210 120 45 10 1"
100
Write the equation of y = x^3 given the following transformations:
Vertical stretch by a factor of 3
A reflection across the x-axis
A vertical translation 2 units up
A horizontal translation 5 units right
What is " y = -3(x - 5)^3 + 2"
200
Divide the following polynomial using Long Division
2x^3 - 3x^2 - 18x - 8 divided by (x - 4)
What is " 2x^2 + 5x + 2"
200
Using the Conjugate Root Theorem, write a polynomial function given the following roots.
5, -5i
What is "x^3 - 5x^2 + 25x - 125"
200
Find all roots of the following polynomial:
x^3 - 5x^2 + 2x + 8 = 0
What is "-1, 2, and 4"
200
Expand the following binomial:
(x^2 - y^2)^3
What is " x^6 - 3(x^4)(y^2) + 3(x^2)(y^4) - y^6"
200
Write the equation of y = x^3 given the following transformations:
A vertical compression by a factor of 1/2
A vertical translation of 8 units down
A horizontal translation of 25 units left
What is " y = (1/2)(x + 25)^3 - 8"
300
Divide the following polynomial using Synthetic Division
x^4 - 6x^2 - 27 divided by (x + 2)
What is "x^3 - 2x^2 - 2x + 4 - 35/(x+2)
300
Using the Rational Root Theorem, list all possible rational roots of the polynomial.
8x^3 + 2x^2 - 5x + 1
What is " +/-1, +/- 1/8, +/- 1/4, +/- 1/2"
300
Find all roots of the following polynomial:
y = x^4 - x^3 - 5x^2 - x - 6
What is " -2, 3, and i"
300
Expand the following binomial:
(3x + 8y)^3
What is " 27x^3 + 216(x^2)y + 576x(y^2) + 512y^3"
300
Find the zero of the function:
y = (1/27)(x - 10)^3 + 343
What is " x = - 11"
400
Divide the following polynomial using Synthetic Division
x^4 - 5x^2 + 4x + 12 divided by (x + 2)
What is "x^3 - 2x^2 - x + 6
400
Using Descartes' Rule of Signs, list the number of possible positive real roots and negative real roots.
3x^3 + 10x^2 - 22x + 15
What is " Two or no positive real roots, One negative real root."
400
Find all roots of the following polynomial:
2x^3 + 11x^2 + 14x + 8 = 0
What is " -4, ((-3 +/- i(7)^1/2)/4))"
400
Expand the following binomial:
(a - b^2)^5
What is " a^5 - 5(a^4)(b^2) + 10(a^3)(b^4) - 10(a^2)(b^6) + 5a(b^8) - b^10"
400
Find the zero of the equation:
y = (1/512)(x + 25)^3 - 1331
What is " 63 "
500
Divide the following polynomial using Synthetic Division
3x^3 + 17x^2 + 21x - 9 divided by (x + 3)
What is "3x^2 + 8x - 3"
500
Using the Rational Root Theorem list the possible rational roots of the polynomial.
4x^3 + 2x - 12