5.1 and 5.2
Simplify
(x^4)^3
x^12
Is this a polynomial in one variable, explain why
6xy^2 -xy +y^2
This is not a polynomial in one variable because it has two variables.
Factor Completely x^3 + 6y^3. If not factorable put prime.
prime
State the possible number of positive, negative and imaginary zeros for the function.
f(x) = -4x^4 - 2x^3 - 12x^2 -12x^2 - x -23
Positive: 0
Negative 4, 2 , or 0
Imaginary: ^
au^2 + bu + c
What is the quadratic form?
Divide 6y^3 +12x^4 / 3y^2 + 12x^3
3y +x
Find p (-2) for the function of p(x) + x^2 + 2x - 3
p(-2) = -3
Find f (-2) for x^2 - 3 using synthetic division.
f(-2) = 1
State the possible number of positive, negative and imaginary zeros for the function.
f(x) = -2x^5 + 4x^4 + x^2 - 3
Positive: 2 or 0
Negative: 1
Imaginary: 4 or 2
has a degree that is one less than the original polynomial
What is a depressed polynomial?
Simplify 3t(tn-5)
3t^2n-15
Find p(x+h) for function p(x) = 3 - 5x^2 + x^3
P(x) = 3 - 5x^2 - 10xh - 5h^2 + x^3 + 3hx^2 + 3h^2x + h^3
Solve 8x^4 - 10x^2 + 3 = 0
plus or minus square root of 3 / 2.
plus or minus square root of 2 / 2.
Find the zeroes of the function F(x) = x^3 + 4x^2 +3x - 2
-2, -1, plus or minus square root of 2
used to determine the number of real zeros of a polynomial function
What is Descarte's rule of signs?
Divide 12x^4y^5 + 8x^3y^7 - 16 x^2 y^6 / 4xy^5
3x^3 + 2x^2y^2 - 4xy
Where are the maxima and minima in this graph.
Between -2 and -1.
Factor 6ay + 4by - 2cy +3az + 2 bz - cz
(2y + z)(3a + 2b - c)
Find the zeroes of the function F(x) = x^3 + 2x^2 +4x + 8
-2, plus or minus 2i
the binomal x - r is a factor of the polynomial P(x) if and only if P(r) = 0
What is the factor theorem?
(m+p)(m^2 - 2mp + p^2)
m^3 - m^2p - mp^2 + p^3
Determine the consecutive integer values of x between which each real zero is located fot g(x) = 4x^4 - 21x^2 + 5
Between -3 and -2, between -1 and 0, between 0 and 1, and between 2 and 3
What are the factors pf 3x^3 + 20x^2 + 23x -10 given that x + 5 is a factor?
x + 2 and 3x - 1
Find the zeroes of the function F(x) = x^4 + 6x^3 + 73x^2 +384x + 576.
x = -3, -3. -8i, 8i
idea where if the value of f(x) changes signs from one value of x to the next, then there is a zero between those two x-values
what is the Location Principle?