A shipping container in the shape of a rectangular solid must have a volume of 84 cubic meters. The client tells the manufacturer that, because of the contents, the length of the container must be one meter longer than the width, and the height must be one meter greater than twice the width. What should the dimensions of the container be?
To find
$\text{\hspace{0.17em}}f(k),\text{\hspace{0.17em}}$ determine the remainder of the polynomial
$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ when it is divided by
$\text{\hspace{0.17em}}x-k.\text{\hspace{0.17em}}$ This is known as the Remainder Theorem. See
[link] .
According to the Factor Theorem,
$\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$ is a zero of
$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ if and only if
$\text{\hspace{0.17em}}(x-k)\text{\hspace{0.17em}}$ is a factor of
$\text{\hspace{0.17em}}f(x).$ See
[link] .
According to the Rational Zero Theorem, each rational zero of a polynomial function with integer coefficients will be equal to a factor of the constant term divided by a factor of the leading coefficient. See
[link] and
[link] .
When the leading coefficient is 1, the possible rational zeros are the factors of the constant term.
Synthetic division can be used to find the zeros of a polynomial function. See
[link] .
According to the Fundamental Theorem, every polynomial function has at least one complex zero. See
[link] .
Every polynomial function with degree greater than 0 has at least one complex zero.
Allowing for multiplicities, a polynomial function will have the same number of factors as its degree. Each factor will be in the form
$\text{\hspace{0.17em}}(x-c),\text{\hspace{0.17em}}$ where
$\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$ is a complex number. See
[link] .
The number of positive real zeros of a polynomial function is either the number of sign changes of the function or less than the number of sign changes by an even integer.
The number of negative real zeros of a polynomial function is either the number of sign changes of
$\text{\hspace{0.17em}}f(-x)\text{\hspace{0.17em}}$ or less than the number of sign changes by an even integer. See
[link] .
Polynomial equations model many real-world scenarios. Solving the equations is easiest done by synthetic division. See
[link] .
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0
then
4x = 2-3
4x = -1
x = -(1÷4) is the answer.
Jacob
4x-2+3
4x=-3+2
4×=-1
4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3
4x=-3+2
4x=-1
4x÷4=-1÷4
x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was 1350 bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after 3 hours?
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?