polynomial - an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Algebra Master (Polynomials)

Free Algebra Master (Polynomials) Calculator - Given 2 polynomials this does the following:

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean o

Consider the following 15 numbers
1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20
- The mean of the last 10 numbers is TWICE the mean of the first 10 numbers
- The sum of the last 2 numbers is FIVE times the sum of the first 3 numbers
(i) Calculate the values of x and y
We're given two equations:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = 2(1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/10
[*]3x - 20 = 5(1 + 2 + y - 4)
[/LIST]
Let's evaluate and simplify:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = (1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5
[*]3x - 20 = 5(y - 1)
[/LIST]
Simplify some more:
[URL='https://www.mathcelebrity.com/polynomial.php?num=x%2B6%2B7%2B8%2By%2B9%2B10%2B12%2B3x%2B20&pl=Evaluate'](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10[/URL] = (4x + y + 72)/10
[URL='https://www.mathcelebrity.com/polynomial.php?num=1%2B2%2By-4%2B4%2B5%2Bx%2B6%2B7%2B8%2By&pl=Evaluate'](1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5[/URL] = (2y + x + 29)/5
5(y - 1) = 5y - 5
So we're left with:
[LIST=1]
[*](4x + y + 72)/10 = (2y + x + 29)/5
[*]3x - 20 = 5y - 5
[/LIST]
Cross multiply equations in 1, we have:
5(4x + y + 72) = 10(2y + x + 29)
20x + 5y + 360 = 20y + 10x + 290
We have:
[LIST=1]
[*]20x + 5y + 360 = 20y + 10x + 290
[*]3x - 20 = 5y - 5
[/LIST]
Combining like terms:
[LIST=1]
[*]10x - 15y = -70
[*]3x - 5y = 15
[/LIST]
Now we have a system of equations which we can solve any of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
(x, y) = [B](-115, -72)[/B]

During a performance, a juggler tosses one ball straight upward while continuing to juggle three oth

During a performance, a juggler tosses one ball straight upward while continuing to juggle three others. The height f(t), in feet, of the ball is given by the polynomial function f(t) = ?16t^2 + 26t + 3, where t is the time in seconds since the ball was thrown. Find the height of the ball 1 second after it is tossed upward.
We want f(1):
f(1) = ?16(1)^2 + 26(1) + 3
f(1) = -16(1) + 26 + 3
f(1) = -16 + 26 + 3
f(1) = [B]13[/B]

Expand Master and Build Polynomial Equations

Free Expand Master and Build Polynomial Equations Calculator - This calculator is the __ultimate__ expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)^{x}

* Polynomial Expansions c(d + e + f)^{x}

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)

* Polynomial Expansions c(d + e + f)

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

For the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t^3 -

For the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t^3 - 5t^2 + 21t, where t is the time in seconds and h is the height in feet. classify this polynomial by degree and by number of terms.
[URL='http://www.mathcelebrity.com/polynomial.php?num=0.3t%5E3-5t%5E2%2B21t&pl=Evaluate']Using our polynomial calculator, we determine[/URL]:
[LIST]
[*]The degree of the polynomial is 3
[*]There are 3 terms
[/LIST]

Function

Free Function Calculator - Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist. Table of Functions Calculator

Functions-Derivatives-Integrals

Free Functions-Derivatives-Integrals Calculator - Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ'(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ'(1)

3) 2^{nd} Derivative ƒ''(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ''(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1

3) 2

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

Interpolation

Free Interpolation Calculator - Given a set of data, this interpolates using the following methods:

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

Matrix Properties

Free Matrix Properties Calculator - Given a matrix |A|, this calculates the following items if they exist:

* Determinant = det(A)

* Inverse = A^{-1}

* Transpose = A^{T}

* Adjoint = adj(A)

* Eigen equation (characteristic polynomial) = det|λI - A|

* Trace = tr(A)

* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form

* Dimensions of |A| m x n

* Order of a matrix

* Euclidean Norm ||A||

* Magic Sum if it exists

* Determines if |A| is an Exchange Matrix

* Determinant = det(A)

* Inverse = A

* Transpose = A

* Adjoint = adj(A)

* Eigen equation (characteristic polynomial) = det|λI - A|

* Trace = tr(A)

* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form

* Dimensions of |A| m x n

* Order of a matrix

* Euclidean Norm ||A||

* Magic Sum if it exists

* Determines if |A| is an Exchange Matrix

Polynomial

Free Polynomial Calculator - This calculator will take an expression without division signs and combine like terms.

It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.

It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.

Polynomial Long Division

Free Polynomial Long Division Calculator - Polynomial Long Division Calculator

Synthetic Division

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem

The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they?

The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they?
A few things to note:
[LIST]
[*]X-intercepts are found when y (or f(x)) is 0.
[*]On the right side, we have 3 monomials.
[*]Therefore, y or f(x) could be 0 when [U]any[/U] of these monomials is 0
[/LIST]
The 3 monomials are:
[LIST=1]
[*]2x - 3 = 0
[*]x - 4 = 0
[*]x + 3 = 0
[/LIST]
Find all 3 x-intercepts:
[LIST=1]
[*]2x - 3 = 0. [URL='https://www.mathcelebrity.com/1unk.php?num=2x-3%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]3/2 or 1.5[/B]
[*]x - 4 = 0 [URL='https://www.mathcelebrity.com/1unk.php?num=x-4%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]4[/B]
[*]x + 3 = 0 [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B3%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]-3[/B]
[/LIST]
So our 3 x-intercepts are:
x = [B]{-3, 3/2, 4}[/B]

The polynomial function P(x) = 75x - 87,000 models the relationship between the number of computer

The polynomial function P(x) = 75x - 87,000 models the relationship between the number of computer briefcases x that a company sells and the profit the company makes, P(x). Find P (4000), the profit from selling 4000 computer briefcases.
Plug in 4,000 for x:
P(4000) = 75(4000) - 87,000
P(4000) = 300,000- 87,000
P(4000) = [B]213,000[/B]

The sum of -4x^2 - 5x + 7 and 2x^2 + 8x - 11 can be written in the form ax^2 + bx + c, where a, b, a

The sum of -4x^2 - 5x + 7 and 2x^2 + 8x - 11 can be written in the form ax^2 + bx + c, where a, b, and c are constants. What is the value of a + b + c?
The sum means we add the polynomials together. We do this by adding the like terms:
-4x^2 - 5x + 7 + 2x^2 + 8x - 11
(-4 +2)x^2 + (-5 + 8)x +(7 - 11)
-2x^2 + 3x - 4
We have (a, b, c) = (-2, 3, -4)
The question asks for a + b + c
a + b + c = -2 + 3 - 4
a + b + c = [B]-3[/B]

Which of the following is equivalent to 3(2x + 1)(4x + 1)?

Which of the following is equivalent to 3(2x + 1)(4x + 1)?
[LIST]
[*]A) 45x
[*]B) 24x^2 + 3
[*]C) 24x^2 + 18x + 3
[*]D) 18x^2 + 6
[/LIST]
First, [URL='https://www.mathcelebrity.com/binomult.php?term1=2x%2B1&term2=4x%2B1&pl=Expand+Product+of+2+Binomials+using+FOIL']multiply the binomials[/URL]:
We get 8x^2 + 6x + 1
Now multiply this polynomial by 3:
3(8x^2 + 6x + 1) = [B]24x^2 + 18x + 3, answer C[/B]