**Algebra 2 online pages**

homework assignment help is most useful online help portal for the students that providing all Online Algebra 2 assignment help. Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra 2 online pages cover the four basic operations such as addition, subtraction, multiplication and division. The most important terms of algebra 2 online pages are variables, constant, coefficients, exponents, terms and expressions. In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, algebra 2 online pages may be regarded as an extension of Arithmetic.

**Polynomials:**

A polynomial is a algebraic expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. The simplest polynomials have one variable. A one-variable polynomial of degree *n* has the following form:

** a _{n}x^{n}**

An algebraic equation whose degree is two is called quadratic equation. The format of the quadratic equation is Ax^{2}+Bx+C=0, where x is variable and A, B and C are constants.

**Formula is (-b±√b ^{2}-4ac)/2a**

**Linear systems:**

An algebraic equation whose degree is one is called linear system. When we plot the linear equation, straight line will be occur on the graph. The example of the linear equation is

**y = 5x + 9,****4x + 8y -2z = 44**

Exponential is power of a number which denotes, how many time, the number has to be multiplied. The exponentials are denoted as e^{x}

**Example 1: **

x + y + z = 4 ------------------- equation 1

-x + y - z = 2 ------------------- equation 2

x - y - z = 2 ------------------- equation 3

**Solution**:

Add equation 1 with equation 2.

x + y + z = 4

-x + y - z = 2

----------------

2y = 6 (divide both sides by 2)

2y / 2 = 6 / 2

y=3

Add equation 2 and equation 3.

-x + y - z = 2

x - y - z = 2

------------------

-2z = 4 (divide both sides by -2)

-2z / -2 = 4 / -2

z = -2

substitute y=3 and z=-2 in equation 1

x + 3 + (-2) = 4

x + 3 - 2 = 4

x + 1 = 4 (add both sides by -1)

x + 1 - 1= 4 – 1

x = 3

The answer is x = 3; y=3;z = -2

**Example 2: **

**Solve the equation by quadratic formula 2x ^{2}+5x+3=0**

**Solution:**

** **Here** **a=2, b=5 and c=3

Discriminate: b^{2}-4ac = 5^{2}-4*2*3 = 1

Discriminate (1) is greater than zero. The equation has two solutions.

x =(-b±√b^{2}-4ac)/2a

x =(-5±√5^{2}-4*2*3)/2*3

or

x_{1,2} = (-5 ± 1) / 2*3

or

x_{1} = -4 / 6 = -2/3

x_{2} = -6 / 6 = -1

or

x_{1,2} = -3/4, -2

**Example 3:**

Solve the equation by using the factorization method x^{2}+4x+3=0

**Solution: **

x^{2}+4x+3=0

x^{2}+3x+x+3=0

(x^{2}+3x)+(x+3)=0

x(x+3)+(x+3)=0

(x+1)(x+3)=0

x+1=0 and x+3=0

x+1-1=0-1 and x+3-3=0-3

x=-1 and x=-3

Therefore, x=-1-3

**Problem 1:**

2*x* + 5*y* + *z *= 4

5*x* -2*y* -6*z* = 1

2*x *-5*y* -2*z* = -1

**Answer:** *x* = 71/83, *y* = 31/83, *z* = 35/83

**Problem 2:**

2*x* + 5*y* = 4

5*x* -2*y* = 1

**Answer:** *x* = 13/29, *y* = 18/29

**Problem 3:**

x² - 2x + 1 = 0

Answer: 1, 1

**Introduction of algebra two :**

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra two vocabulary is associated with four basic operations such as addition, subtraction, multiplication and division. The most important lists of algebra two vocabulary are listed below. Hence, algebra two vocabulary causes the leads of Arithmetic.

- Arithmetic series
- Binomial
- Common difference
- Completing the square
- Conjugates
- Complex conjugates
- Exponent
- Factor
- Function
- Inequality
- Terms
- Coefficient
- Expression
- Equation
- Linear equation
- Polynomials
- Quadratic equations

**Arithmetic series:**

This is the addition of arithmetic sequence’s terms with the finite number of terms.

**Binomial:**

Two terms are concatenated by + or – sign to form the expression.

**Common difference:**

It is, term which is subtracting the preceding term in arithmetic sequence

**Completing the square:**

This is the way of solving quadratic equations.

**Conjugates:**

In tow binomial expression, all terms are same. But they are differentiated by opposite sign. For example, *a** + **bi* and *a** – **bi*.

**Exponent:**

The exponent tells that how many times to multiply the base number. It is appeared as factor form.

**Factor:**

An expression is broken into different pieces. The product of those pieces will give the previous expression.

**Function:**

The function is the relationship among the two or more sets, within which an element of the one set is related with the element in another set.** **

**Inequality: **

The mathematical expression is concatenated with another mathematical expression or value by the relational symbols, such as <, ≤, >, ≥ and ≠.

**Terms:**

The variables are joined together by the values is called terms. In + 4x + 3 = 0, the variables and 4x are called as terms.

**Coefficient:**

The values before the terms are called coefficients. In + 4x + 3 = 0, 7x^2 and 4x are called terms and the values 7 and 4 are called coefficients.

**Expression:**

The terms are joined together by the arithmetic operators +, -, * and / is called expression. Example: x+3.

**Equation:**

An expression is joined with another expression or value by the equal symbol is called equation.

**Example: **

- x +6=6
- x + 7= x + 8

**Linear equation:**

Variable in the algebraic equation has the first power is called linear equation.** **

**Polynomials:**

Polynomial is a algebraic expression which includes one or more variables with constants where the power of the variable is non-negative. Example: x^{2}+xy+5=0

**Quadratic equations:**

An algebraic equation with the degree two is called quadratic equation. The format for the quadratic equation is Ax^{2}+Bx+C=0, where x is called variable and A, B and C are called constants.

**Introduction to logarithms algebra 2:**

In math the logarithm comes under Algebra 2. There are many topics under algebra 2. It is the basis for the higher grade mathematics. Log helps us to solve many complex problems in simpler way. Natural logarithm or log means logarithm with a base e. e is a irrational constant equal to 2.718281828.

The natural log is denoted as ln(x) or log_{ e} (x). We know that e^{0}=1. Here in this topic we are going to see about log in algebra 2. Natural logarithm is defined for all positive real numbers.

**logarithms algebra 2 - Problem 1:**

Solve the given logarithmic expression: ln 3x + ln 5 = 3

**Solution:**

Given logarithmic expression: ln 3x + ln 5 = 3

ln 3x + 1.6094 = 3 ( The value of ln 5 = 1.6094)

Subtract by 1.6094 on both side in the above expression.

ln 3x + 1.6094 - 1.6094 = 3 - 1.6094

ln 3x = 1.3906

log_{e} 3x = 1.3906 (ln x = log_{e} x)

( we know, y = log_{b}P and P = b^{y})

Here, y = 1.3906 P = 3x b = e

So, 3x = e^{1.3906} = 4.0172

3x = 4.0172

Divided by 3 on both side in the above equation.

` (3x)/3` = `4.0172 / 3`

x = 1.3390

**Answer:** The value of x = 1.3390

**logarithms algebra 2 - Problem 2:**

** **Solve the given logarithmic expression: ln 5x + ln 3x = 0

**Solution:**

Given logarithmic expression: ln 5x + ln 3x = 0

ln 5x + ln 3x = 0 ln A + ln B = ln (A + B)

ln (5x * 3x) = 0 (The value of ln 5 = 1.6094)

ln 15x^{2} = 0

log_{e} 15x^{2} = 0 (ln x = log_{e} x)

( we know, y = log_{b}P and P = b^{y})

Here, y = 0 P =15x^{2} b = e

So, 15x^{2} = e^{0} = 1

15x^{2} = 1

Divided by 15 on both side in the above equation.

` (15x^2)/15` = `1 / 15`

x^{2} = 0.066

x = `+- sqrt 0.066`

**Answer:** The value of x = ± 0.2569

**logarithms algebra 2 - Problem 3:**

Solve the given equation and find the x value. 3^{-x2} = `1/27.`

**Solution:**

Given equation 3^{-x2} = `1/27` . exponential form

log_{3}`(1/27)` = -x^{2 }logarithmic form

^{ } -x^{2} = log_{3}`(1/27)`

= log_{3} 1 - log_{3} 27

= 0 - 3

= -3

x = 3^{1/2}.

**Answer:** The value of x = 3^{1/2}.

**logarithms algebra 2 - Problem 4:**

** **Solve the given equation and find the x value: 4 (1.1^{2x+3}) = 160

**Solution:**

Given equation, 4 (1.1^{2x+3}) = 160

1.1^{2x+3} = 40 exponential form

log_{1.1}40 = 2x+3 logarithmic form

2x + 3 = `(ln 40)/(ln 1.1) `

= 38.7039 (approximately)

Subtract by 3 on both side in above equation

2x + 3 - 3 = 38.7039 - 3

2x = 35.7039

Both side divided by 2. So, we get

`(2x)/2` =` 35.7039/2`

x = 17.85

**Answer:** The value of x = 17.85 (approximately)

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