**Algebra 2:**

Algebra 2 is a branch of mathematics that substitute letters for numbers. An algebraic equation represents a balance, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can included real numbers, complex numbers, matrices, vectors etc. Moving from Arithmetic to Algebra will see something like this: Arithmetic: 3 + 4 = 3 + 4 in Algebra. We see more practice problems below.

it would look like: x + y = y + x

Solve the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13.Find the Answer

**Solution** :

Given the equation5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Multiply factors.-15x - 10 - x + 3 = -16x - 20 +13

Group like terms.

-16x - 7 = -16x - 7

Add 16x + 7 to both sides and write the equation as below 0 = 0

**Answer: **

The above statement is true for all values of x.

Therefore all the real numbers are solutions to the given equation.

**Practice algebra 2 Example :**

Factor the following polynomials and find the answer :

a) f(x) = x ^{3} - x ^{2} - 4 x + 4

b) f(x) = 2 x ^{2} - x ^{3}

c) f(x) = -(x ^{2} - 2 x - 3) ^{2}

d) f(x) = x ^{4} + 3 x ^{3} + 3 x ^{2} + x

**Solution:**

a) f(x) = x ^{3} - x ^{2} - 4 x + 4

= x ^{2}(x - 1) - 4(x - 1)

= (x - 1)(x ^{2} - 4)

**Answer** **= (x - 1)(x - 2)(x + 2)**

b) f(x) = 2 x ^{2} - x ^{3}

**Answer** **= x ^{2}(2 - x)**

c) f(x) = -(x ^{2} - 2 x - 3) ^{2}

= -((x + 1)(x - 3)) ^{2}

**Answer** **= -(x + 1) ^{2}(x - 3) ^{2} **

d) f(x) = x

= x (x

** **

**Practice Problem 3:**

**solve for j: Find the Answer**

** **26 + j = 13 + 13 + j

**Solution:**

Combine like terms: 13 + 13 = 26

26 + j = 26 + j

Add '-26' to each side of the equation.

26 + -26 + j = 26 + -26 + j

Combine like terms: 26 + -26 = 0

0 + j = 26 + -26 + j

j = 26 + -26 + j

Combine like terms: 26 + -26 = 0

J = 0 + j

j = j

Add '-1j' to each side of the equation.

j + -1j = j + -1j

Combine like terms: j + -1j = 0

0 = j + -1j

Combine like terms: j + -1j = 0

0 = 0

This equation is an identity, all real numbers are solutions.