1.2 Quadratic equations

Quadratic equations are written in the form y=ax²+bx+c.

When a quadratic equation is graphed, it produces a curved line called a parabola.

• A is the co-efficient of the variable squared
• B is the co-efficient of the variable
• C is the extra added number. It is the same as the b in Linear equations

1.3 Cubic equations

Cubic equations are written in the form y = ax³ + bx² + cx + d. In this form, there are three x-intercepts. When graphed, the line will start going up, then curve to go down, then swich again to go up. (the opposite can occur with negative variables)

• a is the co-efficient of the variable cubed
• b is the co-efficient of the variable squared
• c is the co-efficient of the variable
• d is the non-variable

1.4 Exponential equations

Exponential equations are written in the form y = m^x + b.

2 Factoring trinomials

2.1 Simple factoring

Trinomials are algebraic expressions consisting of three unlike terms, such as x^{2 + 3x + 2. They can be factored using the "FOIL" technique. You factor the expression by using two sets of perenthesis, each consisting of two terms, where the first, outside, inside, and last numbers of both sets multiplied together and added equal the trinomial. E.g.,}

x² + 5x + 6

is equivalent to

(x + 3)(x + 2)

Firsts (x times x) + Outsides (x times 2) + Insides (3 times x) + Lasts (3 times 2) = The trinomial (x^{2 + 5x + 6).}

The last numbers in each set of parenthesis have another relationship. When multiplied together, they always equal the last number (3 times 2 equals 6), and when added, they equal the co-efficient of the variable (3 plus 2 equals 5). The co-efficient is the number in front of the variable that you multiply it by. This is because they're both multiplied by the variable, and then added.

2.2 Two variables

Sometimes, you get expressions such as: 3x^{2 + 8xy + 4y2. In this situation, the factored form will look like: (3x + 2y)(x + 2y). 3x times x is 3x2, 3x times 2y is 6xy, 2y times x is 2xy, and 2y times 2y is 4y2. This time, the co-efficients of x have to be multiplied with the co-efficient of x2, and same with x.}

2.3 Symbols

Depending on whether the numbers are added or subtracted, you may need to use different symbols in the parenthesis.

• If you add the mx and add the b, the symbols are both plus.
• If you add the mx and subtract the b, the symbols are one plus and one minus.
• If you subtract the mx and add the b, the symbols are both minus
• If you subtract the mx and subtract the b, the symbols are one plus and one minus.

3 Symbolic method

The symbolic method is a way to figure out a variable when it's on both sides of the equation. E.g.,

3x + 25 = 5x + 5

• The first step is to isolate the variable. By subtracting 3x from both sides, you get 25 = 2x + 5.

• The second step is to get only the variable on one side. To do this, you subtract 5 from both sides to get 20 = 2x.

• The last step is to get just 1 x. Divide both sides by the co-efficient, in this case 2, and you have 10 = x.

The word algebra is also used for various algebraic structures:

• algebra over a field
• Boolean algebra
• sigma-algebra

4 See also

• Diophantus, "father of algebra"
• Mohammed al-Khwarizmi

5 External links

Our sister project, Wikibooks , provides an electronic book on .

• Algebra Lessons of Life
• Curriculum and Assessment in an Age of Computer Algebra Systems

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