Completing the Square

Completing the Square (Square Root Method) Completing the square is what is says: we take a quadratic in standard form \((y=a{{x}^{2}}+bx+c)\) and manipulate it to have a binomial square in it, like \(y=a{{\left( {x+b} \right)}^{2}}+c\).

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Factoring

How Does Factoring Work? Factoring is a transaction in which a business sells its invoices, or receivables, to a third-party financial company known as a “factor.”

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Graphing

Graphing Quadratic Equations Using Factoring A quadratic equation is a polynomial equation of degree 2 . The standard form of a quadratic equation is 0 = a x 2 + b x + c where a , b and c are all real numbers and a ≠ 0 .

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Group #1: Greatest Common Factor

But in that case we must check that we have found the greatest common factor. Greatest Common Factor Calculator OK, there is also a really easy method: we can use the Greatest Common Factor Calculator to find it automatically.

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Group #2: Grouping

Group x 2 with 3x and 2x with 6 and then factor each group.We get: (x 2 + 3x) + (2x + 6) = x*(x + 3) + 2*(x + 3) = (x + 3) * (x + 2) In this example, if you group x 2 with 2x and 3x with 6, you will get the same answer.

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Group #3: Difference in Two Squares

A Difference Between Two Squares is an expression with two terms (also known as a binomial) in which both terms are perfect squares and one of the two terms is negative. The problems that follow show how to factor a difference between two squares.

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Group #4

Factor out the GCF from each of the two groups. In the second group, you have a choice of factoring out a positive or negative number. To determine whether you should factor out a positive or negative number, you need to look at the signs before the second and fourth terms.

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Group #5: Trinomials

Lessons on the different methods of Factoring Trinomials - Grouping, How to factor trinomials using grouping, examples and step by step solutions

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Group #6: General Trinomials

The general form of a trinomial is ax 2 + bx + c Your goal in factoring trinomials is to make ax 2 + bx + c equal to (? + ?) * (? + ?) When a = 1, the trinomial becomes x 2 + bx + c and it is easier to factor.

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basic-mathematics.com

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Quadratic Formula

For the Quadratic Formula to work, you must have your equation arranged in the form "(quadratic) = 0". Also, the "2a" in the denominator of the Formula is underneath everything above, not just the square root.

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