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Algebra

Factoring Trinomials

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(Back to the Intermediate Algebra Homepage) (Back to the GRE Math Help Page) (Back to the THEA Math Help Page) -------------------------------------------------------------------------------- Intermediate Algebra Tutorial 28: Factoring Trinomials Learning Objectives After completing this tutorial, you should be able to: Factor a trinomial of the form . Factor a trinomial of the form . Factor using substitution. Indicate if a polynomial is a prime polynomial. Introduction

history of algebra

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The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.

Algebra Formulas

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Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn a0 = 1 (am)/(an) = am-n a-m= 1/(am) Quadratic Formula In an equation like ax2 + bx + c = 0 You can solve for x using the Quadratic Formula: Binomial Theorem (a + b)1 = a + b (a + b)2 = a2 + 2ab + b2 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 ...and so on... Difference of Squares a2 - b2 = (a - b)(a + b) Rules of Zero 0/x = 0 where x is not equal to 0. a0 = 1 0a = 0 a*0 = 0 a/0 is undefined (you can't do it)

algebra history

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The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.

Steps for Factoring Polynomials

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1. Pull out greatest common factor or GCF [This is a very important step that is often skipped] Ex: or 2. Look at number of terms a. 2 Terms: If there are two terms (binomial), then check to see if it is i. A difference of squares: Ex: ii. A difference of cubes Ex: iii. A sum of cubes Ex: If there are two terms and the expression is none of the above, it is prime! b. 3 Terms: If there are three terms (trinomial), then factor into two binomials thinking of the FOIL method in reverse. Find factors of c that add up to b. Start by identifying the factors of c. The sign before c determines whether signs are the same or different in the 2 binomials that are produced, .

inverse matrix method

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Inverse Matrix Method The inverse matrix method is a method of solving an unsolved system of equations by using a matrix and the formula AA=I and AX= B to find the solution to the variables where I is the identity matrix. Start with your unsolved linear system. You must make sure that you have an equal number of variables and equations or the method won?t work. Line the coefficients up in a matrix by system. For example, If your systems were: -1x + 1y + 3z = 2 -1 1 3 x 2 2 x + 1y +2z = 2 then you would arrange it as 2 1 2 y 2

Quadratic Formula

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Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution. The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients". The Formula is derived from the process of completing the square, and is formally stated as: For ax2 + bx + c = 0, the value of x is given by:

Algebra Formulas

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Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn a0 = 1 (am)/(an) = am-n a-m= 1/(am) Quadratic Formula In an equation like ax2 + bx + c = 0 You can solve for x using the Quadratic Formula: Binomial Theorem (a + b)1 = a + b (a + b)2 = a2 + 2ab + b2 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 ...and so on... Difference of Squares a2 - b2 = (a - b)(a + b) Rules of Zero 0/x = 0 where x is not equal to 0. a0 = 1 0a = 0 a*0 = 0 a/0 is undefined (you can't do it)

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