Search results
Results from the WOW.Com Content Network
Given a quadratic polynomial of the form + + it is possible to factor out the coefficient a, and then complete the square for the resulting monic polynomial. Example: + + = [+ +] = [(+) +] = (+) + = (+) + This process of factoring out the coefficient a can further be simplified by only factorising it out of the first 2 terms.
In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
x 2 − 5x − 6 = (12 x + 12) ( 1 / 12 x − 1 / 2 ) + 0 Since 12 x + 12 is the last nonzero remainder, it is a GCD of the original polynomials, and the monic GCD is x + 1 . In this example, it is not difficult to avoid introducing denominators by factoring out 12 before the second step.
First-order approximation is the term scientists use for a slightly better answer. [3] Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has 4 × 10 3, or four thousand, residents"). In the case of a first-order approximation, at least one number given is exact.
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 .