Find the factors of the polynomial
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Answer:
The process of factoring is essential to the simplification of many algebraic expressions and is a useful tool in solving higher degree equations. In fact, the process of factoring is so important that very little of algebra beyond this point can be accomplished without understanding it.
In earlier chapters the distinction between terms and factors has been stressed. You should remember that terms are added or subtracted and factors are multiplied. Three important definitions follow.
Terms occur in an indicated sum or difference. Factors occur in an indicated product.
An expression is in factored form only if the entire expression is an indicated product.
Note in these examples that we must always regard the entire expression. Factors can be made up of terms and terms can contain factors, but factored form must conform to the definition above.
Factoring is a process of changing an expression from a sum or difference of terms to a product of factors.
Note that in this definition it is implied that the value of the expression is not changed - only its form.
Step-by-step explanation:
Upon completing this section you should be able to:
Determine which factors are common to all terms in an expression.
Factor common factors.
In the previous chapter we multiplied an expression such as 5(2x + 1) to obtain 10x + 5. In general, factoring will "undo" multiplication. Each term of 10x + 5 has 5 as a factor, and 10x + 5 = 5(2x + 1).
To factor an expression by removing common factors proceed as in example 1.
Next look for factors that are common to all terms, and search out the greatest of these. This is the greatest common factor. In this case, the greatest common factor is 3x.
Proceed by placing 3x before a set of parentheses.
The terms within the parentheses are found by dividing each term of the original expression by 3x.
