For Problems , factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don’t forget to look first for a common monomial factor. (Objective 1)
The given polynomials completely and look first for a common monomial factor also indicate any that are not factorable using integers.
i) The Difference of Two Squares pattern states that .
ii) Multiplication is commutative, so the order of writing the factors is not important. For example, can also be written as .
The following steps have been followed to find out the complete factors:
Step-1: Find out the common monomial factor in the given polynomial and take out.
Step-2: Convert the polynomial in the form of 2 squares with subtraction and compare with the difference of two squares pattern.
Step-3: Replace the value of and in the difference of two squares pattern by the binomial values available from the step-2 and simplify.
1) The given polynomial is .
The common monomial factor available in the above polynomial is 8. So, take it out.
2) The above equation can be written as,
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