For problems 31-56, factor completely each of the trinomials and indicate any that are not factorable using integers. (Objective 2)
The given trinomial .
To factor the trinomials in the form of , we follow the steps given below:
Step-1: Multiply the coefficients of and the constant term. That is .
Step-2: Find the integers whose sum is equal to and whose product is .
Step-3: List out the pairs of factors for preferably using a table.
Step-4: Rewrite the original problem by splitting the appropriate terms.
Step-5: Now, use the factoring by grouping method to factor the rewritten problem and simplify to get the solution.
We need to complete the following with two integers whose sum is and whose product is .
The following table shows the possible pairs of factors of :
|Factors||Sum of the factors|
From the above table, we find that the numbers that we need are and and we can complete the factoring
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