Question 204768: Could you please help me factor this trinomial?
7v^2-21v-280
Thanks!
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Whenever you factor, always start by factoring out the Greatest Common Factor (GCF). The GCF of  ,  and  is 7. So we factor out 7:
After the GCF there are many factoring techniques which can be used and there is no pre-determined order to which ones you should try and when. You just try any and all of them, repeatedly sometimes, until you cannot factor any further. Some of the methods you should know (and try) are:- Patterns
- Trinomial factoring
- Factoring by grouping
- Trial and error of the possible rational roots
In your expression, there is a trinomial (a three term expression) which can be factored. When the trinomial has a leading coefficient of 1, which yours has, then the factoring is relatively simple. You just have to ask yourself (and answer) the following question: What are the factors of the constant term (the number at the end) which add up to the middle coefficient? In your expression the question is: "What are the factors of -40 which add up to -3?" The factors of -40 are -1 and 40, 1 and -40, -2 and 20, 2 and -20, -5 and 8, 5 and -8. The only pair that add up to -3 is the last one: 5 and -8. So the  factors into  . Now we have:
And since no more factoring can be done (just like with reducing fractions, always keep factoring until no more can be done), we are finished.
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