SOLUTION: Hi. My name is Cindy. I am having difficulty with a problem. The question is: factor this expression completely. 6x^2-27x-1 I do not understand how to factor this expression. This

Question 504355: Hi. My name is Cindy. I am having difficulty with a problem. The question is: factor this expression completely. 6x^2-27x-1 I do not understand how to factor this expression. This is one of my review questions so I can see the answer which is 3(2x+1)(x-5), but I do not understand how to get to that answer. The steps I have been using for the other problems are: multiply the first number by the last number, factor the product, then decide which factors together equal the middle number. then common factor the first two terms, and the last two terms. Finally I am supposed to factor the common binomial from each of the two products to get the fully factored expression. I just do not see how this method works here. There must be a simpler method of answering this question, and a method that works. I am just so confused! Can anyone please help me? Thank you.
Found 2 solutions by stanbon, oberobic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
factor this expression completely. 6x^2-27x-15
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Common Factor: 3
= 3[2x^2-9x-5)
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How to factor 2x^2-9x-5
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Think of 2 numbers whose product is 2*-5 = -10
and whose sum is -9
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The numbers are -10 and +1
----
Replace -9 by -10+1
---
2x^2-9x-5 can be written as
2x^2-10x+x-5
----
Factor the 1st 2 and the last 2 terms separately:
2x(x-5) + (x-5)
Factor again to get:
(x-5)(2x+1)
----
Final answer: 3(x-5)(2x+1)
===============================
Cheers,
stan H.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
First of all, you cannot factor 6x^2 -27x -1. You can solve it using the quadratic equation, but it does not factor.
.
Do the multiplication and you will see what you think is the answer is not correct.
.
3(2x+1)(x-5) = (6x+3)(x-5)
.
6x^2 -30x + 3x -15 = 6x^2 -27x -15.
.
That does not equal 6x^2 -27x -1.
.
So, there is no way to get that answer other than by mistake.
.
Factoring depends on your recognizing the patterns of the multiplication table to determine what choices are most likely.
.
There are many resources on this site and on the web, including some very good video lectures on YouTube. You can find many problems that have already been solved. By studying the patterns of how problems are solved you can gain the knowledge you need.
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Finally, using the quadratic equation solver provided on this site, you will see that it cannot be factored using integers.
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Good luck!

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