6x 2 13x 5 Factor

Question 181871: Factor completely and show steps:
6x^2-13x-5

Respond by jim_thompson5910(35256)

(Show Source):

Y'all can put this solution on YOUR website!

Looking at the expression 6x%5E2-13x-5 , nosotros can come across that the commencement coefficient is , the 2d coefficient is , and the last term is .

At present multiply the first coefficient by the last term to get %286%29%28-5%29=-30 .

Now the question is: what two whole numbers multiply to (the previous product)

and add together to the second coefficient

To find these two numbers, nosotros need to list

all of the factors of

(the previous production).

Factors of :
1,two,three,five,half dozen,ten,15,xxx
-1,-two,-3,-5,-6,-x,-15,-xxx

Note: list the negative of each factor. This will let united states of america to find all possible combinations.

These factors pair upwardly and multiply to .
1*(-thirty)
2*(-15)
3*(-ten)
5*(-6)
(-1)*(30)
(-two)*(15)
(-3)*(10)
(-5)*(half-dozen)

Now let's add up each pair of factors to see if 1 pair adds to the middle coefficient :

First Number	Second Number	Sum
ane	-30	one+(-30)=-29
2	-xv	2+(-fifteen)=-thirteen
iii	-10	3+(-10)=-seven
5	-6	5+(-six)=-ane
-ane	30	-one+30=29
-2	15	-ii+fifteen=13
-3	10	-3+x=7
-5	half dozen	-five+6=1

From the table, we tin can come across that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to

and add together to

Now replace the middle term -13x with 2x-15x . Remember, and add to . So this shows us that 2x-15x=-13x .

6x%5E2%2Bhighlight%282x-15x%29-5 Supercede the second term -13x with 2x-15x .

%286x%5E2%2B2x%29%2B%28-15x-5%29 Group the terms into ii pairs.

2x%283x%2B1%29%2B%28-15x-5%29 Factor out the GCF from the offset group.

2x%283x%2B1%29-5%283x%2B1%29 Cistron out from the 2d group. The goal of this stride is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

%282x-5%29%283x%2B1%29 Combine similar terms. Or factor out the mutual term 3x%2B1

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Answer:

And so 6x%5E2-13x-5 factors to %282x-5%29%283x%2B1%29 .

Annotation: y'all can cheque the answer by FOILing %282x-5%29%283x%2B1%29 to get 6x%5E2-13x-5 or by graphing the original expression and the answer (the two graphs should be identical).