6x 2 13x 5 Factor
Question 181871: Factor completely and show steps:
6x^2-13x-5
Respond by jim_thompson5910(35256)



Y'all can put this solution on YOUR website!
Looking at the expression , 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
.
Now the question is: what two whole numbers multiply to (the previous product)
To find these two numbers, nosotros need to list
all of the factors of 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
Now replace the middle term with
. Remember,
and
add to
. So this shows us that
.
Supercede the second term
with
.
Group the terms into ii pairs.
Factor out the GCF
from the offset group.
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.
Combine similar terms. Or factor out the mutual term
---------------------------------------------
Answer:
And so factors to
.
Annotation: y'all can cheque the answer by FOILing to get
or by graphing the original expression and the answer (the two graphs should be identical).
6x 2 13x 5 Factor,
Source: https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.181871.html
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