Question 145363


Looking at {{{6c^2+11c-2}}} we can see that the first term is {{{6c^2}}} and the last term is {{{-2}}} where the coefficients are 6 and -2 respectively.


Now multiply the first coefficient 6 and the last coefficient -2 to get -12. Now what two numbers multiply to -12 and add to the  middle coefficient 11? Let's list all of the factors of -12:




Factors of -12:

1,2,3,4,6,12


-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -12

(1)*(-12)

(2)*(-6)

(3)*(-4)

(-1)*(12)

(-2)*(6)

(-3)*(4)


note: remember, the product of a negative and a positive number is a negative number



Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-12</td><td>1+(-12)=-11</td></tr><tr><td align="center">2</td><td align="center">-6</td><td>2+(-6)=-4</td></tr><tr><td align="center">3</td><td align="center">-4</td><td>3+(-4)=-1</td></tr><tr><td align="center">-1</td><td align="center">12</td><td>-1+12=11</td></tr><tr><td align="center">-2</td><td align="center">6</td><td>-2+6=4</td></tr><tr><td align="center">-3</td><td align="center">4</td><td>-3+4=1</td></tr></table>



From this list we can see that -1 and 12 add up to 11 and multiply to -12



Now looking at the expression {{{6c^2+11c-2}}}, replace {{{11c}}} with {{{-1c+12c}}} (notice {{{-1c+12c}}} adds up to {{{11c}}}. So it is equivalent to {{{11c}}})


{{{6c^2+highlight(-1c+12c)+-2}}}



Now let's factor {{{6c^2-1c+12c-2}}} by grouping:



{{{(6c^2-1c)+(12c-2)}}} Group like terms



{{{c(6c-1)+2(6c-1)}}} Factor out the GCF of {{{c}}} out of the first group. Factor out the GCF of {{{2}}} out of the second group



{{{(c+2)(6c-1)}}} Since we have a common term of {{{6c-1}}}, we can combine like terms


So {{{6c^2-1c+12c-2}}} factors to {{{(c+2)(6c-1)}}}



So this also means that {{{6c^2+11c-2}}} factors to {{{(c+2)(6c-1)}}} (since {{{6c^2+11c-2}}} is equivalent to {{{6c^2-1c+12c-2}}})




------------------------------------------------------------




     Answer:

So {{{6c^2+11c-2}}} factors to {{{(c+2)(6c-1)}}}