Question 368608
I'm assuming you want to factor.




Looking at {{{2x^2-x-10}}} we can see that the first term is {{{2x^2}}} and the last term is {{{-10}}} where the coefficients are 2 and -10 respectively.


Now multiply the first coefficient 2 and the last coefficient -10 to get -20. Now what two numbers multiply to -20 and add to the  middle coefficient -1? Let's list all of the factors of -20:




Factors of -20:

1,2,4,5,10,20


-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -20

(1)*(-20)

(2)*(-10)

(4)*(-5)

(-1)*(20)

(-2)*(10)

(-4)*(5)


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



Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-20</td><td>1+(-20)=-19</td></tr><tr><td align="center">2</td><td align="center">-10</td><td>2+(-10)=-8</td></tr><tr><td align="center">4</td><td align="center">-5</td><td>4+(-5)=-1</td></tr><tr><td align="center">-1</td><td align="center">20</td><td>-1+20=19</td></tr><tr><td align="center">-2</td><td align="center">10</td><td>-2+10=8</td></tr><tr><td align="center">-4</td><td align="center">5</td><td>-4+5=1</td></tr></table>



From this list we can see that 4 and -5 add up to -1 and multiply to -20



Now looking at the expression {{{2x^2-x-10}}}, replace {{{-x}}} with {{{4x+-5x}}} (notice {{{4x+-5x}}} adds up to {{{-x}}}. So it is equivalent to {{{-x}}})


{{{2x^2+highlight(4x+-5x)+-10}}}



Now let's factor {{{2x^2+4x-5x-10}}} by grouping:



{{{(2x^2+4x)+(-5x-10)}}} Group like terms



{{{2x(x+2)-5(x+2)}}} Factor out the GCF of {{{2x}}} out of the first group. Factor out the GCF of {{{-5}}} out of the second group



{{{(2x-5)(x+2)}}} Since we have a common term of {{{x+2}}}, we can combine like terms


So {{{2x^2+4x-5x-10}}} factors to {{{(2x-5)(x+2)}}}



So this also means that {{{2x^2-x-10}}} factors to {{{(2x-5)(x+2)}}} (since {{{2x^2-x-10}}} is equivalent to {{{2x^2+4x-5x-10}}})




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     Answer:

So {{{2x^2-x-10}}} factors to {{{(2x-5)(x+2)}}}