Question 368621
I'll show you how to factor it.




Looking at {{{3x^2-13x-10}}} we can see that the first term is {{{3x^2}}} and the last term is {{{-10}}} where the coefficients are 3 and -10 respectively.


Now multiply the first coefficient 3 and the last coefficient -10 to get -30. Now what two numbers multiply to -30 and add to the  middle coefficient -13? Let's list all of the factors of -30:




Factors of -30:

1,2,3,5,6,10,15,30


-1,-2,-3,-5,-6,-10,-15,-30 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -30

(1)*(-30)

(2)*(-15)

(3)*(-10)

(5)*(-6)

(-1)*(30)

(-2)*(15)

(-3)*(10)

(-5)*(6)


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



Now which of these pairs add to -13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -13


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-30</td><td>1+(-30)=-29</td></tr><tr><td align="center">2</td><td align="center">-15</td><td>2+(-15)=-13</td></tr><tr><td align="center">3</td><td align="center">-10</td><td>3+(-10)=-7</td></tr><tr><td align="center">5</td><td align="center">-6</td><td>5+(-6)=-1</td></tr><tr><td align="center">-1</td><td align="center">30</td><td>-1+30=29</td></tr><tr><td align="center">-2</td><td align="center">15</td><td>-2+15=13</td></tr><tr><td align="center">-3</td><td align="center">10</td><td>-3+10=7</td></tr><tr><td align="center">-5</td><td align="center">6</td><td>-5+6=1</td></tr></table>



From this list we can see that 2 and -15 add up to -13 and multiply to -30



Now looking at the expression {{{3x^2-13x-10}}}, replace {{{-13x}}} with {{{2x+-15x}}} (notice {{{2x+-15x}}} adds up to {{{-13x}}}. So it is equivalent to {{{-13x}}})


{{{3x^2+highlight(2x+-15x)+-10}}}



Now let's factor {{{3x^2+2x-15x-10}}} by grouping:



{{{(3x^2+2x)+(-15x-10)}}} Group like terms



{{{x(3x+2)-5(3x+2)}}} Factor out the GCF of {{{x}}} out of the first group. Factor out the GCF of {{{-5}}} out of the second group



{{{(x-5)(3x+2)}}} Since we have a common term of {{{3x+2}}}, we can combine like terms


So {{{3x^2+2x-15x-10}}} factors to {{{(x-5)(3x+2)}}}



So this also means that {{{3x^2-13x-10}}} factors to {{{(x-5)(3x+2)}}} (since {{{3x^2-13x-10}}} is equivalent to {{{3x^2+2x-15x-10}}})




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     Answer:

So {{{3x^2-13x-10}}} factors to {{{(x-5)(3x+2)}}}