Question 125882


Looking at {{{1x^2+3x-18}}} we can see that the first term is {{{1x^2}}} and the last term is {{{-18}}} where the coefficients are 1 and -18 respectively.


Now multiply the first coefficient 1 and the last coefficient -18 to get -18. Now what two numbers multiply to -18 and add to the  middle coefficient 3? Let's list all of the factors of -18:




Factors of -18:

1,2,3,6,9,18


-1,-2,-3,-6,-9,-18 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -18

(1)*(-18)

(2)*(-9)

(3)*(-6)

(-1)*(18)

(-2)*(9)

(-3)*(6)


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



Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-18</td><td>1+(-18)=-17</td></tr><tr><td align="center">2</td><td align="center">-9</td><td>2+(-9)=-7</td></tr><tr><td align="center">3</td><td align="center">-6</td><td>3+(-6)=-3</td></tr><tr><td align="center">-1</td><td align="center">18</td><td>-1+18=17</td></tr><tr><td align="center">-2</td><td align="center">9</td><td>-2+9=7</td></tr><tr><td align="center">-3</td><td align="center">6</td><td>-3+6=3</td></tr></table>



From this list we can see that -3 and 6 add up to 3 and multiply to -18



Now looking at the expression {{{1x^2+3x-18}}}, replace {{{3x}}} with {{{-3x+6x}}} (notice {{{-3x+6x}}} adds up to {{{3x}}}. So it is equivalent to {{{3x}}})


{{{1x^2+highlight(-3x+6x)+-18}}}



Now let's factor {{{1x^2-3x+6x-18}}} by grouping:



{{{(1x^2-3x)+(6x-18)}}} Group like terms



{{{x(x-3)+6(x-3)}}} Factor out the GCF of {{{x}}} out of the first group. Factor out the GCF of {{{6}}} out of the second group



{{{(x+6)(x-3)}}} Since we have a common term of {{{x-3}}}, we can combine like terms


So {{{1x^2-3x+6x-18}}} factors to {{{(x+6)(x-3)}}}



So this also means that {{{1x^2+3x-18}}} factors to {{{(x+6)(x-3)}}} (since {{{1x^2+3x-18}}} is equivalent to {{{1x^2-3x+6x-18}}})




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     Answer:

So {{{x^2+3x-18}}} factors to {{{(x+6)(x-3)}}}