Question 191471


Looking at {{{3x^2-20x-7}}} we can see that the first term is {{{3x^2}}} and the last term is {{{-7}}} where the coefficients are 3 and -7 respectively.


Now multiply the first coefficient 3 and the last coefficient -7 to get -21. Now what two numbers multiply to -21 and add to the  middle coefficient -20? Let's list all of the factors of -21:




Factors of -21:

1,3,7,21


-1,-3,-7,-21 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -21

(1)*(-21)

(3)*(-7)

(-1)*(21)

(-3)*(7)


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



Now which of these pairs add to -20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -20


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-21</td><td>1+(-21)=-20</td></tr><tr><td align="center">3</td><td align="center">-7</td><td>3+(-7)=-4</td></tr><tr><td align="center">-1</td><td align="center">21</td><td>-1+21=20</td></tr><tr><td align="center">-3</td><td align="center">7</td><td>-3+7=4</td></tr></table>



From this list we can see that 1 and -21 add up to -20 and multiply to -21



Now looking at the expression {{{3x^2-20x-7}}}, replace {{{-20x}}} with {{{x-21x}}} (notice {{{x-21x}}} combines to {{{-20x}}}. So it is equivalent to {{{-20x}}})


{{{3x^2+highlight(x-21x)-7}}}



Now let's factor {{{3x^2+x-21x-7}}} by grouping:



{{{(3x^2+x)+(-21x-7)}}} Group like terms



{{{x(3x+1)-7(3x+1)}}} Factor out the GCF of {{{x}}} out of the first group. Factor out the GCF of {{{-7}}} out of the second group



{{{(x-7)(3x+1)}}} Since we have a common term of {{{3x+1}}}, we can combine like terms


So {{{3x^2+x-21x-7}}} factors to {{{(x-7)(3x+1)}}}



So this also means that {{{3x^2-20x-7}}} factors to {{{(x-7)(3x+1)}}} (since {{{3x^2-20x-7}}} is equivalent to {{{3x^2+x-21x-7}}})




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     Answer:

So {{{3x^2-20x-7}}} factors to {{{(x-7)(3x+1)}}}