Question 147539


Looking at {{{4x^2+7x-2}}} we can see that the first term is {{{4x^2}}} and the last term is {{{-2}}} where the coefficients are 4 and -2 respectively.


Now multiply the first coefficient 4 and the last coefficient -2 to get -8. Now what two numbers multiply to -8 and add to the  middle coefficient 7? Let's list all of the factors of -8:




Factors of -8:

1,2,4,8


-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -8

(1)*(-8)

(2)*(-4)

(-1)*(8)

(-2)*(4)


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



Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-8</td><td>1+(-8)=-7</td></tr><tr><td align="center">2</td><td align="center">-4</td><td>2+(-4)=-2</td></tr><tr><td align="center">-1</td><td align="center">8</td><td>-1+8=7</td></tr><tr><td align="center">-2</td><td align="center">4</td><td>-2+4=2</td></tr></table>



From this list we can see that -1 and 8 add up to 7 and multiply to -8



Now looking at the expression {{{4x^2+7x-2}}}, replace {{{7x}}} with {{{-1x+8x}}} (notice {{{-1x+8x}}} adds up to {{{7x}}}. So it is equivalent to {{{7x}}})


{{{4x^2+highlight(-1x+8x)+-2}}}



Now let's factor {{{4x^2-1x+8x-2}}} by grouping:



{{{(4x^2-1x)+(8x-2)}}} Group like terms



{{{x(4x-1)+2(4x-1)}}} Factor out the GCF of {{{x}}} out of the first group. Factor out the GCF of {{{2}}} out of the second group



{{{(x+2)(4x-1)}}} Since we have a common term of {{{4x-1}}}, we can combine like terms


So {{{4x^2-1x+8x-2}}} factors to {{{(x+2)(4x-1)}}}



So this also means that {{{4x^2+7x-2}}} factors to {{{(x+2)(4x-1)}}} (since {{{4x^2+7x-2}}} is equivalent to {{{4x^2-1x+8x-2}}})




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     Answer:

So {{{4x^2+7x-2}}} factors to {{{(x+2)(4x-1)}}}