How do you factor #7x^2 + 11x - 30 = 0#?

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Answer 1 · 2016-05-04T20:20:55

Note that the integer factors of #-30# could be:

#6# and #-5#

#10# and #-3#

#15# and #-2#

#-6# and #5#

#-10# and #3#

#-15# and #2#

Remember "FOIL"? It implies that you will be multiplying the following:

#(7x pm A)(x pm B)#

#= 7x^2 pm stackrel("Useful Hint")overbrace(color(green)(7Bx pm Ax)) pm AB#

We will need to account for the following relationship:

#color(green)(7x*B + 1x*A = 11x)#,

which is the middle term based on the operation of the outer and inner terms in #(7x pm A)(x pm B)#. It looks like this works:

#7x*color(green)(3) + 1x*color(green)((-10)) = 11x#

Compare and see:

#7x*B + 1x*A" "" " = 11x#
#7x*3 + 1x*(-10) = 11x#

This means #B = 3# and #A = -10#. So, the answer would be:

#= color(blue)((7x - 10)(x + 3))#