How do you write #7x^2+23x+6# in factored form?

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Answer 1 · 2015-09-15T13:46:56

#(x+3)(7x+2)#

Multiply the coefficients of #x^2 and the constant.

#+7 xx +6 = +42#

Find two numbers whose product (multiply) is #42# and whose sum (add) is #+23# (the middle coefficient).

#{: (bb"Pairs whose product is " 42," "" ",bb"Sums of the pairs"), (" "" "1xx42," "," "" "43),(" "" "2xx21," "," "" "23) :}#

STOP! We do not need to go any further.

Use these numbers to split the middle term

#7x^2+2x+21x+6#

Now factor by grouping:

#x(7x+2)+3(7x+2)#

#(x+3)(7x+2)#

Check the answer my multiplying (expanding).