If one of the factors of #6x^2+ 11x +3# is #2x +3#, what is the other factor?

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Answer 1 · 2017-08-07T02:59:19

You know that the other factor is of the form:

#ax+b#

Because, if it were #(ax-b)#, there would be at least one minus sign in the product.

You know that the first terms multiplied together must equal 6:

#2a = 6#

#a = 3#

Similarly, we know that last terms multiplied together must equal 3:

#3b = 3#

#b = 1#

Therefore, other factor is #3x+1#

Check:

#(3x+1)(2x+3) = 6x^2+9x+2x+3#

#(3x+1)(2x+3) = 6x^2+11x+3#

This checks.