(3x+2)(x+4)
FOIL - First Inside Outside Last
first 3x * x = 3x^2
Outside 3x * 4 = 12x
Inside 2 * x = =2x
Last 2 * 4 = 8
then add them all together
3x^2 + 12x + 2x + 8
= 3x^2 + 14x + 8
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and now to move onto the answers given above...
you can't find an answer (the answer is not 11 and it's not 13) also 1x = x not 1 since x is a number, it could be any number (e.g if x=10 1*10 is not 1)
if you were given the problem (3x+2)(x+4) = y, x = 2 find y then you could have an answer
(3*2 + 2)(2 + 4)
(6 + 2)(6)
8*6 = 48, y=48
or if you were given the problem (3x+2)(x+4) = 48 find x
then you'd do
(3x+2)(x+4) = 48
expand the brackets as above
3x^2 + 14x + 8 = 48
subtract 48 from each side
3x^2 + 14x + 8 - 48 = 0
simplify
3x^2 + 14x - 40 = 0
that's a quadratic equation
quadratic equations can be solved either by graphing the equation, and you find where the graph crosses 0 on the x axis
or by using the quadratic equation formula.
quadratic equations come in the form ax^2+bx+c = 0
the formula for solving them is
x = -b +- sqrt(b^2-4ac) / (2a)
(quadratic equations have two possible answers as a x^2 graphed is a curve that will intercept the x axis twice (unless x=0 then it'll only cross the x axis once at x=0))
in this case
x = -b +- sqrt(b^2-4ac) / (2a)
a = 3
b = 14
c = 40
x = [-14 +- sqrt(14^2 - 4*3*-40)] / 2*3
x = [-14 +- sqrt(196 - -480)] / 6
x = [-14 +- sqrt(196 + 480)] / 6
x = [-14 +- sqrt(676)] / 6
x = [-14 +- 26] / 6
so x = [-14 + 26] / 6 = 12/6 = 2
or x = [-14 - 26] / 6 = -40/6 = -6.66666(recurring)
Hopefully that'll have cleared it up for you...
