You can put this solution on YOUR website! Replace -16x by 2x-14x
4x²-16x+7=4x²+2x-14x+7
Group thr expression
=(4x²+2x)-(14x+7)
=2x(2x+1)-7(2x+1)
factor out
=(2x+1)(2x-7)
multiply the coefficient of the x^2 term by the constant term to get 4 * 7 = 28
if the x term is negative and the constant term is positive, you are looking for factors that will add up to - 16 and will be equal to + 7 when multiplied together.
they need to be added together because a negative plus a negative gives you a negative x term and a negative times a negative gives you a positive constant term.
look for factors of 28 that will add up to 16.
1 * 28 is no good.
2 * 14 is good because 2 + 14 = 16.
your middle term factors can be split up into -2x and -14x.
split the middle term to get 4x^2 - 2x - 14x + 7 = 0
your equation is set equal to 0 in order to get it into standard form for factoring.
group the first two term and the last two terms together to get:
(4x^2 - 2x) - (14x - 7) = 0
the grouping of the second set of terms can get tricky with the minus sign, but keep in mind that:
-14x + 7 is equal to -1 * (14x - 7) which is equal to - (14x - 7).
you now have (4x^2 - 2x) - (14x - 7) = 0
factor out 2x from the first set of terms and factor out 7 from the second set of terms to get:
2x * (2x - 1) - 7 * (2x - 1) = 0
the objective here is to factor out so you have 2 common termsthat can then be factored out.
in this case, the common terms are (2x - 1).
factor out the common term of (2x - 1) to get:
(2x - 7) * (2x - 1) = 0
those are your factors.
when you multiply them together, you will get 4x^2 - 16x + 7 as shown below:
