SOLUTION: Factorize 4x^2

SOLUTION: Factorize 4x^2 - 16x + 7

Question 1025602: Factorize 4x^2 - 16x + 7
Found 2 solutions by Timnewman, Theo:
Answer by Timnewman(323) (Show Source): You can put this solution on YOUR website!
Replace -16x by 2x-14x
4x�-16x+7=4x�+2x-14x+7
Group thr expression
=(4x�+2x)-(14x+7)
=2x(2x+1)-7(2x+1)
factor out
=(2x+1)(2x-7)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
start with 4x^2 - 16x + 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:

2x * 2x = 4x^2
2x * -1 = -2x
-7 * 2x = -14x
-7 * -1 = 7

combine like terms and you get 4x^2 - 16x + 7.

since this is your original expression, the factors are good.

the method used is called factoring by grouping or factoring by splitting the middle term.

here's a reference.

http://www.regentsprep.org/regents/math/algtrig/atv1/revfactorgrouping.htm

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