You can put this solution on YOUR website! To factor , we first notice that all of the coefficients are divisible by 7, so we factor 7 out of each term:
There are no other common factors of the coefficients. Now we need to find two numbers whose product is (16)(49) = 784 and whose sum is 56. Let's write out some possible ways to factor 784 and look at the sum of the factors:
(1)(784) sum = 785
(2)(392) sum = 394
(4)(196) sum = 200
(7)(112) sum = 119
(8)(98) sum = 106
(14)(56) sum = 70
(16)(49) sum = 65
(28)(28) sum = 56 <--- this works!
So we've found our combination. We can rewrite the quadratic expression using these two factors:
Now we can factor the quadratic by grouping. The greatest common factor of and is , so we factor that out of the first two terms:
The greatest common factor of and is , so we factor this out of the last two terms:
Now we factor out of both terms:
This completes the factorization.
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