SOLUTION: I am having difficulty in understanding the concept of factoring polynomials. I am having trouble with several problems, so I think the difficulty lies in the lack of understanding

Question 32316This question is from textbook Beginning Algebra
: I am having difficulty in understanding the concept of factoring polynomials. I am having trouble with several problems, so I think the difficulty lies in the lack of understanding on my part of factoring. I have a problem from the Fourth Edition of Beginning Algebra by K. Elayn Martin-Gay by Pearson, Prentice Hall. Here is a couple of the problems that I am having difficulty with. I hope that you are able to help me understand them. Thank you!
These actual problems are from a worksheet from class. The instructions state:
Factor each trinomial. Be sure to "FOIL" your answer and check the middle term when trying number combinations.
1). 7x^2 - 18x + 8 =
(7x - 4) (x - 14) = This is where I get lost.
2). 5x^2 - 9x + 1 =
(5x - ? ) (x - ? ) = Since no two factors equal 9, I'm confused and don't
know how to even begin this one.
3). 7x^2 - 8x + 1 =
(7x - 7) (x - 1) =
I can't seem to get any further with these problems. Hope you can help me. Thank you. This question is from textbook Beginning Algebra

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE THE FOLLOWING EXAMPLE AND TRY..IF STILL IN DIFFICULTY PLEASE COME BACK
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How do you factor trinomials? like 3t^2+16t+5
1 solutions
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Answer 18914 by venugopalramana(1323) on 2006-04-04 10:48:40 (Show Source):
3t^2+16t+5...
IF THERE ARE REAL FACTORS ,WE CAN USE THE FOLLOWING METHOD..
TAKE COEFFICIENT OF X^2..=3
TAKE CONSTANT TERM...=5
FIND THEIR PRODUCT...=3*5=15
FIND 2 FACTORS FOR THE ABOVE PRODUCT SO THAT THEIR SUM IS EQUAL TO THE COEFFICIERNT OF X TYERM....=16
PRODUCT =15...FACTORS ARE 1*15 AND...3*5
WE FIND 1+15=16...SO SPLIT X TERMS AS PER THE FACTORS..THAT IS...
3T^2+1T+15T+5...TAKE COMMON FACTORS OUT...
= T(3T+1)+5(T+3)=(T+5)(3T+1)..IS THE ANSWER.

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