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How to factor completely 70x^4-68x^3+16x^2?

+1 vote
I am having a hard time getting past the first step after factoring the greatest common factor.
I need some help, show step by step please.

Thanks in advance!
asked Jan 21, 2013 in GEOMETRY by linda Scholar

2 Answers

+2 votes

70x4 - 68x3 + 16x2

Take out common factors ' 2x2 '

2x2(35x2 - 34x + 8)

2x2(35x2 - 14x - 20x + 8)                   {35*8 = 280  ,  14*20 = 280 and -14-20 = -34}

Take out common factors.

2x2[ 7x(5x - 2) - 4(5x - 2) ]

Take out common factors.

2x2[ (7x - 4 ) ( 5x - 2 ) ]

answered Jan 22, 2013 by richardson Scholar
0 votes

First you have to take out the greatest common factor, which is 2x^2.

2x^2(35x^2 - 34x + 8)

Then you have to factor the trinomial. To do this, first you have to find the factors of 35*8 (which is 280) that add up to -34. The factors are -14 and -20. Now you have to break the middle term up into two terms using the pair of factors as the coefficients.

2x^2(35x^2 - 20x - 14x + 16)

Now you have to factor by grouping.

2x^2[5x(7x - 4) - 2(7x - 4)

= 2x^2(7x - 4)(5x - 2)

source: http://answers.yahoo.com

answered May 14, 2013 by Naren Answers Apprentice

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