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

Question

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!

Answer 1

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 ) ]

Answer 2

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)

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