Is it possible to factor $y= 35x^2 - 22x + 3$ ? If so, what are the factors?

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Answer 1 · 2016-05-10T21:48:02

$y=35x^2-22x+3=(5x-1)(7x-3)$

Use an AC method:

Find a pair of factors of $AC=35*3 = 105$ with sum $B=22$ .

The pair $15, 7$ works in that $15*7 = 105$ and $15+7=22$

Use this pair to split the middle term and factor by grouping:

$35x^2-22x+3$

$=35x^2-15x-7x+3$

$=(35x^2-15x)-(7x-3)$

$=5x(7x-3)-1(7x-3)$

$=(5x-1)(7x-3)$

Is it possible to factor y= 35x^2 - 22x + 3 y= 35x^2 - 22x + 3 ? If so, what are the factors?