The first step with this example is to factor out x2 from each term:

6x4 − 13x3 + 5x2 = x2(6x2 − 13x+ 5)

Using grouping method on the (6x2 − 13x + 5) part, we have:

So we are looking for 2 terms whose product is 30x2 and whose sum is −13x.

Those 2 terms are −10x and −3x.

So we can factor our trinomial as follows:

6x4 − 13x3 + 5x2

= x2(6x2 − 13x+ 5)

= x2[6x2 − 10x − 3x + 5]

= x2[(6x2 − 10x) − (3x − 5)]

= x2[2x(3x − 5) − (1)(3x − 5)]

= x2[(2x − 1)(3x − 5)]

= x2(2x − 1)(3x − 5)

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