Question

find the factorization of the polynomial 49x^2+70x+25

Answer 1

Are you familiar with the Rational Roots theorem?

Answer 2

no

Answer 3

You find c/d. C is all the multiples of 25. Those are +/-1, +/-5, +/-25. Then you find D which is all the multiples of 49. Those are +/-1, +/-7, +/-49. C/d then is all of those and then the fractions they make, with c on top and d in the denominator. Like this:\[\pm1, \pm5 \pm25, \pm7, \pm49, \pm \frac{ 5 }{ 7 }, \pm \frac{ 5 }{ 49 }, \pm \frac{ 25 }{ 7 }, \pm \frac{ 25 }{ 49 }\]

Answer 4

You test each one of them using synthetic division. The best ones to try first do NOT involve fractions. We will try x-1 first, which is actually x-1=0, so if it's a factor, the first root will be x = 1. So let's try -1 first. I will show you how: