Question

factor completely 35x^2-45 x+10

Answer 1

First, you can take 5 out as a factor as each of those things are divisible by 5.
That gives you, 5(7x^2 - 9x + 2)
Then you need to factorise the inner quadratic.
For that you need to have two brackets that look like (ax+b)(cx+d)
a and c need to multiply to give 7. b and d need to multiply to give 2. And ad + bc needs to give -9.
There are only two factors of 7 and those are 1 and 7 so a and c need to be 1 and 7.
That gives you (7x + b)(x + d).
Now you need to find b and d so that bd=2 and b+7d=-9.
There are only 4 factors of 2. 2 and 1 or -2 and -1. Seeing as the addition gives you a minus, you need to use -2 and -1. Then just put them into the brackets, trying either way until one works.
(7x - 1)(x - 2) gives you (7x^2 - 15x +2) so that isn't right.
(7x - 2)(x - 1) however gives you (7x^2 - 9x + 2). So that is the right combination.
That gives you as the final answer, 5(7x-2)(x-1).