Answer
$30x^2-35x+10 = (5)~(2x-1)~(3x-2)$
Work Step by Step
Let's consider a trinomial in this form: $~ax^2+bxy+cy^2$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = a\times c$
Then the next step is to write the trinomial as follows:
$~x^2+bxy+cy^2 = ax^2+rxy+sxy+cy^2$
Let's consider this trinomial: $~30x^2-35x+10$
First we can factor by using the GCF:
$30x^2-35x+10 = (5)~(6x^2-7x+2)$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = -7$ and $r\times s = 12$. We can see that $(-4)+(-3) = -7~$ and $(-4)\times (-3) = 12$
We can factor the trinomial as follows:
$30x^2-35x+10 = (5)~(6x^2-7x+2)$
$30x^2-35x+10 = (5)~(6x^2-4x-3x+2)$
$30x^2-35x+10 = (5)~[~(6x^2-4x)+(-3x+2)~]$
$30x^2-35x+10 = (5)~[(2x)(3x-2)+(-1)(3x-2)]$
$30x^2-35x+10 = (5)~(2x-1)~(3x-2)$
