Factoring polynomials with a 2nd degree coefficient greater than $1$ I'm learning how to factor polynomials, but I'm having a hard time understanding the approach when the 2nd degree coefficient is greater than $1$.
For example, when I begin to factor $12k^4 + 22k^3 - 70k^2$, I first break it down to $2k^2(6k^2 + 11k - 35)$.
I would think that I'd want to find two numbers that sum up to $11$ and have a product of $-35$, but instead I'm told we need to multiply $-35$ by $6$ so that I now have to find two numbers that sum up to $11$ and have a product of $-210$.
Can anyone help me understand why $-35$ is multiplied by the coefficient $6$?  Why isn't $11k$ also multiplied by $6$?

We can factor your example as follows ,firslty,find roots of equation of $$6k^{ 2 }+11k-35=0\\ k=\frac { -11\pm 31 }{ 12 } =\frac { 5 }{ 3 } ,\frac { -7 }{ 2 } $$
so we can write it

$$2{ k }^{ 2 }\left( 6\left( k-\frac { 5 }{ 3 }  \right) \left( k+\frac { 7 }{ 2 }  \right)  \right) =2{ k }^{ 2 }\left( 3k-5 \right) \left( 2k+7 \right) $$

