how do you factor four term polynomials?

Question

6q2-5pq-6q+5p

i factored and i got (6q-5p)(q-1) then got stuck.

how do i solve the whole equation?

Answer 1

To solve an equation of n number of variables, you need n number of unique equations. Furthermore, an equation must have an equality or inequality symbol somewhere. Your expression does not have such a symbol, therefore it is not an equation. Since you only have one expression and two variables (p and q), you cannot solve for the variables.

As for factoring, there are several ways you could choose to factor it. One way would be to factor 6q out of the 6q² and -6q terms, and -5p out of the -5pq and 5p terms. This would give:

6q(q - 1) - 5p(q - 1).

As you've indicated, this further factors into

(q - 1)(6q - 5p)

via group factoring.

Without anymore information (such as a second equation, values for p or p, and/or an equality/inequality symbol), nothing more can be done with this expression.