Polynomials- can you help me solve this two variable polynomial?

Question

Can you please help me solve this polynomial below

12m^2n2^ – 8mn + 1

Answer 1

12m²n² - 8mn + 1

This factors just like any other polynomial the exception is there are two variables instead of the usual single variable. But don't let that throw you off, just follow the same procedure you would with a single variable.

the answer will be of the form:

(a₁mn - c₁) (a₂mn - c₂)

so that you end up with

(a₁*a₂)*m²n² - (a₁c₂ + a₂c₁) mn + (c₁*c₂)

for the "a" terms you know they have to be factors of 12 so: 1 and 12, 2 and 6, or 3 and 4 are your options

the only factor of 1 is 1 and that means c₁ = c₂ = 1

1*a₂ + 1*a₁ = 8

the only option is 6 and 2

so your answer is:

(6mn - 1)(2mn - 1) = 0

multiply it back out to check

12m²n² - 2mn - 6mn + 1 = 0