Question

How do you factor completely 3xy – 4x + 6y – 8 ?

Answer 1

Hint: We can see that there are 2 variables x and y , we can see that there is one x in the first 2 terms of the given equation , so we can take that common. And then we can take 2 common from the last 2 terms of the given equation.

Complete step-by-step answer:
The given equation in the question is 3xy – 4x + 6y – 8
We can take x common from the first 2 terms of the equation and 2 common from last 2 terms of the equation
So we can write 3xy – 4x + 6y – 8 = x ( 3y – 4 ) + 2 ( 3y – 4 )
Now we can take 3y – 4 common from the equation
By taking 3y – 4 common form the equation we get 3xy – 4x + 6y – 8 = ( x + 2) ( 3y – 4 )
So ( x + 2) ( 3y – 4 ) is the factor form of 3xy – 4x + 6y – 8 .

Note: The factor form of any equation is very helpful to find the root of the equation. If a number b satisfies any polynomial equation f( x ) we can say that x – a is a factor of f( x ) . Let’s assume a, b, and c are roots of a cubic equation f (x) where leading coefficient is 1 then we can write $f\left( x \right)=\left( x-a \right)\left( x-b \right)\left( x-c \right)$