Final answer:
To find the other factor, we set up an equation with the known factor and the other factor and then solve for x.
Step-by-step explanation:
To find the other factor of the given expression, we can use the fact that a factor of an expression will make the expression equal to zero when substituted in. In this case, if 7x−9 is a factor of 49x^2 −126x−81, then when 7x−9 is substituted into the expression, the result should be zero.
So, we can set up the equation: (7x−9)(other factor) = 49x^2 −126x−81 = 0.
Now, we can solve this equation to find the other factor. We can use the distributive property to expand the left side of the equation and then solve for x.
After expanding and simplifying, we get the equation 49x^2 − 126x − 81 = 0.
Then, we can use factoring, the quadratic formula, or completing the square to solve for x and find the other factor.