Final answer:
To divide 12 into two parts with a product of 35, set up a quadratic equation with x and 12-x as the parts. Factoring the equation x^2 - 12x + 35 = 0 yields the parts as 7 and 5.
Step-by-step explanation:
To divide 12 into two parts such that the product of the two parts is 35,
we let one part be x and the other part be 12 - x.
Setting up the equation, we have x(12 - x) = 35.
This is a simple quadratic equation that we can solve.
First, we expand the equation: x(12 - x) = 12x - x2 = 35.
To solve the quadratic equation, we set it to zero: x2 - 12x + 35 = 0.
Factoring the quadratic equation gives us: (x - 7)(x - 5) = 0.
Therefore, the two solutions for x are 7 and 5.
This means the two parts we are dividing 12 into are 7 and 5.