Question

How do you factor completely `45t^4 - 90t^3 + 25t^2`?

Answer 1

Just to clarify what the other contributor was saying...

Explanation:

Factor out the GCF.

`5t^2(9t^2 - 18t + 5)`

The expression inside the parentheses can be factored as a trinomial of the form `y = ax^2 + bx + c, a != 1`. To do this, we must find two numbers that multiply to `a xx c` and that add to b, and then follow the following process. Two numbers that do this are -15 and -3.

`5t^2(9t^2 - 3t - 15t + 5)`

`5t^2(3t(3t - 1) - 5(3t - 1))`

`5t^2(3t - 5)(3t - 1)`

This is completely factored.

Hopefully this helps!