Question

How do i factor these

Answer 1

\[\frac{ 3t^2+5t+2 }{ 4t^2-4t+1 }\]

Answer 2

One at a time?

Numerator
(3t + ____)(t + ____)

Denominator
()()

Answer 3

Similar to factoring any quadratic. The twist here is you can factor them by doing what my math teacher called "factoring by grouping".
The quadratic is in the form ax^2+bx+c. Multiply a and c. For the denominator this is 6. Then you can continue normally. Two numbers that multiply to +6 and add to +5. This one's easy, the numbers are 3 and 2. You can then put this into the quadratic like so;\[3t ^{2} + 3t + 2t + 2\]
You can see that the 3t and 2t add to 5t, so the eqaution still maintains the same value. Then you can group like terms.
You can see that the factors in the brackets are the same, so you've grouped correctly. Then you just factor the like terms. This leaves \[(3t + 2)(t+1)\] Do the same for the denominator, then cancel the facotrs out if at all possible.