Using factoring by grouping, how would you factor these out.
4t^2+3t-4t-3
3t^2-1t-3t+1
To factor using the factoring by grouping method, follow these steps:
For the expression 4t^2 + 3t - 4t - 3:
Step 1: Group the terms into pairs.
(4t^2 + 3t) - (4t + 3)
Step 2: Find the greatest common factor (GCF) of each pair separately.
For the first pair (4t^2 + 3t), the GCF is t: t * (4t + 3)
For the second pair (4t + 3), the GCF is 1: 1 * (4t + 3)
Step 3: Now, notice that both pairs have a common factor of (4t + 3). Therefore, you can factor it out.
(4t + 3)(t - 1)
The factored form of 4t^2 + 3t - 4t - 3 is (4t + 3)(t - 1).
For the expression 3t^2 - 1t - 3t + 1:
Step 1: Group the terms into pairs.
(3t^2 - 1t) - (3t - 1)
Step 2: Find the greatest common factor (GCF) of each pair separately.
For the first pair (3t^2 - 1t), the GCF is t: t * (3t - 1)
For the second pair (3t - 1), the GCF is 1: 1 * (3t - 1)
Step 3: Now, notice that both pairs have a common factor of (3t - 1). Therefore, you can factor it out.
(3t - 1)(t - 1)
The factored form of 3t^2 - 1t - 3t + 1 is (3t - 1)(t - 1).