Final answer:
To factor the polynomial ab+4a+3b+12 by grouping, we can group the terms in pairs and factor out the greatest common factor in each pair. Then, factor out the common factor from both terms to get the factored form.
Step-by-step explanation:
To factor the polynomial ab+4a+3b+12 by grouping, we can group the terms in pairs.
Step 1: Factor out the greatest common factor in each pair. For the pair ab+4a, we can factor out a to get a(b+4). And for the pair 3b+12, we can factor out 3 to get 3(b+4).
Step 2: Now we have a(b+4) + 3(b+4). Notice that both terms have the common factor (b+4). We can factor it out to get (b+4)(a+3).
Therefore, the factored form of the polynomial ab+4a+3b+12 is (b+4)(a+3).