Could you please help me factor the trinomial.
s^2-7s+12
s^2-7s+12
Since the coefficient of s^2 is 1, the factors are of the form (s+/-?)(s+/-?)
What two numbers have a sum of 7 and a product of 12?
Clearly, 3 and 4.
SInce the sum is -7 and the product is +12, the only possibility is (s - 3)(s - 4)
Of course! To factor a trinomial like s^2 - 7s + 12, we need to look for two numbers that multiply to give the constant term (which is 12 in this case) and add up to the coefficient of the middle term (which is -7 in this case).
In this trinomial, the coefficient of the squared term is 1, so we have s^2.
To find the factors of 12, we can start by listing all possible pairs of factors: (1, 12), (2, 6), and (3, 4).
Now we need to determine which pair of factors satisfies the condition of adding up to -7. In this case, the pair (3, 4) satisfies this condition because 3 + 4 = 7.
Next, we will rewrite the middle term, -7s, as the sum of two terms using the factors we found: -3s and -4s.
Now we can rewrite the trinomial by splitting the middle term:
s^2 - 3s - 4s + 12.
Notice that we grouped the terms into pairs: (s^2 - 3s) and (-4s + 12).
Now we can factor each group separately:
s(s - 3) - 4(s - 3).
As you can see, both groups have the same binomial, (s - 3). We can now factor out this common binomial:
(s - 3)(s - 4).
So, the factored form of the trinomial s^2 - 7s + 12 is (s - 3)(s - 4).