Factor the trinomial.Factor completely.
s^2 + 3s – 28 = 4s^2 – 24
Is this correct?? Please and thank you.
no
(s + 7)(s - 4 )
To factor the given trinomial completely, let's first move all the terms to one side of the equation:
s^2 + 3s - 28 - 4s^2 + 24 = 0
Combining like terms:
-3s^2 + 3s - 4 = 0
Now let's try to factor this quadratic trinomial. Due to the negative coefficient of the first term, we need to find two numbers whose product is equal to the product of the first and last term and whose sum is equal to the coefficient of the middle term.
The product of -3 and -4 is 12, and the sum of the two numbers is 3. So, we can rewrite the middle term as follows:
-3s^2 + 3s - 4 = -3s^2 + 12s - 9s - 4
Grouping the terms:
(-3s^2 + 12s) + (-9s - 4) = 0
Factoring out the greatest common factor from each group:
-3s(s - 4) - 1(9s + 4) = 0
Now we have a common factor of (s - 4) between the two terms:
(s - 4)(-3s - 1) = 0
Thus, the factored form of the trinomial -3s^2 + 3s - 4 = 0 is (s - 4)(-3s - 1) = 0.