-6q^2 -40q - 50 how do you solve this i am factoring and having problems
Use the quadratic formula
(40 +/- sqrt((-40)^2 - 4(-6)(-50) ))/(2(-6))
what ever that comes out to be
-6q^2 - 40q -50.
Factor using the AC method:
-2(3q^2 + 20q + 25)
A*C = 3*25 = 75 = 5*15.
Replace 20q with 5q + 15q:
-2(3q^2 +5q+15q + 25).
Group the 4 terms in pairs that can
be factored:
-2(3q^2+15q + 5q+25).
Factor the 2 pairs:
-2(3q(q+5) + 5(q+5).
Factor out q+5:
-2((q + 5) (3q + 5)).
To factor the quadratic expression -6q^2 - 40q - 50, we can follow these steps:
Step 1: Look for a common factor (if any)
At first glance, we can see that all the coefficients (the numbers in front of the variables) are divisible by 2. Let's factor out the greatest common factor (GCF), -2, from the expression:
-2(3q^2 + 20q + 25)
Step 2: Check if it is a perfect square trinomial
Next, let's check if the trinomial within the parentheses can be factored as a perfect square. For this, we compare the middle term, 20q, with the square of half the coefficient of the last term, which is (25/2)^2 = 312.5.
Since 20q is not equal to 312.5, it is not a perfect square trinomial. We move on to the next step.
Step 3: Factor the trinomial
To factor the trinomial inside the parentheses, we need to find two binomials whose product equals the trinomial. The binomials will have the following form:
(ax + b)(cx + d)
In this case, the trinomial is 3q^2 + 20q + 25.
Let's find two numbers that multiply to give 3 * 25 = 75 and add up to give 20. The numbers 15 and 5 satisfy both requirements.
Therefore, we can write 3q^2 + 20q + 25 as:
(3q + 5)(q + 5)
Step 4: Combine the factored terms
Finally, we combine the factors from step 2 and step 3:
-2(3q + 5)(q + 5)
So, the factored form of -6q^2 - 40q - 50 is -2(3q + 5)(q + 5).
Remember to always check your answer by multiplying the factors to ensure you obtain the original expression.