factor trinomial completely of the type ax^2+bx+c.
-9+18x^2+21x
I am not able to solve the solution since the steps are quite confusing any help is great.
To factor the trinomial -9+18x^2+21x, we can use a method called factoring by grouping. Here are the steps:
Step 1: Rearrange the terms in the trinomial so that the quadratic term (ax^2) comes first, the linear term (bx) comes second, and the constant term (c) comes last. In this case, we have 18x^2+21x-9.
Step 2: Find the greatest common factor (GCF) of the coefficients of the quadratic and linear terms. The GCF here is 3, because it divides evenly into 18 and 21.
Step 3: Factor out the GCF from the quadratic and linear terms. We get:
3(6x^2 + 7x - 3)
Step 4: Next, we have to factor the quadratic term inside the parentheses. This can be done by using the FOIL method or trial and error. In this case, the quadratic term can be factored as:
3(2x - 1)(3x + 3)
So the factored form of -9+18x^2+21x is:
3(2x - 1)(3x + 3)
You can always verify your answer by expanding the factored form back into the original trinomial to make sure you get the same expression.