2x^3+7x^2-18x-63
To simplify the expression 2x^3 + 7x^2 - 18x - 63, we can combine like terms:
Step 1: Group the terms with the same exponent:
(2x^3 + 7x^2) - (18x + 63)
Step 2: Factor out the greatest common factor from each group of terms:
x^2(2x + 7) - 9(2x + 7)
Step 3: Notice that both groups have a common factor of (2x + 7). Factor it out:
(2x + 7)(x^2 - 9)
Step 4: Simplify the expression further. Notice that x^2 - 9 is a difference of squares and can be factored further as (x - 3)(x + 3):
(2x + 7)(x - 3)(x + 3)
So the simplified form of the expression 2x^3 + 7x^2 - 18x - 63 is (2x + 7)(x - 3)(x + 3).
The given expression is 2x^3 + 7x^2 - 18x - 63. To simplify or solve this expression, we can follow the steps below:
Step 1: Group and factor common factors (if possible)
Look for any common factors in the expression. In this case, we don't have any common factors among all the terms. So, we move on to the next step.
Step 2: Check for any factorization patterns
Let's check if this expression can be factored using any factorization techniques. Unfortunately, the given expression cannot be easily factored by common factorization methods such as the GCF (Greatest Common Factor) method, the difference of squares, or perfect square trinomials.
Step 3: Use synthetic division or long division (if necessary)
If the expression does not factor easily, we can use synthetic division or long division to find the roots of the expression. However, it seems like you didn't specify that you're looking for the roots of this expression. So, let's move to the next step.
Step 4: Simplify or Evaluate the expression
If you are simply looking to simplify or evaluate the expression for a specific value of x, you can directly substitute the value of x into the expression and calculate the result. For example, if you want to evaluate the expression at x = 2, you can substitute x = 2 into the expression as follows:
2(2)^3 + 7(2)^2 - 18(2) - 63
= 2(8) + 7(4) - 36 - 63
= 16 + 28 - 36 - 63
= -55
So, when x = 2, the value of the expression 2x^3 + 7x^2 - 18x - 63 is -55.
If you have any other specific instructions or requirements for this expression, please let me know, and I'll be happy to assist you further.