Andrews factored expressions
-6x63+9x^2-3x as -3x(2x^2-3x-1). But when Melissa applied the distrubutive law and multiplied out -3x(2x62-3x-1) she got -6x^3+9x^2+3x;thus Andrews solution does not appear to check. Why is that? Please help Andrews to understand this better, explain yout reasoning and correctly factor the orginal expression. If possible, if expression is prime, state this.
The # 1 inside the parenthesis should be
positive.
To understand why Andrew's factored expression doesn't seem to be correct, let's go through the process step by step.
The original expression is:
-6x^3 + 9x^2 - 3x
Andrew factored it as:
-3x(2x^2 - 3x - 1)
Now, let's multiply out the factored expression using the distributive property:
-3x(2x^2 - 3x - 1) = -3x * 2x^2 + (-3x) * (-3x) + (-3x) * (-1)
This simplifies to:
-6x^3 + 9x^2 + 3x
So, both Melissa's multiplication and the original expression result in -6x^3 + 9x^2 + 3x. Therefore, Andrew's factored expression appears to be correct.
Now, let's correctly factor the original expression:
-6x^3 + 9x^2 - 3x
First, let's factor out the greatest common factor, which is -3x:
-3x(2x^2 - 3x + 1)
The quadratic expression 2x^2 - 3x + 1 cannot be factored further, so we can say that the fully factored expression is:
-3x(2x^2 - 3x + 1)
If the expression cannot be factored further, we can say that it is a prime expression.
So, in conclusion, Andrew's solution does indeed check out, and the correctly factored expression is -3x(2x^2 - 3x + 1).