Andrew factored the expression 54x^3-30x^2+15x as 5x(9x^2-6x+3) but when Melissa applied the distributive law and multiplied out 5x(9x^2-6x+3). she got 45x^3-30x^2+15x. thus andrew's solution does not appear to check. why is this? eplain your reasoning and correctly factor the original expression if possible.If the expression is a prime state so

What is your exspresion?

54x^3-30x^2+15x
OR
45x^3-30x^2+15x

54x^3-30x^2+15x=3x*(18x^2-10x+5)

45x^3-30x^2+15x=15x*(3x^2-2x+1)

Andrew made a mistake when factoring the expression. Let's go through the correct factoring process to understand what went wrong and find the correct solution.

To factor the expression 54x^3 - 30x^2 + 15x, we can look for the greatest common factor (GCF) of the terms. In this case, the GCF is 3x, which we can factor out:

54x^3 - 30x^2 + 15x = 3x(18x^2 - 10x + 5)

Now, we have factored out the common term 3x correctly. However, Andrew's mistake lies in the factoring of the quadratic expression 18x^2 - 10x + 5.

Andrew incorrectly factored it as 9x^2 - 6x + 3, but the correct factorization should be different. Let's find the correct factors of the quadratic expression.

To factorize a quadratic expression like 18x^2 - 10x + 5, we need to look for two numbers whose product is equal to the product of the coefficient of x^2 (18) and the constant term (5), which in this case is 90. Additionally, these two numbers should add up to the coefficient of x (-10).

By trial and error or using the quadratic formula, we can find that the correct factors are: (6x - 5) and (3x - 1):

So, the correct factorization of the expression 54x^3 - 30x^2 + 15x is:

54x^3 - 30x^2 + 15x = 3x(6x - 5)(3x - 1)

Now, since we have correctly factored the expression, we can say that it is not a prime state since it can be written as the product of multiple factors.