Andrew factored the expression 28x©ø-6x©÷-10x as 2x(14x©ø-3x©÷-5x) . But when Melissa applied the distributive law and multiplied out 2x(14x©ø-3x©÷-5x), she got 28x©ù-6x©ø-10x©÷; thus, Andrew¡¯s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
I suppose this is
28 x^3 - 6 x^2 -10 x
= 2 x (14 x^2 - 3 x - 5) not 5 x
To understand why Andrew's solution does not appear to check, let's break down the steps he took during factoring and compare it with Melissa's application of the distributive law.
Andrew's factoring step:
Expression: 28x©ø - 6x©÷ - 10x
Factor: 2x(14x©ø - 3x©÷ - 5x)
Melissa's application of the distributive law:
Expression: 2x(14x©ø - 3x©÷ - 5x)
Multiplication: 2x * 14x©ø + 2x * (-3x©÷) + 2x * (-5x)
Result: 28x©ù - 6x©ø - 10x©÷
As you can see, Melissa's result matches the original expression: 28x©ù - 6x©ø - 10x©÷. Therefore, her application of the distributive law appears to be correct.
However, it seems like there was a mistake or misunderstanding in Andrew's factoring step. Let's examine the factor he obtained: 2x(14x©ø - 3x©÷ - 5x).
To correctly factor the original expression, let's factor out the greatest common factor from the terms 28x©ø, -6x©÷, and -10x:
Expression: 28x©ø - 6x©÷ - 10x
The common factor for these terms is 2x, so we can factor it out:
Common factor: 2x
Expression with the common factor factored out: 2x * (14x©ø - 3x©÷ - 5x)
Now we have correctly factored the original expression as 2x * (14x©ø - 3x©÷ - 5x).
It's important to be careful with your calculations and factorization steps to ensure the correctness of the solution.