Andrew factored the expression 28x^3-42x^2+35x as 7x(4x^2+6x-5). But when Melissa applied the distributive law and multiplied out 7x(4x^2+6x-5) , she got 28x^3+42x^2-35x ; 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.
Can someone please help me with this question.
The negative sign is misplaced, and must go before the 6x instead of the 5, making the correct factor:
7x(4x^2-6x+5)
Certainly! Let's break down the process of factoring and multiplying to understand why Andrew's solution does not seem to check.
Andrew factored the expression 28x^3-42x^2+35x as 7x(4x^2+6x-5).
Now, let's multiply out 7x(4x^2+6x-5) to see if it matches the original expression:
7x * 4x^2 = 28x^3
7x * 6x = 42x^2
7x * -5 = -35x
When we add these terms together, we get 28x^3+42x^2-35x, which matches Melissa's result, not the original expression.
The mistake Andrew made was not distributing the 7x to each term inside the parentheses correctly. To correctly factor the original expression, let's go step by step:
First, we can factor out the greatest common factor, which is 7x:
28x^3-42x^2+35x = 7x(4x^2-6x+5)
Now, we can see that the expression inside the parentheses does not have a common factor that can be factored further. Therefore, the fully factored form is:
7x(4x^2-6x+5)
And that is the correct factorization of the original expression.
It's important to be careful when applying the distributive law to ensure that each term inside the parentheses is multiplied by the factor outside correctly.