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.
Variations of this same questions have appeared many times in the last few days.
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Andrew simply messed up, the correct factored answer is
7x(4x^2 - 6x + 5)
Sure! Let's analyze the situation step by step.
Andrew factored the expression 28x^3 - 42x^2 + 35x as 7x(4x^2 + 6x - 5). However, when Melissa applied the distributive law and multiplied out 7x(4x^2 + 6x - 5), she got 28x^3 + 42x^2 - 35x instead of the original expression. This discrepancy suggests that Andrew's solution is incorrect.
To understand the issue, let's review how to factor an expression:
1. Look for a common factor among all the terms in the expression. In this case, the common factor is 7x.
7x * ? = 28x^3 - 42x^2 + 35x
2. Divide each term of the expression by the common factor:
Dividing 28x^3 by 7x gives us 4x^2.
Dividing -42x^2 by 7x gives us -6x.
Dividing 35x by 7x gives us 5.
So far, our factored expression should look like:
7x(4x^2 - 6x + 5)
3. To proceed, we need to check if the expression inside the parentheses (4x^2 - 6x + 5) can be factored further. However, in this case, it cannot be factored further using real numbers.
Therefore, the correctly factored expression is:
7x(4x^2 - 6x + 5)
Now, let's verify if this factored form correctly expands using the distributive law:
7x(4x^2 - 6x + 5) = 28x^3 - 42x^2 + 35x
And as you can see, the expanded form matches the original expression, confirming the correctness of this factorization.