When directed to completely factor the polynomial 4x2y5-8xy3, a student wrote 2xy3(2xy3-4). When the teacher did not give the student full credit, the student complained because when his answer is multiplied out, the result is the original polynomial. What went wrong?

The student didn't fully factorize out the terms to the least factor. He only collected some like terms but there was still more to collect and that's why the Teacher didn't give him full credit

Step-by-step explanation:

The original polynomial is;

4x²y^(5) - 8xy³

Now, if we want to completely factor this properly, we have to do it to the barest minimum.

Thus;

4xy³ is common to both terms so we can bring them out;

4xy³(xy² - 2)

Now this complete factorization is different from the one the student gave which is 2xy³(2xy³ - 4)

Thus, the student at best has factorized but only partly as it has not been reduced to the least of like terms.

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step-by-step explanation: