### Video Transcript

Find the quotient of negative 43π₯ to the power of seven plus 12π₯ cubed minus six π₯ squared divided by π₯.

In order to answer this question, we need to divide each of the terms by π₯: negative 43π₯ to the power of seven divided by π₯, 12π₯ cubed divided by π₯, and negative six π₯ squared divided by π₯.

Using the fact that π₯ is the same as π₯ to the power of one along with our laws of indices, π₯ to the power of π divided by π₯ to the power of π equals π₯ to the power of π minus π helps us work out that negative 43π₯ to the power of seven divided by π₯ is equal to negative 43π₯ to the power of six.

In the same way, 12π₯ cubed divided by π₯ is equal to 12π₯ squared. And finally, negative six π₯ squared divided by π₯ is equal to negative six π₯. Putting these three terms back together gives us an answer of negative 43π₯ to the power of six plus 12π₯ squared minus six π₯.

This means that the quotient of negative 43π₯ to the seven plus 12π₯ cubed minus six π₯ squared divided by π₯ is negative 43π₯ to the power of six plus 12π₯ squared minus six π₯.

You will notice that the exponents or indices in our answer are one less than the exponents in the question. This is because we are dividing by π₯ or π₯ to the power of one. Had we been dividing by π₯ squared, we wouldβve reduced the exponents by two. And in the same way, dividing by π₯ cubed would reduce the exponents by three.