How do you long divide 3x^4 - x^3 - 3x^2 + 7x - 12 div x^2 - 43x4−x3−3x2+7x−12÷x2−4?

1 Answer
David G.
Jan 31, 2016

This is tricky to lay out by typing it, so I have hand written it and posted a photo below. The approach is exactly the same as 'normal' long division with numbers.

Explanation:

The tricky bit with this one is that there is an x^2x2 term and a constant (number) term in the divisor, but no xx term. This leads to 'gaps' in the long division, as you will see in the image below.

I first knew I would need 3x3x 'lots' of the divisor, x^2-4x2−4, to make up the first term, 3x^43x4. That yielded 3x^4 - 12x^23x4−12x2, but no x^3x3 term. Subtracting this from the original expression yielded 9x^29x2, then I brought down the untouched -x^3−x3 term to join it.

It took -x−x times the divisor to match this -x^3 term, and this yielded -x^3 - 4x−x3−4x.

I won't walk through the rest of the calculation as slowly as I have so far, but hopefully the image will make it clear.

Apologies for the quality of the image.

enter image source here

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