# Long Division

Discussion in 'Algebra' started by nycmathguy, Feb 27, 2022.

1. ### nycmathguy

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nycmathguy, Feb 27, 2022

2. ### MathLover1

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$$f(x)=x^3-4x^2-5$$

find $$f(x) /(x-3)$$

________($$x^2-x-3$$
$$(x-3)| x^3-4x^2+0*x-5$$
......... $$x^3-3x^2$$ .................subtract
................. $$-x^2+0*x$$ ........................bring down +$$0*x$$
.................$$-x^2+3x$$..subtract
......................... $$-3x$$ .............bring down $$-5$$
.........................$$-3x-5$$
.........................$$-3x+9$$ .......subtract
..............................$$-14 -$$>reminder

=> $$f(x) /(x-3)=x^2-x-3+(-14/(x-3))$$

or,

$$x^3 - 4 x^2 - 5 = (x^2 - x - 3)(x - 3) -14$$

MathLover1, Feb 27, 2022
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3. ### nycmathguy

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Sorry but I could not follow your steps. Can you do this one on paper and then upload?

nycmathguy, Feb 27, 2022
4. ### MathLover1

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steps in one example:

Step 1: Set up the long division.
Step 2: Divide 1st term of dividend by first term of divisor to get first term of the quotient.
Step 3: Take the term found in step 2 and multiply it times the divisor.
Step 4: Subtract this from the line above.
Step 5: Repeat until done.
Step 6: Write out the answer.

or

MathLover1, Feb 27, 2022
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