Explanation Given: 2 x 3 − 10 x + x 4 − 25 x 2 − 5 Key concept applied: Step 1: Set up the long division. The divisor (what we are dividing by) goes on the outside of the box. The dividend (what we are dividing into) goes on the inside of the box. When you write out the dividend and divisor, make sure that you insert 0's for any missing terms. Step 2: Divide 1st term of divisor by first term of dividend to get first term of the quotient. The quotient (answer) is written above the division box. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. Step 3: Take the term found in step 1 and multiply it times the divisor. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. Step 4: Subtract this from the line above. Make sure that you subtract EVERY term found in step 3, not just the first one. Step 5: Repeat the process from step 1 to step 4 until done. That is till the degree of the subtracted term is less than the degree of the divisor. Step 6: Write out the answer. Your answer is the quotient that you ended up with on the top of the division box. If you have a remainder, write it over the divisor in your final answer. That is in the below format: D i v i d e n d D i v i s o r = Q u o t i e n t + Re m a i n d e r D i v i s o r (Or) D i v i d e n d = ( Q u o t i e n t ) ( D i v i s o r ) + Re m a i n d e r Formula used: D i v i d e n d = ( Q u o t i e n t ) ( D i v i s o r ) + Re m a i n d e r Calculation: Step 1: Set up the long division. The divisor (what we are dividing by) goes on the outside of the box. The dividend (what we are dividing into) goes on the inside of the box. When you write out the dividend and divisor, make sure that you insert 0's for any missing terms x 4 + 2 x 3 + 0 x 2 − 10 x − 25 x 2 + 0 x − 5 Step 2: Divide 1st term of divisor by first term of dividend to get first term of the quotient. The quotient (answer) is written above the division box. Take the quotient and multiply it times the divisor. x 4 x 2 = x 2 x 2 ( x 2 + 0 x − 5 ) = x 4 + 0 x 3 − 5 x 2 Step 3: Write the result of multiplying quotient with divisor and place it under dividend. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. x 2 x 2 + 0 x − 5 x 4 + 2 x 3 + 0 x 2 − 10 x − 25 x 4 + 0 x 3 − 5 x 2 Step 4: Subtract this from the line above. Make sure that you subtract EVERY term found in step 3, not just the first one. x 2 x 2 − 0 x − 5 x 4 + 2 x 3 + 0 x 2 − 10 x − 25 x 4 − 0 x 3 − 5 x 2 ( − ) ( + ) ( + ) _ 2 x 3 − 5 x 2 − 10 x Step 5: Repeat the process from step 2 to step 4 until done. That is till the degree of the subtracted term is less than the degree of the divisor Step 2: Divide 1st term of divisor by first term of dividend to get first term of the quotient. The quotient (answer) is written above the division box. Take the quotient and multiply it times the divisor. 2 x 3 x 2 = 2 x 2 x ( x 2 + 0 x − 5 ) = 2 x 3 + 0 x 2 − 10 x Step 3: Write the result of multiplying quotient with divisor and place it under dividend. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. x 2 + 2 x x 2 − 0 x + 5 x 4 + 2 x 3 + 0 x 2 − 10 x − 25 x 4 − 0 x 3 − 5 x 2 ( − ) ( + ) ( + ) _ 2 x 3 + 5 x 2 − 10 x − 25 2 x 3 + 0 x 2 − 10 x + 0 ( − ) ( − ) ( + ) ( − ) _ 5 x 2 + 0 x − 25 5 x 2 − 0 x − 25 Repeating Step 4: Subtract this from the line above

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Author: Miller

Publisher: McGraw Hil

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Chapter 4.4, Problem 41PE

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Identity the divisor, quotient, and remainder of given long division and check by multiplication

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