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Find (3x4-2x2-17x-23)/(x-5) using long division and write the solution as the division...

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kink | Student, Grade 11 | eNotes Newbie

Posted April 11, 2010 at 11:12 AM via web

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Find (3x4-2x2-17x-23)/(x-5) using long division and write the solution as the division statement P(x) = DQ+R

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neela | High School Teacher | Valedictorian

Posted April 11, 2010 at 3:08 PM (Answer #1)

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Mind there is no x^3 terms. So we take a dummy 0*x^3 in the expression.

x-5)3x^4+0 * x^3 - 2x^2 - 17x -23(3x^3+15x^2+73x+348 = Quotient

3x^4-15x^3

----------------

15x^3 - 2x^2-17x-23

15x^2 -75 x^2

---------------------

73x^3-17x-23

73x^2-365x

--------------------------

348x - 23

348x - 1740

---------------------------------

1717 is the remainder.

Therefore

If P(x) = 3x4-2x2-17x-23 and D(x) = x-5, then

P(x) / D(x)  we get the quotient 3x^3+15x^2+73x+348 and a remainder 1717. Or

3x^4-2x^2-17x-23 = (x-5)(3x^3+15x^2+73x+348)+1717.

 

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neela | High School Teacher | Valedictorian

Posted April 11, 2010 at 4:33 PM (Answer #2)

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Mind there is no x^3 terms. So we take a dummy 0*x^3 in the expression.

x-5)3x^4+0 * x^3 - 2x^2 - 17x -23(3x^3+15x^2+73x+348 = Quotient

3x^4-15x^3

----------------

15x^3 - 2x^2-17x-23

15x^2 -75 x^2

---------------------

73x^3-17x-23

73x^2-365x

--------------------------

348x - 23

348x - 1740

---------------------------------

1717 is the remainder.

Therefore

If P(x) = 3x4-2x2-17x-23 and D(x) = x-5, then

P(x) / D(x)  we get the quotient 3x^3+15x^2+73x+348 and a remainder 1717. Or

3x^4-2x^2-17x-23 = (x-5)(3x^3+15x^2+73x+348)+1717.

 

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