What is the quotient and remainder for (24b^3 + 16b^2 + 20b + 36)/(4b + 4)

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the quotient and remainder for (24b^3 + 16b^2 + 20b + 36)/(4b + 4)

(24b^3 + 16b^2 + 20b + 36)/(4b + 4)

=> (6b^3 + 4b^2 + 5b + 9)/(b + 1)

Now use long division:

b + 1 | 6b^3 + 4b^2 + 5b + 9 | 6b^2 - 2b + 7

............6b^3 + 6b^2

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....................... - 2b^2 + 5b + 9

....................... - 2b^2 - 2b

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......................................7b + 9

......................................7b + 7

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........................................0 + 2

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This gives the quotient as 6b^2 - 2b + 7 and the remainder is 2.

wity's profile pic

wity | Student, Grade 10 | eNotes Newbie

Posted on

the quotient is 6b^2 - 2b + 7 and the remainder is 2, hope its useful.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll factorize by 4 the numerator and denominator:

4(6b^3 + 4b^2 + 5b + 9)/4(b+1) = (6b^3 + 4b^2 + 5b + 9)/(b+1)

Using the long division, we'll get:

6b^3 + 4b^2 + 5b + 9 | b+1

-6b^3 - 6b^2               | 6b^2 - 2b + 7  (quotient)

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/      -2b^2 + 5b

+2b^2 + 2b

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/      +7b +  9

-7b   - 7

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/      +2 = reminder

The quotient is: Q(b) = 6b^2 - 2b + 7 and the reminder is: R(b)=2.

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