Question

divide the polynomial (3m³+4m²+5m+4)÷(m-1)

Answer 1

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Answer 2

By dividing the polynomial (3m³+ 4m² +  5m+ 4) by (m - 1) we get Quotient = 3m² + 7m +12 and remainder = 16.

Given :

Dividend = 3m³+ 4m² +  5m+ 4

Divisor = (m - 1)

To find :

Quotient and Remainder

Concept used :

Division of a Polynomial by a Binomial :

We perform the division steps as follows:

1. Arrange the given terms of the dividend and divisor in descending order of their degrees.

2. Divide the dividend's first term by the divisor's first term to obtain the first term of the quotient.

3. Multiply the divisor's second term by the quotient's first term and subtract the result from the dividend.

4. Take the remainder (if any) as a dividend and proceed as before.

5. Repeat the above process till we get the remainder as zero.

DIVISION ALGORITHM for polynomials :

Dividend = Divisor × Quotient + Remainder

Solution :

Dividing the polynomial (3m³ + 4m² +  5m + 4) by (m - 1)

m - 1)3m³ + 4m² + 5m + 4(3m² + 7m +12

                3m³ - 3m²

                (-)      (+)

           —------------------

                    7m² + 5m + 4

                    7m² - 7m

                    (-)     (+)

             —------------------

                           12 m + 4

                            12m - 12

                             (-)     (+)

                       —------------------

                               16 Remainder

Hence, on dividing the polynomial (3m³+ 4m² +  5m+ 4) by (m - 1) we get Quotient = 3m² + 7m +12 and remainder = 16.

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