Question

Use the long division method to find the result when 6x^3 + 19x2^2 + 17x + 3 is

divided by 2x + 3.

Answer 1

`(6x^3 \ + \ 19x^2 \ + \ 17x \ + \ 3)/(2x \ + \ 3) \ = \ 3x^2 \ + \ 5x \ + \ 1`

Explanation:

Given;

F(x) = 6x³ + 19x² + 17x + 3

Factor of F(x) = 2x + 3

Using long division method;

3x² + 5x + 1

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2x + 3 √ 6x³ + 19x² + 17x + 3

- (6x³ + 9x²)

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10x² + 17x + 3

- (10x² + 15x)

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2x + 3

- (2x + 3)

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

0

`Thus, (6x^3 \ + \ 19x^2 \ + \ 17x \ + \ 3)/(2x \ + \ 3) \ = 3x^2 \ + \ 5x \ + \ 1`