Question

6. On dividing x^3 + 3x + 2 by a polynomial g(x), the
quotient and remainder are x - 2 and 16 respectively.
Find g().​

Answer 1

Answer:

g(x) ,x_2+16 ,18 x

Step-by-step explanation:

dividend , 18

Answer 2

The required polynomial is

$g(x) = x^2 + 2x + 7$

Step-by-step explanation:

We are given the following in the question:

$x^3 + 3x + 2 = g(x)(x-2) + 16$

We have to find the polynomial g(x).

$x^3 + 3x + 2 = g(x)(x-2) + 16\\\\g(x) = \dfrac{x^3 + 3x + 2-16}{x-2}\\\\g(x) = \dfrac{x^3 + 3x - 14}{x-2}\\\\g(x) = \dfrac{(x^2 + 2x + 7)(x-2)}{x-2}\\\\g(x) = x^2 + 2x + 7$

Thus, the required polynomial is

$g(x) = x^2 + 2x + 7$

#LearnMore

On dividing 2x³ +x ²- 3x+5 by a polynomial g(x) the quotient and remainder 2 X + 7 and 16 x minus 2 respectively find g(x)​

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