Question

On dividing 2x2+3x+1 by a polynomial g(x),the quotient and the remainder were 2x-1 and 3 respectively. Find g(x).​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

g(x) = x+2

Step-by-step explanation:

Since we have given that

f(x) = $2x^2+3x+1$

q(x) = 2x-1

r(x) = 3

According to question, we get that

$f(x)=g(x).q(x)+r(x)\\\\2x^2+3x+1=g(x).[2x-1]+3\\\\2x^2+3x+1-3=g(x).2x-1\\\\2x^2+3x-2=(2x-1).g(x)\\\\g(x)=\dfrac{2x^2+3x-2}{2x-1}\\\\g(x)=\dfrac{2x^2+4x-x-2}{2x-1}\\\\g(x)=\dfrac{2x(x+2)-(x+2)}{2x-1}\\\\g(x)=\dfrac{(2x-1)(x+2)}{2x-1}\\\\g(x)=(x+2)$

Hence, g(x) = x+2

# learn more:

On dividing (4x3-8x2+8x+1)by a polynomial g(x). The quotient and remainder were (2x-1) and (x+3) respectively find g(x)

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