Question

On dividing the polynomial 2X^2+3X+1 by a polynomial g(x) the polynomial and reminder where 2X-1 and 3. Find the value of g(x)

Answer 1

Step-by-step explanation:

Given,

p(x) = 2X²+3X+1

q(x) = 2X-1

r(x) = 3

g(x) =?

We know,

p(x) = g(x) × q(x) + r(x)

=>2X²+3X+1 = g(x)(2X-1 ) +3

=>2X²+3X+1-3 = g(x)(2X-1 )

=>2X²+3X-2 = g(x)(2X-1 )

=> (2X²+3X-2)/(2X-1 ) = g(x)

=> (2X²+4X-X-2)/(2X-1 ) = g(x)

=> {2X(X+2) -1(X+2)}/(2X-1 ) = g(x)

=> (X+2) (2X-1) /(2X-1) = g(x)

=> (X+2) = g(x)

Therefore g(x) = X+2

Answer 2

$\huge\bf\fbox\red{Answer:-}$

Given,

P(x) = 2X²+3x+1

q(x) = 2X-1

r(x) = 3

g(x) =?

We know,

P(x) = g(x) xq(x) + r(x)

=> 2X²+3x+1= g(x)(2X-1) +3

=> 2X²+3x+1-3 = g(x)(2x-1)

=> 2x²+3X-2 = g(x)(2X-1)

=> (2X²+3X-2)/(2x-1) = g(x)

=> (2x²+4X-X-2)/(2X-1) = g(x)

=> (2X(X+2)-1(X+2)/(2X-1) = g(x)

=> (X+2) (2X-1)/(2X-1) = g(x)

=> (x+2) = g(x)

Therefore g(x)=X+2.