Question

if the polynomial 5x^4+8x^3+17x^2+21x+7 is divided by another polynomial 3x^2+4x+1 and he remainder comes to be ax+b, then the value of a and b are​

Answer 1

When we divide 6x4 + 8x3 + 17x2 + 21x + 7 by the polynomial 3x2 + 4x + 1, we get

Quetient = 3x2 + 4x + 5

and Remainder = x + 2

Given, remainder = ax + b

On comparing, we get

a = 1 and b = 2

So, the value of a is 1 and b is 2

Answer 2

Correct question :

If the polynomial 6x^4+8x^3+17x^2+21x+7 is divided by another polynomial 3x^2+4x+1 and he remainder comes to be ax+b, then the value of a and b .

Solution :

      Polynomial division method :

$\boxed{\begin{array}{l|n|r}\sf3x^2+4x+1& \sf6x^4 +8x^3 +17x^2 +21x +7 & \sf 2x^2 + 5\\ & \sf 6x^4 + 8x^3 +2x^2\\ & (-)\:\:(-)\:\:(-)\\ & \rule{120}{0.8}\\ & \sf \qquad\qquad\quad 15x^2 +21x +7\\ & \sf \qquad \qquad\quad 15x^2 + 20x +5 \\ & \qquad\qquad\:\:\:\:\:(-) \:\:\:(-)\:\:\:(-)\\ &\qquad\quad \rule {90}{0.8}\\ & \sf \qquad\qquad \qqaud \sf \:\:\:\:\:\:\:\:\:\:\:\: \:\:\:\:\:\:\:\:x + 2\end{array}}$

$\underline{\boldsymbol{According\:to\:the\:question\::}}}$

The remainder comes in form of ax + b

⇒ ax + b =  x + 2

⇒ a = 1 & b = 2