Question

Can (x - 1) be the remainder on division of a
polunomial pix) by 2x + 3? Justify your answer.​

Answer 1

$\large\sf\underline{Correct\:Question}$

• Can (x - 1) be the remainder on division of a polynomial p(x) by 2x + 3? Justify your answer.

$\large\sf\underline{Solution}$

Division algorithm stated that a polynomial f(x) can be written as :

$\small{\underline{\boxed{\mathrm\red{f(x)=g(x)q+r}}}}$

where,

• q and r are unique integers

• 0 < = r < g (x)

Here ,

• $\sf\:g(x) =2x+3$

• $\sf\:r(x) =x-1$

The power / degree of the remainder is always less than the power of the divisor.

Here, the degree of remainder is 1 and the degree of divisor is 1, which is not possible.

Thus, (x−1) cannot be the remainder of p(x) when divided by (2x+3) .

• Thnku :)

Answer 2

Can (x - 1) be the remainder on division of a polynomial p(x) by 2x + 3? Justify your answer.

\large\sf\underline{Solution}

Solution

Division algorithm stated that a polynomial f(x) can be written as :

\small{\underline{\boxed{\mathrm\red{f(x)=g(x)q+r}}}}

f(x)=g(x)q+r

where,

q and r are unique integers

0 < = r < g (x)

Here ,

\sf\:g(x) =2x+3g(x)=2x+3

\sf\:r(x) =x-1r(x)=x−1

The power / degree of the remainder is always less than the power of the divisor.

Here, the degree of remainder is 1 and the degree of divisor is 1, which is not possible.

Thus, (x−1) cannot be the remainder of p(x) when divided by (2x+3) .

Thnku :)