The remainder when the polynomial 2 x^5-3 x^4 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To find the remainder,we perform polynomial long division of $2 x^5-3 x^4+5 x^3-3 x^2+7 x-9$ by $x^2-x-3$:$1$. Divide $2 x^5$ by $x^2$ to get $2 x

Vedclass · Accepted Answer

$41 x+3$

Vedclass · Answer

(B) To find the remainder,we perform polynomial long division of $2 x^5-3 x^4+5 x^3-3 x^2+7 x-9$ by $x^2-x-3$:$1$. Divide $2 x^5$ by $x^2$ to get $2 x^3$. Multiply $(x^2-x-3)$ by $2 x^3$ to get $2 x^5-2 x^4-6 x^3$. Subtracting this from the dividend gives $-x^4+11 x^3-3 x^2+7 x-9$.$2$. Divide $-x^4$ by $x^2$ to get $-x^2$. Multiply $(x^2-x-3)$ by $-x^2$ to get $-x^4+x^3+3 x^2$. Subtracting this gives $10 x^3-6 x^2+7 x-9$.$3$. Divide $10 x^3$ by $x^2$ to get $10 x$. Multiply $(x^2-x-3)$ by $10 x$ to get $10 x^3-10 x^2-30 x$. Subtracting this gives $4 x^2+37 x-9$.$4$. Divide $4 x^2$ by $x^2$ to get $4$. Multiply $(x^2-x-3)$ by $4$ to get $4 x^2-4 x-12$. Subtracting this gives $41 x+3$.Thus,the remainder is $41 x+3$.

List-$I$	List-$II$
$(A)$ The minimum value of $2x^2 + 4x + 5$	$(I)$ $-1$
$(B)$ The maximum value of $\frac{x^2 + 4x + 1}{x^2 + x + 1}$	$(II)$ $1$
$(C)$ If $1 \leq \frac{3x^2 - 5x + 6}{x^2 + 1} \leq 2$, $\forall x \in [a, b]$ then $b =$	$(III)$ $2$
$(D)$ If $1 \leq \frac{3x^2 - 5x + 6}{x^2 + 1} \leq 2$, $\forall x \in [a, b]$ then $a =$	$(IV)$ $3$
	$(V)$ $4$

The remainder when the polynomial $2 x^5-3 x^4+5 x^3-3 x^2+7 x-9$ is divided by $x^2-x-3$ is

Similar Questions

Let $r$ be a root of the equation $x^2+2x+6=0$. The value of $(r+2)(r+3)(r+4)(r+5)$ is equal to

Solve $|x - 2| + |x - 1| = x - 3$

If $x$ is real,the function $f(x) = \frac{(x - a)(x - b)}{(x - c)}$ will assume all real values,provided

If $\alpha$ and $\beta$ are two distinct negative roots of $x^5-5x^3+5x^2-1=0$,then the equation of least degree with integer coefficients having $\sqrt{-\alpha}$ and $\sqrt{-\beta}$ as its roots is

Vedclass Test Series

Exam Paper Generator

Online Exam Module