Long Division Method to Divide Two Polynomials

Q. Select the lettered pair that has the same relationship as the original pair of words.
Film : Producer :: Book : __?

1. Writer
2. Director
3. Publisher
4. Editor

Q.

$\text{Given the area of rectangle is}A=25a^2-35a+69.\text{The length is given}\text{as}(5a-3).\text{Find the width of the}\text{rectangle.}$

1. $5a-3$

2. $5a-4$

3. $4a-5$

4. $a-4$

Q.

$\text{If the dividend =}{x}^4+x^3-2x^2+x+1,\text{divisor =}x-1\text{and remainder =}2,\text{then find the quotient q(x)}.$

1. $x^3+2x^2+x+1$

2. $x^3+x^2+x$

3. $x^3+2x^2+1$

4. $x^3+x^2+1$

Q.

Given P = Product of $x^2$ y and $\frac{x}{y}$ and Q = Quotient obtained when $x^2$ is divided by D. If P = Q, what is the value of D?

1. 0

2. 1

3. x

4. $\frac{1}{x}$

Q.

If one factor of $5+8x-4x^2$ is $(2x+1)$, then the second factor is

1. (5 + 2x)

2. –(5 + 2x)

3. (5 – 2x)

4. (2x - 5)

Q.

When $p\left(x\right)=4x^3-12x^3+11x-5$ is divided by (2x - 1), the remainder is

1. 0

2. -5

3. 2

4. -2

Q. The area of a rectangle is $25a^2-35a+12$. If the length is given as $5a-3$, then the width is .

1. $4a-5$
2. $a-4$
3. $5a-4$
4. $5a-3$

Q. $4x^3+x^2+5x+8$ = $(x+1)$ $\times$ .

1. $(4x^2–3x+8)$
2. $(x^2+8x–3)$
3. $(x^2–3x+8)$
4. $(4x^2+3x–8)$

Q.

$\text{Given the area of rectangle is}A=25a^2-35a+69.\text{The length is given}\text{as}(5a-3).\text{Find the width of the}\text{rectangle.}$

1. $5a-3$

2. $5a-4$

3. $4a-5$

4. $a-4$

Q. If $x^3-6x^2+ax+b$ is exactly divisible by $x^2-3x+2$, then $12a+22b=?$

1. 132
2. 264
3. 0
4. - 66