Tag: linear and synthetic method of division

Questions Related to linear and synthetic method of division

What will be the Remainder when $3x^{3} - 2x^{2} - 7x + 6$ is divided by $x + 1$?

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $4$

  2. $5$

  3. $8$

  4. $0$

Show answer
Correct Option: C
Explanation:

Let $f(x)=3x^3-2x^2-7x+6$

To find out reminder when equation is divided by $x+1$ we should calculate $f(-1)$
$f(-1)=3(-1)^3-2(-1)^3-7(-1)+6$
            $=13-5=8$

A body falling from rest under gravity passes a certain point $P$.It was a distance of $400m$ from P and $4$ sec prior to passage through $P$ If $g=10m/sec^2$,then the height above the point $"P"$ from where the body began to fall is ?

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $900m$

  2. $320m$

  3. $680m$

  4. $720m$

Show answer
Correct Option: B
Explanation:
Distance travelled $=400\ m$.
Time$=4\ sec$
$B=10m/s^{2}$
$s=ut+1/2 at^{2}$
$400=4u-1/2\times 10\times 16\times 5$
$400=4u-80$
$4u=480$
$u=120$
At highest point
$V=0$
${u}^{2}=2\times g\times h$
$120\times 120=2\times 10\times h$
$h=720$
This height is from $400\ mtr$ below $P$ 
So height above $P$ is $720-400=320\ mtrs$

The remainder when $x^3 + 4x^2 - 7x + 6$ is divided by $(x - 1)$ is

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $4$

  2. $0$

  3. $-4$

  4. $3$

Show answer
Correct Option: A
Explanation:

Let $f\left( x \right) =x^{ 3 }+4x^{ 2 }-7x+6$
As $f\left( x \right) $ is divided by $x-1$, substituting $x=1$ in $f\left( x \right) $ we get
$f\left( 1 \right) =1^{ 3 }+4\cdot1^{ 2 }-7\cdot1+6=4$
Hence, $4$ is the remainder.

What will be the Quotient when $4x^{3} - 8x^{2} - x + 5$ is divided by $2x - 1$?

maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

  1. $2x^{2} - 3x - 2$

  2. $3x^{2} - 6x - 2$

  3. $4x^{2} - 6x +4$

  4. $2x^{2} - 6x - 2$

Show answer
Correct Option: A
Explanation:

Given: equation $4x^3-8x^2-x+5$

To find the quotient when divided by $2x-1$
Sol: $2x-1)\overline{4x^3-8x^2-x+5}(2x^2-3x-2)\\quad\quad \quad 4x^3-2x^2\\quad\quad\quad \overline{\quad \quad -6x^2-x}\\quad\quad\quad\quad\quad- 6x^2+3x\\quad\quad\quad\overline{\quad\quad\quad\quad \quad -4x+5}\\quad\quad\quad\quad\quad\quad \quad \quad- 4x+2\\quad\quad\quad\quad\overline {\quad\quad\quad\quad\quad\quad\quad 3} $