Tag: polynomials

Quizzes (3) Questions (5)

Questions Related to polynomials

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

The decimal representation of $2005!$ ends with $m$ zeroes then $m=$

  1. $500$
  2. $501$
  3. $502$
  4. $499$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
We know that a number gets a zero at the end of it if the number has 10 as a factor.
  
So I need to find out how many times 10 is a factor in the expansion of 23!.

But since 5×2 = 10, I need to account for all the products of 5 and 2.
 Looking at the factors in the above expansion, there are many more numbers that are multiples of 2 (2, 4, 6, 8, 10, 12, 14,...) than are multiples of 5 (5, 10, 15,...). 
That is, if I take all the numbers with 5 as a factor, I'll have way more than enough even numbers to pair with them to get factors of 10 (and another trailing zero on my factorial).
No. of multiples of 5 between 1 and 2005!= 401
No. of multiples of 25= 80
no. of multiples of 125=16
no. of multiples of 625=3
Hence total multiples of 5 and hence 10 are 500.
There are 500 zeroes in the end of 2005!.
Multiple choice maths polynomials linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

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 ?

  1. $900m$
  2. $320m$
  3. $680m$
  4. $720m$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $720-400=320\ mtrs$

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

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

  1. $4$
  2. $0$
  3. $-4$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $2x^{2} - 3x - 2$
  2. $3x^{2} - 6x - 2$
  3. $4x^{2} - 6x +4$
  4. $2x^{2} - 6x - 2$
Reveal answer Fill a bubble to check yourself
A Correct answer
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} $