Question

The method of finding a solution by trying out various values for the variable is called:
A) Error method
B) Trial and error method
C) Testing method
D) Checking method

Answer 1

Hint: Consider the following example to answer the question:
Example: Factorise $p\left( x \right)$ = $\mathop x\nolimits^3 - 23\mathop x\nolimits^2 + 142x - 120$.
Sol: Look for all the factors of -120.
They are $ \pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 8, \pm 10, \pm 12, \pm 15, \pm 20, \pm 24, \pm 30, \pm 60$.
Check at every point if it is a zero of the polynomial $p\left( x \right)$.
For x = -1,
$
  p\left( { - 1} \right) = \mathop {\left( { - 1} \right)}\nolimits^3 - 23\mathop {\left( { - 1} \right)}\nolimits^2 + 142\left( { - 1} \right) - 120 \\
   \Rightarrow - 1 - 23 - 142 - 120 \\
   \Rightarrow - 286 \\
 $
$\because p\left( { - 1} \right) \ne 0,{\text{ }}$thus $\left( {x + 1} \right)$is not a factor of $p\left( x \right)$ = $\mathop x\nolimits^3 - 23\mathop x\nolimits^2 + 142x - 120$
 For x = 1
$
  p\left( 1 \right) = \mathop {\left( 1 \right)}\nolimits^3 - 23\mathop {\left( 1 \right)}\nolimits^2 + 142\left( 1 \right) - 120 \\
   \Rightarrow 1 - 23 + 142 - 120 \\
   \Rightarrow 0 \\
 $
$\because p\left( 1 \right) = 0,{\text{ }}$thus $\left( {x - 1} \right)$is a factor of $p\left( x \right)$ = $\mathop x\nolimits^3 - 23\mathop x\nolimits^2 + 142x - 120$
Likewise for other factors of $p\left( x \right)$, find the value of the polynomial, $p\left( x \right)$ at x = $ \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 8, \pm 10, \pm 12, \pm 15,....$

Complete step-by-step solution:
Let's understand all the definition one by one:
Error method: There is no specified method known as the error method.
Trial and error method: In this method, we put the different values of the variable in an equation repeatedly, various attempts are taken till the success is achieved or we stop trying.
Testing method: in this method, we put a specified value of a variable to test whether the equation is correct or not. The testing method is used in different fields also, chemical testing, software testing etc. It is a definitive procedure that produces a test result.
Checking method: The dictionary meaning of check is examining (something) to determine its accuracy, quality, or condition, or to detect the presence of something. Thus the checking method is to reassure the condition in a regular time interval.
Therefore, The method of finding the solution by trying out various values for the variable is called trial and error method. Thus, option (B) is correct.

Note:
In mathematics equations, expressions involving variables trial and error is the common method to simplify them.