Question

If we have x=2, then \[\left( {x - 1} \right)\left( {2x - 3} \right) = ?\]
\[\left( 1 \right)\] \[1\]
\[\left( 2 \right)\] \[3\]
\[\left( 3 \right)\] \[ - 1\]
\[\left( 4 \right)\] \[0\]
\[\left( 5 \right)\] \[ - 3\]

Answer 1

Hint: We have to find the value of the given expression \[\left( {x - 1} \right)\left( {2x - 3} \right)\] for the value of \[x = 2\]. We will solve this question using the concept of solving equations and using the concept of multiplication of terms having the same sign. We will simply solve this question by putting the value of \[x\] in the given expression and then we will solve the expression using the concept of multiplication of terms having the same sign. Using this concept we will get the value of the given expression.

Complete step-by-step solution:
Given :
The value of the expression \[\left( {x - 1} \right)\left( {2x - 3} \right)\] at \[x = 2\]
Putting the value of \[x = 2\] in the expression, we get
\[\left( {x - 1} \right)\left( {2x - 3} \right) = \left( {2 - 1} \right) \times \left( {2 \times 2 - 3} \right)\]
\[\left( {x - 1} \right)\left( {2x - 3} \right) = 1 \times \left( {4 - 3} \right)\]
Further solving, we get
\[\left( {x - 1} \right)\left( {2x - 3} \right) = 1 \times 1\]
Now using the concept of multiplication of terms having the same signs, we know that the product of two positive or negative terms is always a positive number.
Using the concept of multiplication of terms having same signs, the expression of product becomes
\[\left( {x - 1} \right)\left( {2x - 3} \right) = 1\]
Hence, the value of the given expression \[\left( {x - 1} \right)\left( {2x - 3} \right)\] at \[x = 2\] is \[1\].
Thus, the correct option is \[\left( 1 \right)\].

Note: We can also solve this question without using the concept of multiplication of terms having the same sign. For that we will expand the given expression using the concept of multiplication of variables. After expanding the given expression we will obtain a polynomial equation and then by putting the value of \[x\] in the polynomial equation we will get the value of the expression.
We can also conclude that the product of two numbers having the same signs always gives us a positive number as a result.