Question

The value of the expression ${x^4} - 17{x^3} + 17{x^2} - 17x + 17$ at x = 16 is
A) 0
B) 1
C) 2
D) 3

Answer 1

Hint:
We will solve this question by putting the value of x = 16 in the algebraic expression ${x^4} - 17{x^3} + 17{x^2} - 17x + 17$. Since we are required to find the value of the algebraic expression at $x = 16$, therefore, we will put the given value of x directly in the expression. After that, we will check if any of the options are matching the obtained answer or not. If yes, then that option will be correct.

Complete step by step solution:
We are given an algebraic expression: ${x^4} - 17{x^3} + 17{x^2} - 17x + 17$
We need to find its value when the value of x is 16 i.e., x = 16.
We will put this value of x in the expression directly because we need to find its value at a point where x has its value equal to 16.
Therefore, at x = 16, the value of the given algebraic expression becomes
$ \Rightarrow $${x^4} - 17{x^3} + 17{x^2} - 17x + 17$ at x = 16
$ \Rightarrow {\left( {16} \right)^4} - 17{\left( {16} \right)^3} + 17{\left( {16} \right)^2} - 17\left( {16} \right) + 17$
$
   \Rightarrow 65536 - 17\left( {4096} \right) + 17\left( {256} \right) - 272 + 17 \\
   \Rightarrow 65536 - 69632 + 4352 - 272 + 17 = 1 \\
 $
Therefore, the value of the algebraic expression ${x^4} - 17{x^3} + 17{x^2} - 17x + 17$ at x = 16 is found to be 1.

Hence, option (B) is correct.

Note:
In this question, you may go wrong while solving the algebraic expression after substituting the value of x = 16. You may get confused while calculating the powers of 16 after putting the value of x in the given algebraic expression.
In mathematics, algebraic expressions are defined as expressions which are formed with variables, integer constants and basic algebraic operations such as addition, multiplication, subtraction, etc.