The problem is asking for a value of 'k' such that the expression (x + 1)(x + 2)(x + 4)(x + k) + 1 is a perfect square.

Step 1:
We know that a perfect square always has an even power. So, the expression (x + 1)(x + 2)(x + 4)(x + k) must be an odd power for the whole expression to be a perfect square (since we are adding 1 to it).

Step 2:
The expression (x + 1)(x + 2)(x + 4)(x + k) is a product of four linear factors. The highest power of x in this expression is x^4, which is even.

Step 3:
To make the power odd, we need 'k' to be 0. This is because if 'k' is 0, the term (x + k) becomes x, and the expression becomes (x + 1)(x + 2)(x + 4)x, which is a cubic polynomial and has an odd power.

Step 4:
However, 'k = 0' is not an option in the given choices. Therefore, there seems to be a mistake in the problem or the given choices. The value of 'k' that makes the expression a perfect square is not listed in the options.

Question

The problem is asking for a value of 'k' such that the expression (x + 1)(x + 2)(x + 4)(x + k) + 1 is a perfect square.

Step 1: 
We know that a perfect square always has an even power. So, the expression (x + 1)(x + 2)(x + 4)(x + k) must be an odd power for the whole expression to be a perfect square (since we are adding 1 to it).

Step 2: 
The expression (x + 1)(x + 2)(x + 4)(x + k) is a product of four linear factors. The highest power of x in this expression is x^4, which is even.

Step 3: 
To make the power odd, we need 'k' to be 0. This is because if 'k' is 0, the term (x + k) becomes x, and the expression becomes (x + 1)(x + 2)(x + 4)x, which is a cubic polynomial and has an odd power.

Step 4: 
However, 'k = 0' is not an option in the given choices. Therefore, there seems to be a mistake in the problem or the given choices. The value of 'k' that makes the expression a perfect square is not listed in the options.

Knowee AI · Accepted Answer

The problem is asking for a value of 'k' such that the expression (x + 1)(x + 2)(x + 4)(x + k) + 1 is a perfect square.

Step 1: 
We know that a perfect square always has an even power. So, the expression (x + 1)(x + 2)(x + 4)(x + k) must be an odd power for the whole expression to be a perfect square (since we are adding 1 to it).

Step 2: 
The expression (x + 1)(x + 2)(x + 4)(x + k) is a product of four linear factors. The highest power of x in this expression is x^4, which is even.

Step 3: 
To make the power odd, we need 'k' to be 0. This is because if 'k' is 0, the term (x + k) becomes x, and the expression becomes (x + 1)(x + 2)(x + 4)x, which is a cubic polynomial and has an odd power.

Step 4: 
However, 'k = 0' is not an option in the given choices. Therefore, there seems to be a mistake in the problem or the given choices. The value of 'k' that makes the expression a perfect square is not listed in the options.

If (x + 1)(x + 2)(x + 4)(x + k) + 1 is a perfect square then the value of k isSelect an answerA3B4C5D8

Question

If $(x + 1)(x + 2)(x + 4)(x + k) + 1$ is a perfect square then the value of k is

Solution

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