See explanation below
Step-by-step explanation:
Given expression: x² + 4x + 1
For the above expression to be factored, we need to have two numbers that can be added together to give 4 and the product of those number to give 1
For a quadratic expression: ax² + bx + c
a = 1, b = 4, c = 1
there are no factors where the addition of both numbers give b = 4 and the product of those number give 1.
Also, we can apply the formula: b² = 4ac to determine if we can factorise wihout getting complex root or decimals. When we factor, we get only whole numbers, no decimals.
4² = 4(1)(1)
16 = 4
We can see the above contradict it self as 16 is no equal to 4