X^2+2x+1
are you solving for x?
factors to
(x+1)(x+1) or (x+1)^2
The expression you provided is a quadratic polynomial, specifically in the form of a trinomial. To simplify it further, you can try factoring or using the quadratic formula to find the solutions.
To factor the expression, you need to determine two numbers whose product is equal to 1 and whose sum is equal to 2 (the coefficient of the x term). In this case, the numbers are 1 and 1. Factoring the expression, we have:
x^2 + 2x + 1 = (x + 1)(x + 1)
By factoring, we can see that the expression simplifies to (x + 1)^2. This means that x^2 + 2x + 1 is equivalent to (x + 1)^2.
Alternatively, you can use the quadratic formula to find the solutions for x. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 2, and c = 1. Plugging those values into the quadratic formula, we have:
x = (-2 ± √(2^2 - 4(1)(1))) / (2(1))
x = (-2 ± √(4 - 4)) / 2
x = (-2 ± √0) / 2
x = (-2 ± 0) / 2
x = -2 / 2
x = -1
So, the quadratic equation x^2 + 2x + 1 has a double root of -1.