Factor
s^2+4s+4
(s+ 1 )(s+ 4)
This doesn't seem right.
s²+4s+4=(s+2)²
(s+2)(s+2)
Simple as that.
To factor the quadratic expression s^2 + 4s + 4, you need to find two binomial factors whose product is equal to the given expression.
One way to approach factoring is by using the quadratic formula. The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, we have s^2 + 4s + 4 = 0. Comparing this to the standard form ax^2 + bx + c = 0, we find that a = 1, b = 4, and c = 4. Plugging these values into the quadratic formula, we get:
s = (-4 ± √(4^2 - 4(1)(4))) / (2(1))
= (-4 ± √(16 - 16)) / 2
= (-4 ± √0) / 2
= (-4 ± 0) / 2
= -4 / 2
= -2
Hence, the solutions to the quadratic equation s^2 + 4s + 4 = 0 are s = -2, -2. This means that when factoring the expression s^2 + 4s + 4, both binomial factors should have s = -2 as a root.
Therefore, the correct factorization of s^2 + 4s + 4 is (s + 2)(s + 2), or simply (s + 2)^2.