is this factorable its a trinomial:
x^2+2x+3
No, not factorable in the real number system. b^2 -4ac is negative, so the roots are imaginary.
To determine if a trinomial is factorable, you can use the quadratic formula or try to factor it using factoring techniques. Let's go through the steps to see if the trinomial x^2 + 2x + 3 is factorable:
Step 1: Check if the trinomial is in the form ax^2 + bx + c, where a, b, and c are coefficients.
In this case, the trinomial x^2 + 2x + 3 fits the form.
Step 2: Calculate the discriminant (b^2 - 4ac) of the trinomial.
The discriminant is calculated as follows:
Discriminant = (2^2) - 4 * 1 * 3
= 4 - 12
= -8
Step 3: Analyze the value of the discriminant.
If the discriminant is positive, the trinomial is factorable in the real number system.
If the discriminant is zero, the trinomial has a double root and is factorable.
If the discriminant is negative, the trinomial is not factorable in the real number system because it will have no real roots, and the roots will be imaginary.
In this case, the discriminant is -8, which is negative. Therefore, the trinomial x^2 + 2x + 3 is not factorable in the real number system.