Find the domain of the expression
4x^2-10x+3 and is this factorable?
all polynomials have domain of all real values.
since the discriminant is positive, it is factorable.
To find the domain of an expression, we need to determine the values of x for which the expression is defined. In this case, we have the expression 4x^2 - 10x + 3.
Since this is a polynomial expression, it is defined for all real values of x. Therefore, the domain of the expression is the set of all real numbers, or (-∞, ∞).
Now, to find out if the expression is factorable, we can check if it can be factored using the quadratic formula or by factoring the quadratic equation. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are coefficients.
In this case, a = 4, b = -10, and c = 3. We can determine if the expression is factorable by calculating the discriminant, which is the value inside the square root in the quadratic formula. The discriminant is given by Δ = b^2 - 4ac.
For the expression 4x^2 - 10x + 3, the discriminant is Δ = (-10)^2 - 4(4)(3) = 100 - 48 = 52.
If the discriminant is a perfect square, then the expression is factorable. Since 52 is not a perfect square, the expression 4x^2 - 10x + 3 is not factorable.
Therefore, the domain of the expression is (-∞, ∞), and the expression is not factorable.