Final answer:
The question involves solving a quadratic equation, not long division, by using the quadratic formula. The equation is in the form ax² + bx + c = 0, and by substituting a = 1, b = -14, and c = 48, we can find the solutions for x.
Thus the corret opction is:a
Step-by-step explanation:
When using long division to find the quotient of a polynomial such as x² - 14x + 48, we would typically divide it by a linear factor.
However, in this case, none of the options provided (x = 6, x = -40, x = -6, x = 40) represent a linear factor to divide by; they are values that might be solutions to the equation if set equal to zero.
To find the solutions, we use the quadratic formula, which is applicable to equations of the form ax² + bx + c = 0. The equation given is already in this form, with a = 1, b = -14, and c = 48.
To apply the quadratic formula, we use the formula x = (-b ± √(b² - 4ac)) / (2a). Substituting the values from the quadratic equation x² - 14x + 48, we find the solutions which could match the given options.
The correct approach is to find the discriminant first, which is b² - 4ac. After calculating the discriminant, we can then use it in the quadratic formula to find the two possible values of x and see which one, if any, matches the given options.
The complete question is:content loaded
Use long division to find the quotient below. (x² - 14x + 48)
a. x = 6
b. x = - 40
c. x = - 6
d. x = 40