Question

Suppose f(x)=x^2 −11x+30. Enter f(x) as an equation in factored form, using function notation.

a. f(x)=(x−5)(x−6)
b. f(x)=(x+5)(x−6)
c. f(x)=(x−5)(x+6)
d. f(x)=(x+5)(x+6)

Answer 1

The equation f(x)=x^2-11x+30 can be factored as (x-5)(x-6). So, the correct option is: a. f(x) = (x - 5) (x - 6)

Step-by-step explanation:

To factor the quadratic function fx = x^2 - 11x + 30, we are looking for two numbers whose product is the constant term (30) multiplied by the leading coefficient (1) and whose sum is the coefficient of the linear term 11.

The numbers -5 and -6 satisfy these conditions, as -5 times -6 = 30 and -5 + -6 = -11.

Therefore, the factored form of f(x) is given by:

f(x) = (x - 5)(x - 6)

So, the correct option is:

a. f(x) = (x - 5) (x - 6)

This represents the expression in factored form using function notation.