Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3) a) quadratic function; quadratic term: 6x^2; linear term: 24x; constant term: −6 b) linear function; linear term: −21x; constant term: −6 c) quadratic function; quadratic term: −18x^2; linear term: −21x; constant term: −6 d) linear function; linear term: −18x^2; constant term: −6

The correct Option is C).  quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6

Step-by-step explanation:

Given : f(x) = (3x + 2)(-6x - 3)

Now, f(x) = -18x² -9x -12x - 6

⇒ f(x) = -18x² - 21x - 6

Now, since the highest degree of the given function f(x) is 2 so the function f(x) is quadratic.

Now, quadratic term is one which has highest power x = 2 So, quadratic term = -18x²

Linear term is one which has  power x = 1 So, linear term = -21x

Constant term is one which has power of x = 0. So, constant term = -6

Hence, The correct Option is C).  quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6