Question

which statement about $f(x) = 12x^2 - 36x + 27$ is true?
a the only zero is $\frac{2}{3}$ because $f(x) = 3(2x - 3)^2$
b the zeros are $pm\frac{3}{2}$ because $f(x) = 3(2x - 3)(2x + 3)$
c the zeros are $pm\frac{2}{3}$ because $f(x) = 3(2x - 3)(2x + 3)$
d the only zero is $\frac{3}{2}$ because $f(x) = 3(2x - 3)^2$

Explanation:

Step1: Factor out the GCF

$f(x) = 3(4x^2 - 12x + 9)$

Step2: Factor the quadratic

$f(x) = 3(2x - 3)^2$

Step3: Find zeros by setting to 0

$2x - 3 = 0 \implies x = \frac{3}{2}$

Answer:

D. The only zero is $\frac{3}{2}$ because $f(x) = 3(2x - 3)^2$