Question

question 3.
mr. rios placed a polynomial expression on the board.
\\(18x^2 - 48x + 32\\)
which expressions are equivalent to the polynomial?
select two correct answers.
a. \\(\square\\ 2(3x - 4)(3x + 4)\\)
b. \\(\square\\ (3x - 4)(3x - 4)\\)
c. \\(\square\\ 2(3x - 4)^2\\)
d. \\(\square\\ 2(3x + 4)^2\\)
e. \\(\square\\ 2(9x^2 - 24x + 16)\\)

Explanation:

Step1: Factor out common term

Original polynomial: \(18x^2 - 48x + 32\). Factor out 2: \(2(9x^2 - 24x + 16)\) (matches option E).

Step2: Factor quadratic inside

Quadratic \(9x^2 - 24x + 16\) is a perfect square: \((3x - 4)^2\). So polynomial becomes \(2(3x - 4)^2\) (matches option C).

Step3: Check other options

Option A: \(2(3x - 4)(3x + 4) = 2(9x^2 - 16) = 18x^2 - 32\) (not equal). Option B: \((3x - 4)^2 = 9x^2 - 24x + 16\) (missing factor 2). Option D: \(2(3x + 4)^2 = 2(9x^2 + 24x + 16) = 18x^2 + 48x + 32\) (sign error). Thus correct options are C and E.

Answer:

C. \(2(3x - 4)^2\), E. \(2(9x^2 - 24x + 16)\)