Question

Which one of the following is a correct factorization of the expression \(-16 x^{2}+36 x+52 ?\). A) \((-16 x+26)(x-2)\) (B) \((-4 x-13)(4 x+4)\) (C) \(-1(4 x-13)(4 x+4)\) (D) \(-1(4 x-4)(4 x+13)\)

Short answer

The correct factorization of the expression -16x^{2}+36 x+52 is -1(4 x-13)(4 x+4), thus Option C is correct.

Step-by-step solution

Check Option A

Expand \((-16 x+26)(x-2)\) using the FOIL method. It should equate to -16x^2 +56x -52, which doesn't equal to -16x^{2}+36 x+52. Thus, option A is incorrect.

Check Option B

Expand \((-4 x-13)(4 x+4)\) using the FOIL method. It should equate to -16x^2 +4x + 52, which again doesn't equal to -16x^{2}+36 x+52. Thus, option B is incorrect.

Check Option C

Expand \(-1(4 x-13)(4 x+4)\) using the FOIL method. It should equate to -16x^2 +36x + 52, which is exactly the expression given. Thus, option C is correct.

Check Option D

Although we have found the correct option, it's good practice to verify all options. Expand \(-1(4 x-4)(4 x+13)\) using the FOIL method. It should equate to -16x^2 +0x -52, which doesn't equal to -16x^{2}+36 x+52. Thus, option D is incorrect.