Question

What is the factored form of 16x2 – 16x – 12?
4(2x – 2)(2x + 2)
4(4x – 6)(x + 2)
4(2x – 2)(2x + 3)
4(2x – 3)(2x + 1)

What is the factored form of 3x2 + 21x – 24?
3(x + 8)(x – 1)
3(x + 6)(x – 3)
3(x + 5)(x – 3)
3(x + 7)(x – 3)

Answer 1

Q1. The answer is 4(2x - 3)(2x + 1)

16x² – 16x – 12 = 4 * 4x² - 4 * 4x - 4 * 3 =
                          = 4(4x² - 4x - 3) =
                          = 4(4x² + 2x - 6x - 3) = 
                          = 4(2x * 2x + 2x - (2x * 3 + 3)) =
                          = 4(2x(2x + 1) - (3(2x + 1))) =
                          = 4((2x + 1)(2x - 3)) =
                          = 4(2x - 3)(2x + 1)


Q2. The answer is 3(x + 8)(x - 1)

3x² + 21x – 24 = 3 * x² + 3 * 7x - 3 * 8 =
                         = 3(x² + 7x - 8) =
                         = 3(x *x - x + 8x - 8) =
                         = 3((x(x - 1) + 8(x - 1)) =
                         = 3(x + 8)(x - 1)