Step-by-step explanation:
1. D
[tex] {x}^{2} + 6x - 16 = {x}^{2} - 2x + 8x - 16 \\ = x(x - 2) + 8(x - 2) \\ = (x - 2)(x + 8)[/tex]
2. A
[tex]15 {x}^{2} + 20x = 5x(3x + 4)[/tex]
3. C
[tex]2 {x}^{2} - 24x + 54 = 2 {x}^{2} - 6x - 18x + 54 \\ = 2x(x - 3) - 18(x - 3) \\ = (2x - 18)(x - 3) \\ = 2(x - 9)(x - 3)[/tex]
4. D
[tex]4 {x}^{2} + 31x - 8 = 4 {x}^{2} - x + 32x - 8 \\ = x(4x - 1) + 8(4x - 1) \\ = (4x - 1)(x + 8)[/tex]
5. B
[tex]6 {x}^{2} + 27x + 21 = 6 {x}^{2} + 6x + 21x + 21 \\ = 6x(x + 1) + 21(x + 1) \\ = (6x + 21)(x + 1) \\ = 3(2x + 7)(x + 1)[/tex]
6. B
[tex]5 {p}^{2} - 5 = 5( {p}^{2} - 1) \\ = 5( p - 1)(p + 1)[/tex]
7.D
8.A
