a,x² - 13x + 36

= x² - 4x - 9x + 36

= x(x - 4) - 9(x - 4)

= (x - 4)(x - 9)

b,x² + 3x - 18

= x² - 9 + 3x - 9

= (x - 3)(x + 3) + 3(x - 3)

= (x - 3)(x + 3 + 3)

= (x - 3)(x + 6)

c,x² - 5x - 24

= x² + 3x - 8x - 24

= x(x + 3) - 8(x + 3)

= (x + 3)(x - 8)

d,3x² - 16x + 5

= 3x² - 15x - x + 5

= 3x(x - 5) - (x - 5)

= (x - 5)(3x - 1)

e, 8x² + 30x + 7

= 8x² + 2x + 28x + 7

= 2x(4x + 1) + 7(4x + 1)

= (4x + 1)(2x + 7)

g,2x² - 5x - 12

= 2x² - 8x + 3x - 12

= 2x(x - 4) + 3(x - 4)

= (x - 4)(2x + 3)

i,x⁴ + 4

= x⁴ + 4x² + 4 - 4x²

= (x² + 2)² - (2x)²

= (x² + 2 - 2x)(x² + 2 + 2x)