i. x² - 23x + 120

x² - 23x + 120

= x² - 15x - 8X + 120

= x(x - 15) - 8(x - 15)

= (x - 8)(x - 15) (Answer)

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ii. 3x² + 13x + 4

3x² + 13x + 4

= 3x² + 12x + x + 4

= 3x(x + 4) + 1(x + 4)

= (3x + 1)(x + 4) (Answer)

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iii. p² - 17p - 38

p² - 17p - 38

= p² - 19p + 2p - 38

= p(p - 19) + 2(p - 19)

= (p + 2)(p - 19) (Answer)

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iv. r² - 10r + 21

r² - 10r + 21

= r² - 7r - 3r + 21

= r(r - 7) - 3(r - 7)

= (r - 3)(r - 7) (Answer)

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v. p² + 8p - 84

p² + 8p - 84

= p² - 6p + 14p - 84

= p(p - 6) + 14(p - 6)

= (p + 14)(p - 6) (Answer)

i. 8xy³ + 12x²y²

8xy³ + 12x²y²

= 4xy²(2y + 3x) (Answer)

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ii. 3x³ + 2x² - 19x + 6

3x³ + 2x² - 19x + 6

= 3x³ + 9x² - 7x² - 21x + 2x + 6

= 3x²(x + 3) - 7x(x + 3) + 2(x + 3)

= (x + 3)(3x² - 7x + 2)

= (x + 3)[3x² - 6x - x + 2]

= (x + 3)[3x(x - 2) - 1(x - 2)]

= (x + 3)(3x - 1)(x - 2) (Answer)

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iii. x³ - 23x² + 142X - 120

x³ - 23x² + 142x - 120

= x³ - x² - 22x² + 22x + 120x - 120

= x²(x - 1) - 22x(x - 1) + 120(x - 1)

= (x - 1)[x² - 22x + 120]

= (x - 1)[x² - 10x - 12x + 120]

= (x - 1)[x(x - 10) - 12(x - 10)]

= (x - 1)(x - 10)(x - 12) (Answer)

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iv. x³ - 6x² + 11x - 6

x³ - 6x² + 11x - 6

= x³ - x² - 5x² + 5X + 6x - 6

= x²(x - 1) - 5x(x - 1) + 6(x - 1)

= (x - 1)[x² - 5x + 6]

= (x - 1)[x² - 3x - 2x + 6]

= (x - 1)[x(x - 3) - 2(x - 3)]

= (x - 1)(x - 2)(x - 3) (Answer)