Question

Factorise:

(i) y³ - 7y + 6

(ii) 2x³ - 5x² - 19x + 42

(iii) 3z³ - 4z² - 12z + 16

(iv) x³ - 6x² + 11x-6​

Answer 1

$\sf \boxed {2{x}^{3} - 5 {x}^{2} - 19x + 42}$

$\sf \ = 2 {x}^{3} - 4 {x}^{2} - {x}^{2} + 2x - 21x + 42$

$\sf \: \: = 2{x}^{2} (x - 2) - x(x - 2) - 21(x - 2)$

$\sf \: = (x - 2)(2 {x}^{2} - x - 2)$

$\sf \: = (x - 2)(2 {x}^{2} + 6x - 7x - 21)$

$\sf \: = (x - 2)(2 {x}^{2} (x - 3) - 7(x + 3))$

$\sf \: = (x - 2)(2x - 7)(x + 3)$

$\bold\red { = (x - 2)(2x - 7)(x + 3)}$

$\sf \boxed{3 {x}^{2} - 4 {x}^{2} - 12x + 16}$

$\sf \: = {z}^{2}(3z - 4) - 4(3z - 4)$

$\sf \: = (3z - 4)( {z }^{2} - 4)$

$\bold \pink{ = 3z - 4)(z + 3)(z - 2)}$

Question number (i) and (iv) is in above attachment!