Question

Factorise x^3-10x^2-53x-42

Answer 1

x³ - 10x² - 53x - 42
= x³ + x² - 11x² - 11x - 42x - 42
= x²(x + 1) - 11x(x + 1) - 42(x + 1)
= (x + 1)(x² - 11x - 42)
= (x + 1)(x² - 14x +3x - 42)
= (x + 1){x(x - 14) + 3(x - 14) }
= (x + 1)(x + 3)(x - 14)

Hence, (x + 1), (x + 3) and (x - 14) are factors of x³ - 10x² - 53x - 42

Answer 2

Answer:

x^3 - 10 x square - 53x ×42

= X Cube + x square - 11 x square - 11 x - 42 x - 42

=x square (x + 1) - 11 x (x + 1) - 42 (x + 1)

(x + 1) (x square - 11 x - 42)

(x + 1) (x square - 14 x + 3 x - 42)

(x + 1) {x(x-14) +3 (x+41)}

(x + 1) (x + 3) (x - 14)