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

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

Step-by-step explanation:

=> x³-10x²-53x-42

We'll break 10x² and -53x into parts

=> x³+x²-11x²-11x-42x-42

Taking common

=> x²(x+1)-11x(x+1)-42(x+1)

Taking x+1 as common will make it

=> (x+1)(x²-11x-42)

Using mid term break formula

=> (x+1)(x²-14x+3x-42)

=> (x+1)[x(x-14)+3(x-14)]

Taking (x-14) as common

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

This is the required factorized form.

Hope it helps :)