Using factor theorem, factorize each of the following polynomials : `x^3-10 x^2-53 x-42`

Explanation

`x^3-10x^2-53x-42`
let `p(x)=x^3-10x^2-53x-42`
let `x=-1`
`p(-1)=(-1)^3-10(-1)^2-53(-1)-42`
`=-1-10+53-42`
`=0`
Hence`(x+1)` is a factor of polynomial
`p(x)=x^3+x^2-11x^2-42x-11x-42`
`=x^2(x+1)-11x(x+1)-42(x+1)`
`=(x+1)(x^2-11x-42)`
`x^2-11x-42=x^2-14x+3x-42`
`=x(x-14)+3(x-14)`
`=(x+3)(x-14)`
Therefore,`p(x)=(x+1)(x+3)(x-14).`