Question

factorise x cube - 10x square - 53x - 42

Answer 1

hope it helps you out...

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Here,

$\Large{\boxed{\sf\:{Algebraic\;sum\;of\; coefficient\;not\;equal\;to\;zero}}}$

But,

The polynomial becomes zero when we put (x = -1)

Hence,

(x + 1) is factor of this polynomial

Now,

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 - 14)(x + 3)

$\boxed{\begin{minipage}{9 cm} Additional Information \\ \\ \ 1)(x+y)^2=x^2+y^2+2xy \\ \\ 2)(x-y)^2=x^2+y^2-2xy \\ \\ 3)(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx \\ \\ 4)(x+y)^3=x^3+y^3+3xy(x+y) \\ \\ 5)(x-y)^3=x^3-y^3-3xy(x-y) \end{minipage}}$