Question

factorise this if done in 20 mins then i will mark you brainliest
x^4 + 5x^3 + 5x^2 - 5x - 6

Answer 1

$\textbf{\huge{ANSWER:}}$

p(x) = $x^{4} + 5x^{3} + 5x^{2} - 5x - 6$

Factors of 6:- (+1), (-1), (+2), (-2), (+3), (-3), (+6), (-6)

CASE I:- When g(x) = (+1);

=》 $(1)^{4} + 5(1)^{3} + 5(1)^{2} - 5(1) - 6$

=》 $\textbf{0}$

Means, $\textbf{x - 1}$ is a factor of p(x)

CASE II:- When g(x) = (-1);

=》 $(-1)^{4} + 5(-1)^{3} + 5(-1)^{2} -5(-1) -6$

=》 $\textbf{0}$

Means, $\textbf{x + 1}$ is also a factor of p(x)

Now-;

=》 ( x - 1 ) ( x + 1 )

=》 $x^{2} - 1$ = f(x)

p(x) ÷ f(x)

{The division is shown in the picture attached}

Now-;

=》 $x^{2} + 5x + 6$

=》 $x^{2} + 2x + 3x + 6$

=》 $x ( x + 2 ) + 3 ( x + 2 )$

=》 $( x + 3 ) ( x + 2 )$

Answer-;

$x^{4} + 5x^{3} + 5x^{2} - 5x - 6$ = ( x + 1 ) ( x - 1 ) ( x + 2 ) ( x + 3 )