Question

Using factor theorem show that x - 2 is a factor of x3 + x2 - 4x - 4. Hence factorise the
polynomial
fadh

Answer 1

$\huge{\underline{\underline{\sf{\red{Given\::}}}}}$

• $\bf{x}^{3}\:{+\:x}^{2}\:{-\:4x}\:{-\:4}$

${ }$

$\huge{\underline{\underline{\sf{\red{Show\::}}}}}$

• $\bf{Factor\:Theorem}$

${ }$

$\huge{\underline{\underline{\sf{\red{Solution\::}}}}}$

• $\sf{Let\:f(x)\:=\:x}^{3}\:+\:{x}^{2}\:{-\:4x\:-\:4}$
• $\sf{Putting,\:x\:=\:2\:;\:We\:get\:-}$

${ }$

$\:\:\:\:\:\:\::\:\Longrightarrow\sf\small\:{f(2)\:=\:(2)}^{3}\:{+\:(2)}^{2}\:{-\:4\:\times\:2\:-\:4}$

$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{8\:+\:4\:-\:8\:-\:4}$

$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{12\:-\:12}$

$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{0}$

$\therefore\:\sf{\small{\footnotesize{By\:factor\:theorem\:,\:(x\:-\:2)\:is\:a\:factor\:of\:f(x)}}}$

${ }$

• ${\underline{\sf{\small{Hence,\:{\bold{(x\:-\:2)}}\:are\:factors\:of\:{\bold{x}}^{3}\:{\bold{+\:x}}^{2}\:{\bold{-\:4x\:-\:4}}}}}}$