Question

1 st question 2nd subdivision

Answer 1

$\huge\bf\mathfrak\pink{\underline{\underline{\underline{Answer}}}}$

$\boxed{\bf{(x-3)[(x-1)(x+5)]} }$

$\huge\bf\red{\underline{\underline{\underline{Step-by-Step\:Explanation}}}}$

$\huge\bf\green{\underline{\underline{Given,}}}$

$\boxed{\bf{{x}^{3}+{x}^{2}-17x+15=0}}$

$\bf{To\:factorise\:we\:will\:find\:the\:first\:factor\:by\: substituting\:the\: values\:and\:find\:a\:factor}$

$\bf{So,\:we\: substitute\:+1,\:-1\:,+2\:,\:-2 \: and \:so\:on\:to\:find\:the\:first\:factor}$

$\bf{If\:we\:substitute\:+1\: , \:-1 \:,\: +2 \:,\: -2 \:the \:remainder \:is \:not \:zero}$

$\bf{But,if \:we \:substitute\: +3 \:in\: the\: equation, \:the \:remainder \:is \:zero}$

$\bf{\underline{LHS}}$

$\bf\red{{3}^{3}+{3}^{2}-17*3+15}$

$\bf\red{27+9+15-51}$

$\bf\red{0}$

$\bf{\underline{RHS}}$

$\bf\red{0}$

$\boxed{\bf{LHS=RHS}}$

$\bf{So,(x-3) is the first factor of equation}$

$\bf{After calculating the first factor, we divide the equation with the first factor.}$

$\bf{The \:quotient \:received \:will \:be\: the \:product \:of \:the \:two\: more\: factors\: of \:the \:equation.}$

$\bf{I\:have\:attached \:the \:image\: of division\: because\: I \:can't \:solve\: on\: brainly. \:Please \:see \:it\: below \:for\: the\: answer.}$

$\bf{From\: the \:image, \:the\: quotient\: is \:{x}^{2}+4x-5=0}$

$\bf{Solving \:the \:above\: quadratic\: equation, \:we\: get}$

$\boxed{\bf{{x}^{2}-x+5x-5}}$

$\boxed{\bf{x(x-1)+5(x-1)}}$

$\boxed{\bf{(x-1)(x+5)}}$

$\bf{So,\: the\: three \:factors \:of \:the\: equation\: are \:(x-3) \:{ \:( x-1 )\: ( x + 5 ) \:} }$

$\boxed{\bf{Factors\:of\:{x}^{3}+{x}^{2}-17x+15=(x-3)[(x-1)(x+5)]}}$

$\bf\green{Please\:mark\: the\: answer\: as \:brainliest}$

$\bf{ Stay \:Home \:And \:Stay\:Safe}$

$\huge\bf{\underline{\underline{Thanks}}}$

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