Question

3. Factorise:3x^2+x-1 by splitting the middle term.

Answer 1

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

• $\tt{A\: quadratic\: polynomial\:is\: given\:to\: us.}$
• $\tt{The\: Polynomial\:is\:3x^2+2x-1.(correct)}$

$\large{\underline{\underline{\red{\sf{To\:Find:}}}}}$

• $\tt{The\:factorised\:form\:of\: polynomial.}$

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

$\underline{\purple{\bf{\mapsto How\:to\:do\: middle\: term\: splitting?}}}$

$\tt{Here\:are\:the\:steps:-}$

$\tt{\green{Step\:1:-}\:\:\orange{Multiply\: constant\:term\:with\: coefficient\:of\:x^2.}}$

$\tt{\green{Step\:2:-}\:\:\orange{Split\: middle\:term\:in\:such\: way\:that\:it\:is\:equal\:to\:above\: product.}}$

$\tt{\green{Step\:3:-}\:\:\orange{Take\:out\: common\: terms\:by\: grouping\:them\:properly.}}$

$\tt{\green{Step\:4:-}\:\:\orange{Then\:from\: obtained\: two\: terms\:take\:out\: common\:term.}}$

$\underline{\purple{\bf{\mapsto Following\:\:the\: above\:steps:}}}$

$\tt{:\leadsto 3x^2+2x-1. }$

$\tt{:\leadsto 3x^2+3x-x-1}$

$\sf{\green{[Splitting\: middle\:term\:into\:3x\:and\:(-x.)]}}$

$\tt{:\leadsto 3x(x+1)-1(x+1) }$

$\sf{\green{[Taking\:out\: common\:terms\:by\:grouping.]}}$

$\pink{\tt{:\leadsto (3x-1)(x+1) }}$

$\sf{\green{[Taking\:out\: common\: terms \:which\:is\:(x+1).]}}$

$\underline{\purple{\tt{\hookrightarrow Hence\:the\:factorised\:form\:is\:(3x-1)(x+1).}}}$