Question

Factorise: 6x"2 + 5x - 6 using factor theorem pls say correctly......and fast...

Answer 1

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{The \ factorised \ form \ is \ (2x+3)(3x-2)}$

$\sf\orange{Given:}$

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{6x^{2}+5x-6}}$

$\sf\pink{To \ find:}$

$\sf{Factorised \ form.}$

$\sf\blue{Explanation}$

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{6x^{2}+5x-6}}$

$\sf{Here, \ a=6, \ b=5 \ and \ c=-6}$

$\sf{a\times \ c=6(-6)=-36}$

$\sf{Middle \ term \ should \ be \ split \ such}$

$\sf{that \ it's \ multiplication \ is \ -36 \ and}$

$\sf{addition \ is \ 5.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{\implies{6x^{2}+5x-6}}$

$\sf{\implies{6x^{2}+9x-4x-6}}$

$\sf{\implies{3x(2x+3)-2(2x+3)}}$

$\sf{\implies{(2x+3)(3x-2)}}$

$\sf\purple{\tt{\therefore{The \ factorised \ form \ is \ (2x+3)(3x-2)}}}$

Answer 2

★$\color{darkblue}\underline{\underline{\sf Corrected \ Question:}}$

$\rm{Factorise \ following \ quadratic \ polynomial }$

$\rm{using \ factor \ theorem}$

$6 {x}^{2} + 5x - 6$

_________________________________________

★$\color{orange}\underline{\underline{\sf Answer:}}$

$\sf\underline\pink{The \ Factorised \ form \ is :}$

$\sf\underline\pink{(3x - 2)(2x + 3)}$

_________________________________________

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

$\rm{Quadratic \ Polynomial \ is : \ 6 {x}^{2} + 5x - 6 }$

_________________________________________

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

$\rm{Factorised \ Form}$

_________________________________________

★$\color{blue}\underline{\underline{\sf Solution:}}$

$\rm{Given \ quadratic \ polynomial \ is}$

$6 {x}^{2} + 5x - 6$

$\rm{now, \ we \ have \ to \ find \ terms \ in \ which }$

$\rm{multiplication \ of \ first \ and \ last \ term}$

$\rm{is \ -36 \ and \ addition \ of \ them \ is \ 5}$

⇛$6 {x}^{2} + 5x - 6$

⇛$6 {x}^{2} + 9x - 4x - 6$

⇛$3x(2x + 3) - 2(2x + 3)$

⇛$(3x - 2)(2x + 3)$

$\sf\underline\pink{The \ Factorised \ form \ is :}$

$\sf\underline\pink{(3x - 2)(2x + 3)}$

_________________________________________

$\rm\purple{Hope \ it \ helps \ :))}$