Math, asked by harshit81117, 10 months ago

20 x² + 13x - 72 factorise

Answers

Answered by rohithkumarr1792004

Step-by-step explanation:

the total answer for this question is 7/5 and 9/4

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{\fcolorbox{red}{#ffdfff}{( 4x + 9 )( 5x - 8 )}}$

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

$20 {x}^{2} + 13x - 72$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

Factors of the above given polynomial.

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Factorisation of polynomials

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

We already have,

$20 {x}^{2} + 13x - 72$

$= 20 {x}^{2} + (45 - 32)x - 72 \longrightarrow [ \because (45 \times - 32 = 20 \times - 72) \: and \: (45 + ( - 32)) = 13 \: ]$

$= 20 {x}^{2} + 45x - 32x - 72$

$= 5x( + 4x) + 5x( + 9) - 8( + 4x) - 8( + 9)$

$= 5x(4x + 9) - 8(4x + 9)$

$= (4x + 9)(5x - 8)$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

$\large\boxed{ \: 20 {x}^{2} + 13x - 72 \: \: = \: \: (4x + 9)(5x - 8) \: }$

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