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Factorisation — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSFactorisation2 Marks
Question
Find trinomial $($quadratic expression$),$ given below$,$ find whether it is factorisable or not. Factorise$,$ if possible.$x^2- 3x - 54$
✓

Answer

Given expression $: x^2 - 3x - 54$
Comparing with $ax^2 + bx + c$, we get $a = 1, b = -3$, and $c = - 54$
$\therefore b^2 - 4ac = (-3)^2 - 4(1)(-54) = 9 + 216 = 225,$ which is a perfect square.
$\therefore x^2 - 3x - 54$ is factorisable.
Now, $x^2 - 3x - 54 = x^2 - 9x + 6x - 54$
$= x( x - 9 ) + 6( x - 9 )$
$= ( x - 9 )( x + 6 )$

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