Question
Find trinomial $($quadratic expression$), $ given below $,$ find whether it is factorisable or not. Factorise $,$ if possible.$2x^2- 7x - 15$
✓
Answer
Given expression $ :2x^2- 7x - 15$
Comparing with $ax^2 + bx + c$, we get $a = 2, b = -7$, and $c = -15$
$\therefore b^2 - 4ac = (-7)^2 - 4(2)(-15) = 49 + 120 = 169,$ which is a perfect square.
$\therefore 2x^2 - 7x - 15$ is factorisable.
Now $, 2x^2 - 7x - 15$
$= 2x2 - 10x + 3x - 15$
$= 2x( x - 5 ) + 3( x - 5 )$
$= ( 2x + 3 )( x - 5 )$
Comparing with $ax^2 + bx + c$, we get $a = 2, b = -7$, and $c = -15$
$\therefore b^2 - 4ac = (-7)^2 - 4(2)(-15) = 49 + 120 = 169,$ which is a perfect square.
$\therefore 2x^2 - 7x - 15$ is factorisable.
Now $, 2x^2 - 7x - 15$
$= 2x2 - 10x + 3x - 15$
$= 2x( x - 5 ) + 3( x - 5 )$
$= ( 2x + 3 )( x - 5 )$
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