Factorise:2 x^{2}-7 x-15 | vedclass

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Question

(A) To factorise the quadratic polynomial $2 x^{2}-7 x-15$,we look for two numbers $p$ and $q$ such that their sum is the coefficient of $x$,which is

Vedclass · Accepted Answer

$(x-5)(2 x+3)$

Vedclass · Answer

(A) To factorise the quadratic polynomial $2 x^{2}-7 x-15$,we look for two numbers $p$ and $q$ such that their sum is the coefficient of $x$,which is $-7$,and their product is the product of the coefficient of $x^{2}$ and the constant term,which is $2 	imes (-15) = -30$.We need $p+q = -7$ and $p q = -30$.By testing factors of $-30$,we find that $-10$ and $3$ satisfy these conditions: $(-10) + 3 = -7$ and $(-10) 	imes 3 = -30$.Now,split the middle term $-7 x$ as $-10 x + 3 x$:$2 x^{2}-7 x-15 = 2 x^{2}-10 x+3 x-15$Factor by grouping:$= 2 x(x-5) + 3(x-5)$Taking $(x-5)$ as a common factor:$= (x-5)(2 x+3)$

Factorise:
$2 x^{2}-7 x-15$

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Factorise:$2 x^{2}-7 x-15$