Factorise: 2 x^{2}+7 x+3 | vedclass

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Question

(A) To factorise the quadratic expression $2 x^{2}+7 x+3$,we use the splitting the middle term method.Here,the expression is in the form $ax^{2} + bx

Vedclass · Accepted Answer

$(2x+1)(x+3)$

Vedclass · Answer

(A) To factorise the quadratic expression $2 x^{2}+7 x+3$,we use the splitting the middle term method.Here,the expression is in the form $ax^{2} + bx + c$,where $a = 2$,$b = 7$,and $c = 3$.We need to find two numbers $l$ and $m$ such that $l + m = b = 7$ and $l 	imes m = a 	imes c = 2 	imes 3 = 6$.The two numbers that satisfy these conditions are $1$ and $6$,since $1 + 6 = 7$ and $1 	imes 6 = 6$.Now,rewrite the middle term $7x$ as $x + 6x$:$2 x^{2} + 7 x + 3 = 2 x^{2} + x + 6 x + 3$Group the terms and factor out common factors:$= x(2 x + 1) + 3(2 x + 1)$Finally,factor out the common binomial $(2 x + 1)$:$= (2 x + 1)(x + 3)$Thus,the factors are $(2 x + 1)(x + 3)$.

Factorise: $2 x^{2}+7 x+3$

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