Question

Factorising 2x^2 + 7x + 3
by splitting the middle term

Answer 1

$\sf \bigcirc \: Factorising \: \red{ 2x^2 + 7x + 3}\: by \\ \\ \sf splitting \: the \: middle \: term.$

$\sf \red {\underline{{2x}^{2} + 7x + 3}} \\ \\ \sf{2x}^{2} + 6x + x + 3 \\ \\ \sf2x(x + 3) + 1(x + 3) \\ \\{\underline{\boxed{\bf\red{(2x+1)(x+3)}}}} \\\\ \sf( 2x + 1)(x + 3) = 0 \\ \\ \sf 2x + 1 = 0⠀⠀⠀⠀⠀ x + 3 = 0 \\ \\ \sf 2x = - 1⠀⠀⠀⠀⠀ x = - 3 \\ \\ \sf x = \frac{ - 1}{2}⠀⠀⠀⠀⠀ x = - 3$

Answer 2

To factorize : $2x^{2} + 7x + 3$

Solution :

• According to question we are asked to split the given expression by splitting the middle term.
• We spilt the middle term such that product of the numbers is last term and sum or difference of those numbers is middle term.
• Here, $7x$ is the middle term and multiplying constants of first and last term i.e. $2$ and $3$ we get $6$ as the last term.
• $2x^{2} + 7x + 3$

       $= 2x^{2} + x +6x +3 \\= x (2x +1 ) + 3 (2x +1 ) \\= (2x +1 ) (x + 3 )$

• $x = \frac{-1}{2}$ and $x = -3$

Hence, on splitting the middle term of $2x^{2} + 7x + 3$ we get value of $x$ as$x = \frac{-1}{2}$   or $x = -3$ .