Question

2x^2+7/2 x +3/4 middle term splitting

Answer 1

Answer:

$(x + \frac{1}{4} )(2x + 3)$

Step-by-step explanation:

ATQ,

${2x}^{2} + \frac{7}{2} x + \frac{3}{4}$

Converting 2x² into a fraction

${ \frac{2}{1}x }^{2} + \frac{7}{2}x + \frac{3}{4}$

Multiplying each fraction according to the denominators' LCM

${ \frac{8}{4}x }^{2} + \frac{14}{4}x + \frac{3}{4}$

Multiplying 8 and 3, we get 24.

Other combinations of its factors are:

1×24

2×12

3×8

4×6

Out of these combinations, the sum of the combination (2×12) matches the numerator of the middle term.

So after splitting the middle term,

${ \frac{8}{4}x }^{2} + \frac{12}{4}x + \frac{2}{4} x + \frac{3}{4}$

Applying redistribution method

$\frac{4}{4}x( \frac{2}{1}x + \frac{3}{1} ) + \frac{1}{4}( \frac{2}{1}x + \frac{3}{1} )$

Simplifying

$x(2x + 3) + \frac{1}{4}(2x + 3)$

So, on solving this, we get:

$(x + \frac{1}{4} )(2x + 3)$