Question

Factorise the following by splitting the middle term
2x^2+3√5x+5

Answer 1

$2 {x}^{2} + 3 \sqrt{5} x + 5 \\ \\ 2 {x}^{2} + \sqrt{5} x + 2 \sqrt{5} x + 5 \\ \\ x(2x + \sqrt{5} ) + \sqrt{5} (2x + \sqrt{5} ) \\ \\ (x + \sqrt{5}) (2x + \sqrt{5} )$

Answer 2

Hi there !!

Given,

to factorise 2x² + 3✓5x + 5 by splitting the middle term,
according to the rule ,

ab = 2 × 5 = 10 = 2✓5 × 1✓5
a + b = 3✓5x = 2✓5 + 1✓5

So,

$2x {}^{2} + 3 \sqrt{5} + 5$

$= 2 {x}^{2} + 2 \sqrt{5}x + \sqrt{5}x + 5$

Taking out common factors,
we have,


$2x(x + \sqrt{5} ) + \sqrt{5} (x + \sqrt{5} )$
Taking x + ✓5 as common factor,
we have,

$(2x + \sqrt{5} )(x + \sqrt{5} )$
is the answer