Question

factorise the following by splitting the middle term
s²+11s+30​

Answer 1

Step-by-step explanation:

the sum = 11

product = 30

The numbers that satisfies this equation are 6 and 5 .

s²+6s + 5s+30

s(s+6) +5(s+6)

(s+5)(s+6)

Answer 2

Question :

Factorise by splitting the middle term :

$s^2+11s+30$.

Solution :

$\: \: \: \: \: : \implies {s}^{2} + 11s + 30$

According to the sum-product pattern :

$\: \: \: \: \: : \implies30 {s}^{2} = (6s)(5s) = 11s$

$\: \: \: \: \: : \implies {s}^{2} + 6s + 5s + 30$

Removing the common term from $s^2+6s$

$\: \: \: \: \: : \implies s(s + 6) + 5s + 30$

Removing the common term from $5s+30$

$\: \: \: \: \: : \implies s(s + 6) + 5(s + 6)$

Getting two factors :

${\bf \: \: \: \: \: \underline{ \therefore \: \: (s+5)(s + 6) \: are \: the \: factors \: of \: {s}^{2} + 11s + 30.}}$