Factorizing monic quadratics

Factorise:

 $x^2+5x+6$  

Answer explanation

We want to find two numbers which multiply to give us 6 and add to give us 5. Those two numbers are: 3 and 2 because: $3\times2=6$  and  $3+2=5$  

Factorise:

 $p^2+12p+20$  

Answer explanation

We are looking for two numbers that multiply together to give 20 and add together to give 12. 
 $10\times2=20\$  and  $10\text{ +2=12}$  

Factorise:

 $b^2-8b+15$  

Answer explanation

We are looking for factors of 15 which add up to -8. These numbers are: -3 and -5.
 $-3\times-5=15$  and  $-3+-5=-8$  

Factorise:

 $t^2-15t+50$  

Answer explanation

We are looking for factors of 50 that add up to -15.
These numbers are -5 and -10.
 $-5\times-10=50$  and  $-5+-10=-15$  

Factorise:

 $n^2-n-30$  

Answer explanation

We are looking for factors of -30 that add up to 1. 
They are: 6 and -5
 $6\times-5=-30$  and  $6+-5=1$  

Factorise:

 $v^2-7v-60$  

Answer explanation

We are looking for numbers that multiply to give -60 and add to give -7.
 $-12\times5=-60$  and  $-12+5=-7$  

Factorise:

 $x^2+18x+81$  

Answer explanation

We are searching for factors of 81 that add up to 18. These numbers are 9 and 9

 $9\times9=81$  and  $9+9=18$  

Factorise:

 $k^2-10k+25$  

Answer explanation

We are looking for numbers that multiply to give us 25 and add to give us -10. These numbers are: -5 and -5 because:

 $-5\times-5=25\$  and  $-5+-5=-10$  

What is the factorised form of the quadratic expression:

 $x^2-13x+30$  

•  $\left(x+3\right)\left(x+10\right)$  

•  $\left(x-3\right)\left(x+10\right)$  

•  $\left(x-15\right)\left(x-2\right)$  

•  $\left(x-10\right)\left(x-3\right)$  

•  $\left(x+3\right)\left(x-10\right)$  

What is the factorised form of the quadratic expression:
 $h^2+6h-27$  ?

•  $\left(h-9\right)\left(h-3\right)$  

•  $\left(h+9\right)\left(h-3\right)$  

•  $h\left(h+6\right)-27$  

•  $\left(h+3\right)\left(h-9\right)$  

•  $h^2+3\left(2h-9\right)$