Question

hello people ~
factorise: x² + 9x + 20
​

Answer 1

Answer:

$(x+4)(x+5)$

Step-by-step explanation:

To factorize $x^2+9x+20$

$\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b\\ \textsf{ and group into} \ (ax^2+vx)+(wx+c)$

$a \cdot c=1 \cdot 20=20$

$b=9$

Therefore, the 2 numbers that multiply together to give 20 and add together to give 9 are:  4 and 5

$\implies x^2+4x+5x+20$

$\implies (x^2+4x)+(5x+20)$

Factor the parentheses:

$\implies x(x+4)+5(x+4)$

Factor out the common term $(x+4)$:

$\implies (x+4)(x+5)$

Answer 2

$\\ \rm\rightarrowtail x^2+9x+20$

• Use mid term splitation

$\\ \rm\rightarrowtail x^2+4x+5x+20$

$\\ \rm\rightarrowtail x(x+4)+5(x+4)$

$\\ \rm\rightarrowtail (x+5)(x+4)$

Done!