Question

Hello people ~
factorise: x² + 9x + 20
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Answer 1

`\\ \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!

Answer 2

`(x+4)(x+5)`

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)`