Question

Hello people ~
x² + 4x - 77​

Answer 1

`\\ \rm\rightarrowtail x^2+4x-77`

`\\ \rm\rightarrowtail x^2+11x-7x-77`

`\\ \rm\rightarrowtail x(x+11)-7(x+11)`

`\\ \rm\rightarrowtail (x-7)(x+11)`

Done!

Answer 2

`(x+11)(x-7)`

Explanation:

To factorize
`x^2+4x-77`

`\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 -77=-77`

`b=4`

Therefore, the 2 numbers that multiply together to give -77 and add together to give 4 are: 11 and -7

`\implies x^2+11x-7x-77`

`\implies (x^2+11x)+(-7x-77)`

Factor the parentheses:

`\implies x(x+11)-7(x+11)`

Factor out the common term
`(x+11)`:

`\implies (x+11)(x-7)`