Question

Hello people ~
x² + 4x - 77​

Answer 1

Answer:

$(x+11)(x-7)$

Step-by-step 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 $(x+11)$:

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

Answer 2

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

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

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

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

Done!