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37 votes
37 votes
Hello people ~
x² + 4x - 77​

User Nishant Shah
by
3.3k points

2 Answers

18 votes
18 votes


\\ \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!

User Eric Xin Zhang
by
2.8k points
12 votes
12 votes

Answer:


(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)

User Zruty
by
3.2k points