Respuesta :

Nayefx

Answer:

[tex] \huge \colorbox{red}{ \rm (3x - 7)(x + 1)}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • factoring
  • PEMDAS

tips and formulas:

  • quadratic expression:ax²+bx+c

factoring quadratic:

  1. Find two numbers that multiply to give ac, and add to give b
  2. rewrite the middle with those numbers
  3. factor out common terms
  4. group

let's solve:

a is 3 and b is -7

[tex]\quad ac=3\times -7[/tex]

therefore

[tex]\quad ac=-21[/tex]

now we need to find two numbers that give -21

to do so we need to find the factors of 21

which are

[tex]\quad 1,3,7[/tex]

likewise,

[tex]\quad -1,-3,-7[/tex]

in this case we can take any two numbers from negative and positive factors that give us -21 and -4

3 and -7 are the two numbers that multiply to give -21 (3×-7=-21) and add to give -4. (3+(-7)=-4)

now let's factor:

  1. [tex] \sf rewrite \: - 4x \: as \: 3x - 7x : \\ \rm {3 x}^{2} + 3x - 7x - 7 [/tex]
  2. [tex] \sf factor \: out \: 3x : \\ \rm 3x(x + 1) - 7x - 7[/tex]
  3. [tex] \sf factor \: out \: - 7 : \\ \rm 3x(x + 1) - 7(x + 1)[/tex]
  4. [tex] \sf \quad group : \\ \quad \rm (3x - 7)(x + 1)[/tex]

[tex]\text{And we are done!}[/tex]

Answer:

3x²-4x-7=0

doing middle term factorization

3x²-7x+3x-7=0

x(3x-7)+1(3x-7)=0

(3x-7)(x+1)=0

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