Respuesta :
regroup: (2x³+4x²)-(2x+4)
factor: 2x²(x+2)-2(x+2)
(2x²-2)(x+2)
2(x²-1)(x+2)
2(x+1)(x-1)(x+2) is the final answer.
factor: 2x²(x+2)-2(x+2)
(2x²-2)(x+2)
2(x²-1)(x+2)
2(x+1)(x-1)(x+2) is the final answer.
Answer:
2(x-1)(x+1)(x+2)
Step-by-step explanation:
Given : [tex]2x^3+4x^2-2x-4[/tex]
To Find: Express the polynomial as a product of linear factors
Solution:
[tex]2x^3+4x^2-2x-4[/tex]
[tex](2x^3+4x^2)-(2x-4)[/tex]
[tex]2x^2(x+2)-2(x+2)[/tex]
[tex](2x^2-2)(x+2)[/tex]
[tex]2(x^2-1)(x+2)[/tex]
Using identity : [tex]x^2-a^2=(x-a)(x+a)[/tex]
[tex]2(x-1)(x+1)(x+2)[/tex]
So, [tex]2x^3+4x^2-2x-4[/tex] as a product of linear factors :
[tex]2x^3+4x^2-2x-4=2(x-1)(x+1)(x+2)[/tex]
