kenzbecker kenzbecker
  • 19-10-2018
  • Mathematics
contestada

Factor the polynomial completely given that k=4 is a zero. Also list the zeroes of P(x).

P(x) x^4-2x^3-7x^2-4x

Respuesta :

frika
frika frika
  • 20-10-2018

If it is known that k=4 is polynomial's zero, then the polynomial should have x-4 as its factor.

Factor the polynomial:

1) [tex]P(x)=x^4-2x^3-7x^2-4x=x(x^3-2x^2-7x-4)[/tex]

2) Consider the polynomial [tex]x^3-2x^2-7x-4=x^3-4x^2+4x^2-2x^2-7x-4=x^2(x-4)+2x^2-7x-4=x^2(x-4)+2x^2-8x+8x-7x-4=x^2(x-4)+2x(x-4)+(x-4)=(x-4)(x^2+2x+1)[/tex]

3) The expression [tex]x^2+2x+1[/tex] is a perfect square:

[tex]x^2+2x+1=(x+1)^2[/tex]

Therefore,

[tex]P(x)=x(x-4)(x+1)^2.[/tex]

Answer: [tex]P(x)=x(x-4)(x+1)^2.[/tex] Zeroes: 0, 4, -1 (twice)

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