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3. A fourth-degree polynomial equation is shown below. Y= x^4 – 10x^2 + 9 Use this problem to complete the following questions. 1) Write the equation in factored form. 2) Use what you have learned to find the solutions to the polynomial equation.

Relax

Respuesta :

Answer:

1) [tex]y=(x-3)(x+3)(x-1)(x+1)[/tex]

2) [tex]x=3,\:x=-3,\:x=1,\:x=-1[/tex]

Step-by-step explanation:

Factor by grouping

[tex]y=x^4-10x^2+9\\\\y=x^4-x^2-9x^2+9\\\\y=x^2(x^2-1)-9(x^2-1)\\\\y=(x^2-9)(x^2-1)\\\\y=(x-3)(x+3)(x-1)(x+1)[/tex]

Solutions

[tex]y=(x-3)(x+3)(x-1)(x+1)\\\\0=(x-3)(x+3)(x-1)(x+1)\\\\x=3,\:x=-3,\:x=1,\:x=-1[/tex]

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