Question

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.

Answer 1

1)
`y=(x-3)(x+3)(x-1)(x+1)`

2)
`x=3,\:x=-3,\:x=1,\:x=-1`

Explanation:

Factor by grouping

`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)`

Solutions

`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`