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

Answer:

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

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

Step-by-step 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

$y=(x-3)(x+3)(x-1)(x+1)\\\\0=(x-3)(x+3)(x-1)(x+1)\\\\x=3,\:x=-3,\:x=1,\:x=-1$