Final answer:
To factor the polynomial x^4 + x^2 - 30 using substitution, we substitute x^2 with a new variable, factor the resulting quadratic equation, and then substitute x^2 back in for the variable to get the factored polynomial (x^2 + 6)(x^2 - 5).
Step-by-step explanation:
To factor the polynomial x^4 + x^2 - 30 using substitution, we first substitute a variable for one of the terms. Let's substitute x^2 with a new variable, let's say y. Our polynomial becomes y^2 + y - 30. Now, we can factor this quadratic equation. The factors of 30 that add up to 1 are 6 and -5. Therefore, we can rewrite the equation as (y + 6)(y - 5). Finally, we substitute x^2 back in for y, and our factored polynomial is (x^2 + 6)(x^2 - 5).