Question

Factor over the integers the polynomial that is quadratic in form. x⁴-29x²+100

Answer 1

To factor the given quadratic polynomial x⁴-29x²+100 over the integers, we can use the method of grouping. The factored form is (x² - 4)(x² - 25).

Step-by-step explanation:

To factor the given polynomial x⁴-29x²+100 over the integers, we can use a factoring method called grouping.

First, notice that the polynomial is quadratic in form. Let's substitute a variable to represent x². Let's say a = x². Now the polynomial becomes a² - 29a + 100.

We can factor this quadratic expression by factoring the trinomial a² - 29a + 100. We can use the fact that a² - 29a + 100 factors as (a - 4)(a - 25).

Substituting back x² for a, we have (x² - 4)(x² - 25) as the factored form of the given polynomial.