r^4 – 2tr^2 – 35t^2

Answer 1

To factor the polynomial r^4 - 2tr^2 - 35t^2, we can treat it as a quadratic in r^2.

Let x = r^2. Then the polynomial becomes x^2 - 2tx - 35t^2.

To factor this quadratic, we need to find two numbers that multiply to -35t^2 and add up to -2t.

The numbers that satisfy this condition are -7t and 5t.

So, we can rewrite the polynomial as:

(x - 7t)(x + 5t)

Substitute back x = r^2:

(r^2 - 7t)(r^2 + 5t)

Therefore, the factored form of r^4 - 2tr^2 - 35t^2 is (r^2 - 7t)(r^2 + 5t).