Question

F(x) = 1/4 * x ^ 4 - 9/4 * x ^ 2 - x + 3 Rewrite f(x) as the product of a rational number and a polynomial with integer coefficients.

Answer 1

F(x) = 1/4 × (x⁴ - 9x² - 4x + 12)

Explanation:

Since F(x) = x⁴/4 - 9x²/4 - x + 3

The L.C.M of the right hand side is 4.

So, we have

F(x) = (4 × x⁴/4 - 4× 9x²/4 - 4 × x + 4 × 3)/4

F(x) = (x⁴ - 9x² - 4x + 12)/4

F(x) = 1/4 × (x⁴ - 9x² - 4x + 12)