How to Factor Decimal Polynomials?

Factorizing the Polynomials with Integer constants as coefficients is relatively simple as compared to factorizing polynomials with decimal coefficients. To have Decimals in polynomials means to solve Fractions. Let us learn how to factor decimal polynomials with help of examples:

Example 1: Suppose we have fraction with decimal polynomial expressions both in the numerator and the denominator like (0.4 x² + 2.8 x + 4.0) / (0.1 x² + 2.5 x + 10.0). Simplify this fraction?

Solution: To simplify the above fraction we need to 1st remove the decimal points to get:

(0.4 x² + 2.8 x + 4.0) / (0.1 x² + 2.5 x + 10.0) = ((4 /10) x² + (28 /10) x + 40 /10) / ((1 /10) x² + (25 /10) x + 100 /10).

Taking 1 /10 common from the numerator and denominator we can write:

= (1 /10) (4 x² + 28 x + 40) / (1 /10) (x² + 25 x + 100).

Cancelling 1 /10 from the numerator and the denominator we can write our fraction as:

= (4 x² + 28 x + 40) / (x² + 25 x + 100).

Now the polynomials in the fraction can be easily factorized by using mid – term splitting method as follows:

(4 x² + 28 x + 40) / (x² + 25 x + 100) = (4 x² + 20 x + 8 x + 40) / (x² + 20 x + 5 x + 100),

= (4 x (x + 5) + 8 (x + 5)) / (x (x + 20) + 5 (x + 20)) = (4 x + 8) (x + 5) / (x + 5) (x + 20)).

(0.4 x² + 2.8 x + 4.0) / (0.1 x² + 2.5 x + 10.0) = (4 x + 8) / (x + 20).