Question

5. Use synthetic substitution evaluate (x* + 3x - 2) at f(-4).

Answer 1

You have the following function:

`f(x)=x^2+3x\text{ -2}`

In order to evaluate the given function with synthetic susbtotution, for x=-4, you use synthetic division, just as follow

1 + 3 - 2 -4

-4 4

1 -1 2

remind that for synthetic division you use the coefficients of all terms of the polynomial. The reminder of the division, which is the last number obtained, in this case, number 2, is the result of the function evaluated in x=-4. Hence

f(-4)=2

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- -

If the polynomial is:

`f(x)=x^4+3x^2-2`

To get the value of f(-4) you procede as before, but remeber that coefficients of variables with exponents that don't appear in the polynomial as consider as 0.

1 0 3 0 -2 -4

-4 16 -76 304

1 -4 19 -76 302

The zeros appear because there are no terms with power 3 or power 1 in the polynomial, however, it is necessary to include the coeeficient of such a terms.

Hence, for f(-4) = 302