How do I translate a polynomial with C programming without exponent operators?

Question

I was looking in my C textbook and inside there was a page where the prompt told me to translate a polynomial into C code. We have not discussed exponent operators yet and are specifically instructed not to use them at this point and find another way with basic operators. The polynomial goes as such: 5x^(2)+3x-2 .

How do I do this?

Answer 1

Note that ax^2 + bx + c can be written as

c + x*(b + x*(a))

This can easily be extended to any order of polynomial.

Answer 2

There is no such thing as an exponent operator in C. While you can accomplish the same thing using pow() . I suspect your book does not want this. Given this limitation you can do the operation of x^2 as simply x * x where x is a variable for your function.

ie You can do something like this:

int poly(int x) {
    int y = ((5 * x * x) + (3 * x) - 2);
    return y;
}

Addendum:

If you want to have a general formula that you can easily extend for any polynomial degree, you can use this formula instead, with inputs for a , b , c and x :

int poly(int a, int b, int c, int x) {
    int y = c + x*(b + x*(a));
    return y;
}

Thanks to chux and FredK for this.

Answer 3

I think you should parameter a,b,c and x in the second polynomial function

int poly2(int a, int b, int c, int x)
{
    int y = a*x*x+b*x+c;
    return y; 
}

when using this function for your case you can call

int result = poly2(a,b,c, x) 

with a specific set of a,b,c,x

Answer 4

C doesn't have an exponent operator.

One really handy way to model polynomials is to use an array to store the coefficients, such that the array index corresponds to the power of x . IOW, to model 5x 2 + 3x - 2 , use

double coef[] = {-2.0, 3.0, 5.0}; // -2.0 + 3.0x + 5.0x^2

To evaluate the polynomial, use a loop, taking into account the property that FredK mentions in his answer - 5x 2 + 3x - 2 == ((5)x + 3)x - 2 :

size_t num_elements = sizeof coef / sizeof coef[0]; // yields 3 in this case
double result = 0;
for (size_t i = num_elements - 1; i > 0; i--)
  result += x * ( result + coef[i] );
result += coef[0];

This method will work for polynomials of any degree.