can you always use synthetic division for dividing polynomials? explain
No, you cannot always use synthetic division for dividing polynomials. Synthetic division is specifically for dividing a polynomial by a linear binomial of the form (x - a).
To use synthetic division, the divisor must be in the form (x - a). If the divisor is a polynomial of higher degree or has multiple terms, you cannot apply synthetic division. In such cases, you would have to use long division to divide the polynomials.
For example, if you want to divide a polynomial by (x^2 + 2x + 1), which is not a linear binomial, you cannot directly use synthetic division. Instead, you would have to use long division to divide the two polynomials.
Synthetic division is a simpler and quicker method for dividing polynomials when the divisor is a linear binomial. However, for more complex divisors, long division remains the appropriate method.