Question

The condition under which we may use synthetic division to divide polynomials

Polynomial division
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asked 2021-02-20
The condition under which we may use synthetic division to divide polynomials

Answers (1)

2021-02-21
Given:
- Synthetic division of polynomial
Key concepts applied:
Synthetic division can be used whenever we need to divide a polynomial function by a binomial of the form x—c . By doing synthetic division, we can find the actual quotient and also the remainder we get when we divide the polynomial function by x—c.
The Remainder Theorem states that the remainder that we end up with when synthetic division is applied actually gives us the functional value. Another use is finding factors and zeros.
The Factor Theorem states that if the functional value is 0 at some value c, then x—c is a factor. Thus, we can not only find that functional value by using synthetic division, but also the quotient found can help with the factoring process.
It is to be noted that, to divide polynomials using synthetic division, we must be dividing by a linear expression and the leading coefficient must be a 1. If the leading coefficient is not a 1, then we can perform synthetic division after dividing by the leading coefficient to turn the leading coefficient into a1.
Conclusion:
To divide polynomials using synthetic division, we must be dividing by a linear expression and the leading coefficient must be a 1. If the leading coefficient is not a 1, then we can perform synthetic division after dividing by the leading coefficient to turn the leading coefficient into a 1.
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