Synthetic Division

Front

What is Synthetic Division?

Back

Synthetic Division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is used to find the quotient and remainder without performing long division.

Front

What is the purpose of finding zeros of a polynomial?

Back

Finding the zeros of a polynomial helps identify the x-values where the polynomial equals zero, which are crucial for graphing the polynomial and solving equations.

Front

How do you determine if a number is a potential zero of a polynomial?

Back

A number 'c' is a potential zero of a polynomial if substituting 'c' into the polynomial results in a value of zero.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of this division is equal to f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

How do you perform Synthetic Division?

Back

1. Write down the coefficients of the polynomial. 2. Use the zero of the divisor (c) on the left. 3. Bring down the leading coefficient. 4. Multiply and add down the column. 5. The last number is the remainder.

Front

What is the significance of the remainder in Synthetic Division?

Back

The remainder indicates the value of the polynomial at the zero of the divisor. If the remainder is zero, it confirms that the divisor is a factor of the polynomial.

Front

What is the reduced polynomial after Synthetic Division?

Back

The reduced polynomial is the quotient obtained after dividing the original polynomial by the linear binomial, excluding the remainder.

Front

How do you find the zeros of a polynomial using Synthetic Division?

Back

By performing Synthetic Division with potential zeros, you can determine which values yield a remainder of zero, indicating they are actual zeros.

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

A polynomial of degree n can have at most n real zeros, according to the Fundamental Theorem of Algebra.