Remainder Theorem and Factor Theorem.

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

Synthetic division is a simplified form of polynomial long division. It involves using the coefficients of the polynomial and the root of the divisor to find the quotient and remainder.

Front

What is the significance of a zero remainder in polynomial division?

Back

A zero remainder indicates that the divisor is a factor of the polynomial.

Front

If f(x) = 2x^3 - 5x - 7, what is f(2)?

Back

f(2) = 2(2)^3 - 5(2) - 7 = 16 - 10 - 7 = -1.

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What does it mean if a polynomial leaves a remainder when divided?

Back

It means that the divisor is not a factor of the polynomial.

Front

What is the first step in synthetic division?

Back

The first step is to write down the coefficients of the polynomial in descending order.

Front

How do you determine if (x - c) is a factor of f(x)?

Back

Evaluate f(c). If f(c) = 0, then (x - c) is a factor of f(x).

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What is the role of the constant term in synthetic division?

Back

The constant term is the last number in the synthetic division process, representing the remainder.

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What is the result of dividing 5x^3 + 34x^2 + 26x + C by (x + 6) if C = 12?

Back

The result is a polynomial with a remainder of 0, indicating (x + 6) is a factor.