Synthetic Division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c) without using long division.

Front

How do you set up synthetic division?

Back

To set up synthetic division, write the coefficients of the polynomial in a row, and place the zero of the divisor (c) to the left.

Front

What is the purpose of using zero placeholders in synthetic division?

Back

Zero placeholders are used to represent missing terms in the polynomial, ensuring that the division process is accurate.

Front

What does the remainder represent in synthetic division?

Back

The remainder represents the value of the polynomial at the divisor's root, indicating whether the divisor is a factor of the polynomial.

Front

If dividing x^3 + 2x^2 - 5 by (x - 1), what is the first step in synthetic division?

Back

The first step is to write the coefficients: 1 (for x^3), 2 (for x^2), 0 (for x), and -5 (constant term).

Front

What is the significance of the number of zeros needed in synthetic division?

Back

The number of zeros corresponds to the degree of the polynomial minus the degree of the divisor, ensuring proper alignment during division.

Front

How do you determine if (x - c) is a factor of a polynomial using synthetic division?

Back

If the remainder is zero after performing synthetic division, then (x - c) is a factor of the polynomial.

Front

What is the result of synthetic division if the divisor is (x + 2) and the polynomial is x^2 - 4?

Back

The result is x - 2 with a remainder of 0, indicating that (x + 2) is a factor.

Front

What mistake did Cam make in his synthetic division process?

Back

Cam did not use a zero placeholder for the x^3 term, which is essential for accurate calculations.

Front

What does it mean if the remainder is not zero in synthetic division?

Back

If the remainder is not zero, it means that the divisor is not a factor of the polynomial.