Remainder Theorem

Front

What is the Remainder Theorem?

Back

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

Front

How do you find f(5) for f(x) = 3x² - 9x - 20 using synthetic division?

Back

To find f(5), perform synthetic division with 5. The result is 10.

Front

Is (x-2) a factor of (x³ - 8x² + 14x - 4)?

Back

Yes, (x-2) is a factor and the remainder is zero.

Front

What is the degree of the polynomial x³ - 8x² + 14x - 4?

Back

The degree of the polynomial is 3.

Front

What is the factorization of k³ - 27?

Back

The factorization is (k - 3)(k² + 3k + 9).

Front

How many zeros does the polynomial x⁴ + 2x³ + x² + 2 have?

Back

The polynomial has 4 imaginary zeros.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor.

Front

What does it mean if a polynomial has a remainder of zero when divided by (x - c)?

Back

It means that (x - c) is a factor of the polynomial.

Front

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

Back

The degree of a polynomial indicates the maximum number of zeros (real or complex) it can have.

Front

How can you determine if (x - c) is a factor of a polynomial?

Back

Evaluate the polynomial at c; if f(c) = 0, then (x - c) is a factor.