Alg2 Polynomial Remainder Theorem

Front

What is the Polynomial Remainder Theorem?

Back

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

Tags

CCSS.HSA.APR.B.2

Front

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

Back

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

Tags

CCSS.HSA.APR.D.6

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used specifically for dividing by linear factors of the form (x - c).

Tags

CCSS.HSA.APR.D.6

Front

If f(x) = 3x³ - 5x² - 4x + 1, what is the remainder when divided by (x + 3)?

Back

The remainder is -113.

Tags

CCSS.HSA.APR.B.2

Front

What is the remainder when a³ - 4 is divided by a + 2?

Back

The remainder is -12.

Tags

CCSS.HSA.APR.B.2

Front

What does the remainder represent in polynomial division?

Back

The remainder represents the value of the polynomial at the root of the divisor, indicating how much is left over after division.

Tags

CCSS.HSA.APR.B.2

Front

How can you verify the result of polynomial division?

Back

You can verify the result by multiplying the quotient by the divisor and adding the remainder; it should equal the original polynomial.

Tags

CCSS.HSA.APR.D.6

Front

What is the significance of the degree of a polynomial in division?

Back

The degree of the polynomial determines the highest power of x in the polynomial, affecting the number of times you can divide.

Tags

CCSS.HSA.APR.D.6

Front

What is the result of dividing a polynomial by a linear factor?

Back

The result is a polynomial of one degree lower than the original polynomial, plus a remainder.

Tags

CCSS.HSA.APR.D.6

Front

If p(x) = x³ - 5x² + 2x - 10, what is the remainder when divided by (x - 5)?

Back

The remainder is 0.

Tags

CCSS.HSA.APR.B.2