Remainder Theorem & Factor Theorem

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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 f(c).

Tags

CCSS.HSA.APR.B.2

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.

Tags

CCSS.HSA.APR.B.2

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How do you find the remainder of a polynomial when divided by a linear factor?

Back

To find the remainder of a polynomial f(x) when divided by (x - c), evaluate f(c).

Tags

CCSS.HSA.APR.B.2

Front

What is the significance of the Remainder Theorem in polynomial division?

Back

The Remainder Theorem allows us to quickly find the remainder without performing full polynomial long division.

Tags

CCSS.HSA.APR.B.2

Front

If P(x) = 2x^4 + x^3 - 3x^2 - x - 15, what is P(2)?

Back

P(2) = 11.

Tags

CCSS.HSF.IF.A.2

Front

Is (x - 3) a factor of the polynomial x^3 - 3x^2 + 2x + 2?

Back

No, (x - 3) is not a factor.

Tags

CCSS.HSA.APR.B.2

Front

What is the result of dividing 3x^3 - 5x^2 - 4x + 1 by (x + 3)?

Back

The remainder is -113.

Tags

CCSS.HSA.APR.B.2

Front

What does it mean if f(c) = 0 for a polynomial f(x)?

Back

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

Tags

CCSS.HSA.APR.B.2

Front

How can you determine if a polynomial has a specific factor?

Back

Evaluate the polynomial at the root of the factor; if the result is zero, the factor exists.

Tags

CCSS.HSA.APR.B.2

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by linear factors.

Tags

CCSS.HSA.APR.D.6