Remainder theorem/Factor theorem

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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).

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 division?

Back

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

Tags

CCSS.HSA.APR.B.2

Front

What is synthetic division?

Back

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

Tags

CCSS.HSA.APR.D.6

Front

If f(x) = x^3 - 3x^2 + 4, what is f(1)?

Back

f(1) = 1^3 - 3(1^2) + 4 = 2.

Tags

CCSS.HSF.IF.A.2

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What is the result of dividing (2x^3 - 5x^2 + 3x + 7) by (x - 2)?

Back

The result is 2x^2 - x + 1 with a remainder of 9.

Tags

CCSS.HSA.APR.D.6

Front

What does it mean if the remainder is 0 when dividing a polynomial?

Back

If the remainder is 0, it means that the divisor is a factor of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

How can you use the Remainder Theorem to evaluate polynomials?

Back

You can evaluate a polynomial at a specific value c by using the Remainder Theorem, which states that f(c) gives the value of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

What is the relationship between the degree of a polynomial and its factors?

Back

The degree of a polynomial is equal to the number of its linear factors, counting multiplicities.

Tags

CCSS.HSA.APR.B.2

Front

If f(x) = 3x^2 - 9x - 20, what is f(5)?

Back

f(5) = 3(5^2) - 9(5) - 20 = 10.

Tags

CCSS.HSF.IF.A.2