division, factor and remainder theorem review

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What is the Factor Theorem?

Back

The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

Tags

CCSS.HSA.APR.B.2

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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 is f(c).

Tags

CCSS.HSA.APR.B.2

Front

How do you perform polynomial long division?

Back

1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by this result. 3. Subtract this from the dividend. 4. Repeat with the new polynomial until the degree of the remainder is less than the degree of the divisor.

Tags

CCSS.HSA.APR.D.6

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function f(x) is a value x = c such that f(c) = 0.

Tags

CCSS.HSF-IF.C.7C

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x.

Front

What is synthetic division?

Back

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

Tags

CCSS.HSA.APR.D.6

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Back

Tags

CCSS.HSA.APR.D.6

Front

Back

The remainder is 96.

Tags

CCSS.HSA.APR.B.2

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Back

The zeros are x = 0, 2, 5.

Front

How do you determine if a polynomial has a specific zero?

Back

Substitute the value into the polynomial. If the result is zero, then it is a zero of the polynomial.

Tags

CCSS.HSF-IF.C.7C