Remainder Theorem

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What is the Remainder Theorem?

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

Tags

CCSS.HSA.APR.B.2

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How do you find the remainder when dividing a polynomial by a linear divisor?

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To find the remainder when dividing a polynomial f(x) by a linear divisor (x - c), evaluate f(c).

Tags

CCSS.HSA.APR.B.2

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What is synthetic division?

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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

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What is the value of k in the polynomial x^3 - kx^2 + 2x + 5 if the remainder is 2 when divided by x - 3?

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The value of k is 4.

Tags

CCSS.HSA.APR.B.2

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How do you evaluate a polynomial function at a specific value?

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To evaluate a polynomial function f(x) at a specific value a, substitute a into the polynomial and simplify.

Tags

CCSS.HSF.IF.A.2

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What is the remainder when a^3 - 4 is divided by a + 2?

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The remainder is -12.

Tags

CCSS.HSA.APR.B.2

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

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

Tags

CCSS.HSA.APR.B.2

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How can you use the Remainder Theorem to find roots of a polynomial?

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By applying the Remainder Theorem, if f(c) = 0 for some value c, then (x - c) is a factor of the polynomial f(x).

Tags

CCSS.HSA.APR.B.2

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What is the significance of the coefficients in synthetic division?

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The coefficients in synthetic division represent the coefficients of the polynomial being divided, and they are used to perform the division process.

Tags

CCSS.HSA.APR.D.6

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What is the result of evaluating f(5) for the polynomial f(x) = 5x^2 - 7x - 10?

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The result is 80.

Tags

CCSS.HSF.IF.A.2