Question

Use synthetic division and the Remainder Theorem to evaluate $P(c)$. $P(x)=5 x^{4}+30 x^{3}-40 x^{2}+36 x+14, \quad c=-7$

Name: Problem 45, Chapter 3: College Algebra
Uploaded: 2020-08-08T06:59:19-08:00
Duration: 5 min 19 s
Channel: Ankit Gupta
Description: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x)=5 x^4+30 x^3-40 x^2+36 x+14, c=-7

   Use synthetic division and the Remainder Theorem to evaluate $P(c)$.
$P(x)=5 x^{4}+30 x^{3}-40 x^{2}+36 x+14, \quad c=-7$

College Algebra

James Stewart,… 7th Edition

Chapter 3, Problem 45

Instant Answer

Solved by Expert Ankit Gupta

08/08/2020

Step 1

According to the Remainder Theorem, the remainder of the division of $P(x)$ by $x-c$ is equal to $P(c)$. Show more…

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Use synthetic division and the Remainder Theorem to evaluate $P(c)$. $P(x)=5 x^{4}+30 x^{3}-40 x^{2}+36 x+14, \quad c=-7$

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Key Concepts

Synthetic Division

Synthetic division is an algorithmic technique used to divide a polynomial by a linear factor of the form (x - c). It streamlines the division process by focusing solely on the coefficients and performing a series of multiplications and additions, which makes it much simpler and less error-prone than the traditional long division method.

Remainder Theorem

The Remainder Theorem states that when a polynomial P(x) is divided by a linear divisor (x - c), the remainder of that division is equal to P(c). This theorem provides an efficient way to evaluate the polynomial at a particular point, as it removes the need to substitute and directly calculate every term.

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