Use the remainder theorem to determine the remainder when (3 x^3-2 x^2+x-5) is divided by (x+2)

Name: Problem 31, Chapter 1: Higher Engineering Mathematics
Uploaded: 2021-12-22T07:40:47-08:00
Duration: 1 min 51 s
Channel: Varsha Aggarwal
Description: Use the remainder theorem to determine the remainder when (3 x^3-2 x^2+x-5) is divided by (x+2) By the remainder theorem, the remainder is given by a p^3+b p^2+c p+d, where a=3, b=-2, c=1, d=-5 and p=-2 Hence the remainder is: 3(-2)^3+(-2)(-2)^2+(1)(-2)+(-5) =-24-8-2-5 =-39

step 1 In this question using Remindered theorem we have to find Reminder when TXQ minus 2 x squared x

Question

Use the remainder theorem to determine the remainder when $\left(3 x^{3}-2 x^{2}+x-5\right)$ is divided by $(x+2)$ By the remainder theorem, the remainder is given by $a p^{3}+b p^{2}+c p+d$, where $a=3, b=-2, c=1$, $d=-5$ and $p=-2$ Hence the remainder is: $$ \begin{aligned} &3(-2)^{3}+(-2)(-2)^{2}+(1)(-2)+(-5) \\ &\quad=-24-8-2-5 \\ &\quad=-39 \end{aligned} $$

    Use the remainder theorem to determine the remainder when $\left(3 x^{3}-2 x^{2}+x-5\right)$ is divided by $(x+2)$
By the remainder theorem, the remainder is given by $a p^{3}+b p^{2}+c p+d$, where $a=3, b=-2, c=1$, $d=-5$ and $p=-2$
Hence the remainder is:
$$
\begin{aligned}
&3(-2)^{3}+(-2)(-2)^{2}+(1)(-2)+(-5) \\
&\quad=-24-8-2-5 \\
&\quad=-39
\end{aligned}
$$

Higher Engineering Mathematics

John Bird 8th Edition

Chapter 1, Problem 31

Instant Answer

Solved by Expert Varsha Aggarwal

12/22/2021

Step 1

In this case, $a=3, b=-2, c=1, d=-5$ and $p=-2$. Show more…

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Use the remainder theorem to determine the remainder when $\left(3 x^{3}-2 x^{2}+x-5\right)$ is divided by $(x+2)$ By the remainder theorem, the remainder is given by $a p^{3}+b p^{2}+c p+d$, where $a=3, b=-2, c=1$, $d=-5$ and $p=-2$ Hence the remainder is: $$ \begin{aligned} &3(-2)^{3}+(-2)(-2)^{2}+(1)(-2)+(-5) \\ &\quad=-24-8-2-5 \\ &\quad=-39 \end{aligned} $$

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Key Concepts

Remainder Theorem

The remainder theorem states that if a polynomial f(x) is divided by (x - k), then the remainder of that division is equal to f(k). This theorem simplifies the process of finding remainders, as it replaces the division process with a simple substitution of the value k into the polynomial.

Polynomial Evaluation

Polynomial evaluation involves substituting a given value into a polynomial and calculating the result. This concept is crucial in applying the remainder theorem, as the process requires computing f(k) to determine the remainder when the polynomial is divided by (x - k).

Polynomial Division

Polynomial division is the process of dividing one polynomial by another, similar to numeric long division. When the divisor is a linear polynomial, the remainder theorem can be used to quickly determine the remainder without performing detailed division steps.

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