Question

Find the remainder when 2x^2 - 7x – 1 is divided by ( x + 3)​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{Polynomial\;is\;2x^2-7x-1}$

$\underline{\textbf{To find:}}$

$\mathsf{The\;remainder\;when\;2x^2-7x-1\;is\;divided\;by\;(x+3)}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Remainder theorem:}}$

$\textsf{The remainder when P(x) is divided by (x-a) is P(a)}$

$\textsf{The remainder when P(x) is divided by (x+a) is P(-a)}$

$\mathsf{P(x)=2x^2-7x-1}$

$\mathsf{The\;remainder\;when\;P(x)\;is\;divided\;by\;(x+3)}$

$\mathsf{=P(-3)}$

$\mathsf{=2(-3)^2-7(-3)-1}$

$\mathsf{=2(9)+21-1}$

$\mathsf{=18+21-1}$

$\mathsf{=38}$

$\therefore\textbf{The remainder when P(x) is divided by (x+3) is 38}$

$\boxed{\mathsf{}}$

$\underline{\textbf{Find more:}}$

x^2-ax^3+bx^2-cx+8=0 divided by [x-1] leaves a remainder of 4 divided by [x+1] leaves a remainder of 3 then b=

https://brainly.in/question/47381249

Answer 2

Step-by-step explanation:

Let x - 1 = 0 , then x = 1.

Substitute value of x = 1 in f(x):

f(x) = 2x ^ 3 - 3x ^ 2 + 7x - 8

f(1) = 2 * (1) ^ 3 - 3 * (1) ^ 2 + 7(1) - 8

f(1) = 2 - 3 + 7 - 8

f(1) = - 2.

Hence, the required remainder is -2.