Question

find the remainder when x3-ax2+6x-a is divided by x-a. please give answer fast.

Answer 1

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

$\mathsf{x^3-a\,x^2+6x-a}$

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

$\textsf{The remainder when}\;\mathsf{x^3-a\,x^2+6x-a}$

$\textsf{is divided by (x-a)}$

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

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

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

$\mathsf{Let\;P(x)=x^3-a\,x^2+6x-a}$

$\textsf{By remainder theorem,}$

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

$\mathsf{=P(a)}$

$\mathsf{=(a)^3-a(a)^2+6(a)-a}$

$\mathsf{=a^3-a^3+6a-a}$

$\mathsf{=6a-a}$

$\mathsf{=5\,a}$

$\underline{\textbf{Answer:}}$

$\textbf{The remainder is 5a}$

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

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

https://brainly.in/question/42854690

Answer 2

Answer:

We have x³ - ax² + 6x - a

Apply remainder theorem

x-a=0

x=a

Put x = a in equation.

(a)³ − a(a)² + 6a - a

= a³ - a³ + 6a

= 6a - a

= 5a

Then reminder is 5a

Step-by-step explanation:

Dividend = (Divisor × Quotient) + Remainder

Let

Dividend is x3 – ax2 + 6x – a

Divisor is x – a

Let divisor be zero

x – a = 0

x = a

p(x) = x3 – ax2 + 6x – a

put x = a in the above equation

p(a) = (a)3– a(a2) + 6(a) – a

p(a) = a3– a3 + 6a – a

p(a) = 5a

∴ Reminder p(a) = 5a