Question

if x³-x²-5x+6 is divided by x-2,then the remainder is

pls use the remainder theorem formula

answer the question I will mark them as brainliest answer ​

Answer 1

Answer:

remainder theorem: let f(x) be an equation in x and when f(x) is divided by (x- a) then the remainder is f(a).

in the question ,the equation

f(x) = x³-x²-5x+6

when it is divided by x-2 then the remainder is f(2)

= (2)³-(2)²-5(2)+6

= 8-4-10+6

=0

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Answer 2

Answer :

By Remainder Theorem we need to find that Whether x - 2 is a factor of p(x) or not

Given g(x) = x - 2

• x = 2

Substituting value of x in Given p(x)

›› 2³ - (2)² - 5 × 2 + 6

›› 8 - 4 - 10 + 6

›› 14 - 14

›› 0

So,

• x - 2 is a Factor of given p(x)

By long division

x - 2)x³ - x² - 5x + 6(x² - x - 3

⠀⠀⠀x³ - 2x²

⠀⠀⠀(-)⠀⠀(+)⠀⠀⠀⠀

⠀⠀⠀⠀⠀ x² - 5x + 6

⠀⠀⠀⠀⠀ x² + 2x

⠀⠀⠀⠀⠀ (-) ⠀⠀(-)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀- 3x + 6

⠀⠀⠀⠀⠀⠀⠀⠀ - 3x + 6

⠀⠀⠀⠀⠀⠀⠀⠀⠀(+)⠀(-)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 0