Question

find the remainder if x cube -5 x square +4x -3 is divided by (x-2)
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Answer 1

Answer:

remainder is -7 please mark as brainliest

Answer 2

By Remainder Theorem :

___________...

g(x) = x - 2

→ x - 2 = 0

→ x = 0 + 2

.°. x = 2

p(x) = x³ - 5x² + 4x - 3

Putting the value of x

→ (2)³ - 5(2)² + 4(2) - 3

→ 8 - 5(4) + 8 - 3

→ 8 - 20 + 8 - 3

→ -12 + 5

→ -7

So,the remainder is -7...

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What is Remainder Theorem ?

Let p(x) be a polynomial of degree 1 or more ans let a be any real number. If p(x) is divided by (x - a) then the remainder is p(a).

Proof :-

Let p(x) be a polynomial of degree 1 or more.

Suppose that when p(x) is divided by (x - a) then the quotient is q(x) and remainder is r(x).

By division algorithm,we have

→ p(x) = (x - a) . q(x) + r(x),

where degree r(x) < degree (x - a) = 1

[ °.° degree (x - a) = 1 ]

→ But, degree r(x) < 1 => degree r(x) = 0

→ r(x) is a constant, equal to r

.°. p(x) = (x - a) . q(x) + r .....i)

Putting x = a on both sides of i) we get

→ p(a) = 0 × q(r) + r => r = p(a).

Thus,when p(x) is divided by (x - a) then the remainder is p(a).