Question

When the polynomial p(x)=2x^3-x+k is divided by (x-3), leaved a remainder 13. Find ‘k’

Answer 1

Step-by-step explanation:

Given :-

the polynomial p(x)=2x^3-x+k is divided by (x-3), leaved a remainder 13.

To find:-

Find the value of ‘k’ ?

Solution:-

Given quadratic polynomial is

p(x) = 2x³-x+k

Given divisor = (x-3)

Given remainder = 13

We know that

Remainder Theorem:-

Le p(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if p(x) is divided by x-a then the remainder is p(a).

On applying this theorem to the given problem

p(x) is divided by (x-3)

=> The remainder = p(3)

=>2(3)³-(3)+k

=> 2(27)-3+k

=> 54-3+k

=> 51+k

According to the given problem

The remainder = 13

=> 51+k = 13

=> k = 13-51

=> k = -38

Therefore,k = -38

Answer:-

The value of k for the given problem is -38

Used formulae:-

Remainder Theorem:-

Le p(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if p(x) is divided by x-a then the remainder is p(a).

Check:-

If k = -38 then p(x) = 2x³-x-38

On dividing p(x) by (x-3) then

x-3) 2x³-x-38 (2x²+6x+17

2x³-6x²

(-) (+)

____________

6x²-x

6x²-18x

(-) (+)

_____________

17x-38

17x-51

(-) (+)

_____________

13

______________

Remainder = 13

Verified the given relations in the given problem.

Answer 2

Answer:

The ans is 6

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