Question

using remainder theorem to find the value of k , it given that when x3 + 2x2 + kx + 3 is divided by ( x-3) , then the remainder is 21​

Answer 1

$\huge\bf\underline{Answer}$

The value of k is -9

Solution:-

Given,

f(x) = x³ + 2x² + kx + 3 when divided by the linear polynomial g(x) = (x - 3) gives the remainder 21.

At first we will find out zero of the polynomial g(x) = (x - 3)

=> (x - 3) = 0

=> x = 3

From the remainder thereom,

The required remainder = f(3)

Putting the value of x in f(x) :-

=> x³ + 2x² + kx + 3 = 21

=> (3)³ + 2.(3)² + k.3 + 3 = 21

=> 27 + 2.9 + 3k + 3 = 21

=> 27 + 18 + 3k + 3 = 21

=> 3k + 48 = 21

=> 3k = 21 - 48

=> 3k = -27

=> k = -27/3

=> k = -9

Hence, the value of k is -9.

Verification:-

L.H.S

x³ + 2x² + kx + 3

Putting the value of k and x, we get:-

=> (3)³ + 2.(3)² + (-9).3 + 3

=> 27 + 2.9 + (-27) + 3

=> 27 + 18 - 27 + 3

=> 21

R.H.S = Already, 21.

Therefore, L.H.S = R.H.S

Hence, Proved.

Answer 2

$\mathsf{\huge{\underline{\boxed{\red{k = -9}}}}}$

$\rule{200}{2}$

$\mathfrak{\large{\underline{\underline{\blue{Explanation:-}}}}}$

Proof :-

Reminder left = 3

Now,

Find zero of equation

x-3=0

x=3 ......(i)

Put value of x = 3 in the given equation

x³+2x²+kx+3= 21

(3)³+2 × (3)² + k(3) +3 = 21

27 + 2 × 9 + 3k + 3 = 21

27 + 18 + 3k + 3 = 21

3k + 48 = 21

3k = 21 - 48

3k = -27

k = -27/3

k = -9

$\rule{200}{2}$

Hope it helped

Mark as brainliest

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