Find the Value of K Remainder Theorem

The expression x³ ─ kx² +2x +5 leaves a remainder of 2 when divided by x ─ 3. Find the value of k.

• 4

• -4

• 8

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³ - 5x² + 2x - 10

• 0

• 2x-10

• -2x-10

• 2x+10

find the value of k when x³-2kx²+3x-1 is divided by x-1 and the remainder is -3

• 3

• -3

• 2

• 6

If dividing polynomial g(x) by (x – 5) yields a remainder of 3, which must be true?

• g(5) = 3

• g(-5) = 3

• g(3) = 5

• g(3) = -5

When a polynomial function f(x) is divided by
 (x - 8), the remainder is 12. 
What is f(8)?

• -8

• 8

• 12

• cannot be determined

The expression x³ - kx² +2x +5 leaves a remainder of 2 when divided by x - 3. Find the value of k.

• 4

• -4

• 8

What is the reminder when p(x) is divided by x+4?

• x-4

• -4

• 0

• 4

For what value of k is the polynomial

2x⁴ + 3x³ + 2kx² + 3x + 6

is divisible by (x + 2).

Answer explanation

Let

f(x)  =  2x⁴ + 3x³ + 2kx² + 3x + 6

Here, the divisor is (x + 2). 

Equate the divisor to zero. 

x + 2  =  0

Solve for x. 

x  =  -2

To find the remainder, substitute -2 for x into the function f(x). 

f(-2)  =  2(-2)⁴ + 3(-2)³ + 2k(-2)² + 3(-2) + 6

f(-2)  =  2(16) + 3(-8) + 2k(4) - 6 + 6

f(-2)  =  32 - 24 + 8k - 6 + 6

f(-2)  =  8 + 8k

So, the remainder is (8 + 8k).

If f(x) is exactly divisible by (x + 2), then the remainder must be zero.

Then, 

8 + 8k  =  0

Solve for k.

8k  =  -8

k  =  -1

Therefore, f(x) is exactly divisible by (x+2) when k  =  –1.

Answer explanation

c=2

The function f(x)=−3x3+px2+5x+10f(x)=−3x3+px2+5x+10 leaves a remainder of 9494 when divided by (x+3)

Answer explanation

p=-2