Question

Find the value of K if the division of kx 3 + 9x 2 +4x -10 by x +3 leaves a remainder -22.

Answer 1

Given:

In the division of kx³ + 9x² +4x -10 by x +3 leaves a remainder -22.

To find:

The value of k

Solution:

Here we have given that the division of kx³ + 9x² +4x -10 by x +3 leaves a remainder -22.

so on putting the value of x as -3 we should get the remainder as -22

Putting the value of the x as -3 we get the value as:

• kx³ + 9x² +4x -10 = -22
• k(-3)³ + 9(-3)² +4(-3) -10 = -22
• -27k +81 -12 - 10 = -22
• 27k = 81
• k = 81/27
• k = 3

Hence, The value of k is 3

Answer 2

Answer:

Given p(x) = kx^3 + 9x^2 - 4x - 10.

Given g(x) = x - 3.  

By the remainder theorem, we get  

= > x - 3 = 0  

= > x = 3.  

plug x = 3 in p(x), we get

= > k(3)^3 + 9(3)^2 - 4(3) - 10 = -22  

= > 27k + 81 - 12 - 10 = -22  

= > 27k + 59 = -22  

= > 27k = -81

= > k = -3.  

Therefore the value of k = -3.

Step-by-step explanation:

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