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For what value of m is x³ - 2mx² + 16 divisible by x + 2 ?

Solution:

Given, the polynomial is p(x) = x³ - 2mx² + 16

We have to find the value of m if p(x) is divisible by x + 2.

Let g(x) = x + 2

Given, p(x) is divisible by g(x)

So, g(x) = 0

x + 2 = 0

x = -2

Substitute x = -2 in p(x),

As p(x) is divisible by g(x), p(-2) = 0

p(-2) = x³ - 2mx² + 16 = 0

(-2)³ - 2m(-2)² + 16 = 0

-8 - 2m(4) + 16 = 0

-8m + 8 = 0

8m = 8

m = 1

Therefore, m = 1

✦ Try This: If x+1 is a factor of the polynomial 3x² - kx,then find the value of k.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 19

For what value of m is x³ - 2mx² + 16 divisible by x + 2

Summary:

The division of polynomials is an arithmetic operation where we divide a given polynomial by another polynomial which is generally of a lesser degree in comparison to the degree of the dividend. The value of m when x³ - 2mx² + 16 divisible by x + 2 is 1

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