# Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x + 5, g(x) = 2x + 1

**Solution:**

Given, p(x) = 2x³ - 11x² - 4x + 5

Also, g(x) = 2x + 1

We have to check whether p(x) is a multiple of g(x) or not.

We know that if p(x) is a multiple of g(x) then g(x) must be divisible by p(x)

Let g(x) = 0

2x + 1 = 0

2x = -1

x = -1/2

Put x = -1/2 in p(x)

p(2) = 2(-1/2)³ - 11(-1/2)² - 4(-1/2) + 5

= -2/8 - 11/4 + 2 + 5

= -1/4 - 11/4 + 7

= (-1 - 11 + 7(4))/4

= (-1 - 11 + 28)/4

= 16/4

= 4

p(x) ≠ 0

Since the __remainder__ is not zero, g(x) is not divisible by p(x)

Therefore, p(x) is not a multiple of g(x).

**✦ Try This: **Check whether p(x) is a multiple of g(x) or not, where p(x) = x³ + 2x + 8, g(x) = 2x - 3

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

**NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 15(ii)**

## Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x + 5, g(x) = 2x + 1

**Summary:**

p(x) is not a multiple of g(x) or not, where p(x) = 2x³ - 11x² - 4x + 5, g(x) = 2x + 1 since p(x) ≠ 0 when x = 2

**☛ Related Questions:**

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