# Show that : 2x - 3 is a factor of x + 2x³ - 9x² + 12

**Solution:**

Let the given __polynomial__ be p(x) = x + 2x³ - 9x² + 12

Let the given __factor__ be g(x) = 2x - 3.

We have to check if x + 3 is a factor of x + 2x³ - 9x² + 12

Let g(x) = 0

2x - 3 = 0

2x = 3

x = 3/2

Substitute x = 3/2 in p(x),

p(3/2) = (3/2) + 2(3/2)³ - 9(3/2)² + 12

= 3/2 + 2(27/8) - 9(9/4) + 12

= 3/2 + 27/4 - 81/4 + 12

= (3(2) + 27 - 81 + 12(4))/4

= (6 + 27 - 81 + 48)/4

= (33 + 48 - 81)/4

= (81 - 81)/4

= 0/4

= 0

Since p(x) = 0 when x = 3/2, 2x - 3 is the factor of p(x)

Therefore, 2x-3 is the factor of x + 2x³ - 9x² + 12.

**✦ Try This:** Find the values of x for which the functions f(x) = 3x^{2} -1 and g(x) = 3+ x are equal.

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

**NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 16(ii)**

## Show that : 2x - 3 is a factor of x + 2x³ - 9x² + 12

**Summary:**

A factor is a number that divides the given number without any remainder. It is shown that 2x - 3 is a factor of x + 2x³ - 9x² + 12 as p(x) = 0 when x = 3/2

**☛ Related Questions:**

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