# Factorise : 2x³ - 3x² - 17x + 30

**Solution:**

Given, the __polynomial__ is 2x³ - 3x² - 17x + 30

We have to __factorise the polynomial__.

Let p(x) = 2x³ - 3x² - 17x + 30

The constant term of p(x) is 30.

Factors of 30 = ±1, ±2, ±3, ±5, ±6, ±10, ±15, ±30

Let us take x = 2

Substitute x = 2 in p(x),

p(2) = 2(2)³ - 3(2)² - 17(2) + 30

= 2(8) - 3(4) - 34 + 30

= 16 - 12 - 4

= 16 - 16

= 0

So, x - 2 is a factor of 2x³ - 3x² - 17x + 30.

Now splitting the x² and x terms,

2x³ - 3x² - 17x + 30 = 2x³ - 4x² + x² - 2x - 15x + 30

Taking (x - 2) as a common factor,

= 2x²(x - 2) + x(x - 2) - 15(x - 2)

= (2x² + x - 15)(x - 2)

On factoring 2x² + x - 15 by splitting the middle term,

= 2x² + 6x - 5x - 15

= 2x(x + 3) - 5(x + 3)

= (2x - 5)(x + 3)

Therefore, the factors of p(x) are (x - 2)(x + 3)(2x - 5)

**✦ Try This: **Factorise : x³ - x² - 10x + 30

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

**NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 24(i)**

## Factorise : 2x³ - 3x² - 17x + 30

**Summary:**

The highest sum of the exponents is known as the degree of a polynomial. The factors of 2x³ - 3x² - 17x + 30 are (x - 2)(x + 3)(2x - 5)

**☛ Related Questions:**

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