Question

Factorise : 2x3 - 3x2 – 17x + 30.​

Answer 1

Answer :

• 2x³ - 3x² - 17x + 30 = (x - 2) (x + 3) (2x - 5)

Given :

• 2x³ - 3x² - 17x + 30

Solution :

Method (1) :

➞ 2x³ - 3x² - 17x + 30

➞ 2x³ - 4x² + x² - 2x - 15x + 30

➞ 2x²(x - 2) + x(x - 2) - 15(x - 2)

➞ (x - 2) (2x² + x - 15)

➞ (x - 2) (2x² + 6x - 5x - 15)

➞ (x - 2) [2x (x + 3) - 5 (x + 3)]

➞ (x - 2) (x + 3) (2x - 5)

Hence

2x³ - 3x² - 17x + 30 = (x - 2) (x + 3) (2x - 5)

Method (2) :

➞ 2x³ - 3x² - 17x + 30

we know that x = 2 is a zero of polynomial so,

➞ p(2) = 2(2)³ - 3(2)² - 17(2) + 30

➞ 2(8) - 3(4) - 34 + 30

➞ 16 - 12 - 34 + 30

➞ 46 - 46

➞ 0

so, x - 2 is a factor of p(x)

Now, polynomial is divisible by x - 2 we Get,

➞ 2x³ - 3x² - 17x + 30 ÷ x - 2

➞ 2x² + x - 15

Then,

➞ 2x³ - 3x² - 17x + 30 = (x - 2) (2x² + x - 15)

➞ (x - 2) (2x² + 6x - 5x - 15)

➞ (x - 2) [2x(x + 3) - 5(x + 3)]

➞ (x - 2) (2x - 5) (x + 3)

2x³ - 3x² - 17x + 30 = (x - 2) (x + 3) (2x - 5)