Question

using factor theorem factorise 2x cube - 3 x square - 7 x + 30​

Answer 1

we have to factorize 2x³ - 3x² - 17x + 30 using factor theorem.

prime factors of 30 = 1 × 2 × 3 × 5

let f(x) = 2x³ - 3x² - 17x + 30

f(1) = 2 - 3 - 17 + 30 ≠ 0

f(2) = 2(2)³ - 3(2)² - 17(2) + 30 = 46 - 46 = 0

so, (x - 2) is a factor of 2x³ - 3x² - 17x + 30.

now, x - 2)2x³ - 3x² - 17x + 30(2x² + x - 15

2x³ - 4x²

............................................

x² - 17x

x² - 2x

..................................

-15x + 30

-15x + 30

........................................

so, 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)

therefore, factorisation of 2x³ - 3x² - 17x + 30 is (x - 2)(2x - 5)(x + 3)