Question

Factories :

$2{x}^{3} - 3 {x}^{2} - 17x + 30$

Answer 1

hey!!!

given :- 2x³ - 3x² - 17x + 30

factors of 30 = ±1, ±30, ±2, ±15, ±3, ±10

first, let us substitute 1 in the polynomial.

>> 2(1)³ - 3(1)² - 17(1) + 30
= 2 - 3 - 17 + 30
= 12

now, -1

>> 2(-1)³ - 3(-1)² - 17(-1) + 30
= -2 - 3 + 17 + 30
= 42

now, 30

>> 2(30)³ - 3(30)² - 17(30) + 30
= 54000 - 2700 - 510 + 30
= 50820

now, -30

>> 2(-30)³ - 3(-30)² - 17(-30) + 30
= -54000 -2700 + 510 + 30
= -56620

now, 2

>> 2(2)³ - 3(2)² - 17(2) + 30
= 16 - 12 - 34 + 30
= -30 + 30
= 0

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

now, refer to the attachment ⬆⬆⬆

we got 2x² + x - 15 after division.

now factorise it by splitting method.

>> 2x² + x - 15
= 2x² + (6x - 5x) - 15
= 2x² + 6x - 5x - 15
= 2x(x+3)-5(x+3)
= (x+3)(2x-5)

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

cheers!!!