Factorize: 2x^3 – 3x^2 – 17x + 30

Explanation:

Given polynomial is, 2x³ – 3x² – 17x + 30

Substituting x = 2 in the expression we get,

2 x (2)³ – 3 x (2)2 – 17 x 2 + 30 = 2 x 34 + 30

= 16 – 12 – 34 + 30

= 0

Hence, x = 2 is a zero of the polynomial.

Then, (x – 2) is factor of 2 x 3 – 3 x 2 – 17x + 30

Now, Factoring the polynomial we get,

2x³ – 3x² – 17x + 30 = 2x²(x – 2) + x^□ (x – 2) – 15(x – 2)

= (x – 2)(2x² + x – 15)

= (x – 2)(2x² + 6x – 5x – 15), middle term factor

= (x – 2){2x(x + 3) – 5(x + 3)}

= (x – 2)(x + 3)(2x – 5)

Final Answer:

Hence the correct option is (D) i.e. (x - 2) (x + 3) (2x - 5)