Question

Please Factorise this question..

$2x ^{3} + 5x {}^{2} - 11x + 4$
​

Answer 1

Answer:

(x - 1)(2x - 1)(x + 4)

Step-by-step explanation:

Given : p(x) = 2x³ + 5x² - 11x + 4

By hit and trial method.

Putting x = 1, we get

→ p(1) = 2(1)³ + 5(1)² - 11(1) + 4

= 2 + 5 - 11 + 4

= 11 - 11

= 0

Hence, (x - 1) is a factor of above polynomial.

Dividing the above polynomial by (x - 1), we get

(For division, see the attachment.)

→ 2x² + 7x - 4

Using Middle Term Factorisation

→ 2x² + 8x - x - 4

→ 2x(x + 4) - 1(x + 4)

→ (2x - 1)(x + 4)

Hence,

2x³ + 5x² - 11x + 4 = (x - 1)(2x - 1)(x + 4)