Question

Factorise 2x3

– 11x

2 + 17x – 6 using factor

theorem. ​

Answer 1

sorry by mistake my answer is wrong,

Answer 2

Question :- Factorise 2x³- 11x² + 17x - 6 using factor theorem. ?

Solution :-

Let f(2) is a factor of given polynomial .

check :-

→ f(x) = 2x³- 11x² + 17x - 6

→ f(2) = 2(2)³ - 11(2)² + 17*2 - 6

→ f(2) = 2*8 - 11*4 + 34 - 6

→ f(2) = 16 - 44 + 28

→ f(2) = 44 - 44

→ f(2) = 0 .

As, Remainder is zero we can conclude that, 2 is a factor of given polynomial.

By factor theorem we know that, if a is a factor of polynomial , than, (x - a) divides the polynomial .

Now, Dividing the polynomial 2x³- 11x² + 17x - 6 by (x - 2) we get :-

x - 2 )2x³- 11x² + 17x - 6(2x² - 7x + 3

2x³ - 4x²

-7x² + 17x

-7x² + 14x

3x - 6

3x - 6

0

we get :-

→ Remainder = 0

→ Quotient = 2x² - 7x + 3

So,

→ 2x³- 11x² + 17x - 6 = (x - 2)(2x² - 7x + 3) + 0

Now, Solving the quotient by splitting the middle term,

→ 2x² - 7x + 3

→ 2x² - 6x - x + 3

→ 2x(x - 3) - 1(x - 3)

→ (x - 3)(2x - 1)

Therefore,

→ 2x³- 11x² + 17x - 6 = (x - 2)(x - 3)(2x - 1). (Ans.)