Question

Factorise : 9x^3-27x^2-100x +300

Answer 1

Ans is (x-3)(3x+10)(3x-10)
By trail and error, x= 3 satisfies it.
divide the polynomial by x-3
You will get 9x²-100 = 3x+10 * 3x-10
So factors are (x-3)(3x+10)(3x-10)

Answer 2

The factorisation of $9x^3-27x^2-100x+300=(x-3)(3x+10)(3x-10)$.

Step-by-step explanation:

We have,

$9x^3-27x^2-100x+300$

To find, the factorisation of $9x^3-27x^2-100x+300=?$

∴ $9x^3-27x^2-100x+300$

$=9x^2(x-3)-100(x-3)$

$=(x-3)(9x^2-100)$

$=(x-3)[(3x)^2-10^2]$

Using the algebraic identity,

$a^{2} -b^{2}=(a+b)(a-b)$

$=(x-3)(3x+10)(3x-10)$

∴ The factorisation of $9x^3-27x^2-100x+300=(x-3)(3x+10)(3x-10)$

Hence, the factorisation of $9x^3-27x^2-100x+300=(x-3)(3x+10)(3x-10)$.