Question

9x³-27x²-100x+30 factorise using factor theorem... pls give step by step answer​

Answer 1

Step-by-step explanation:

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

3

−27x

2

−100x+300=(x−3)(3x+10)(3x−10) .:

We have,

9x^3-27x^2-100x+3009x

3

−27x

2

−100x+300

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

3

−27x

2

−100x+300=?

∴ 9x^3-27x^2-100x+3009x

3

−27x

2

−100x+300

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

2

(x−3)−100(x−3)

=(x-3)(9x^2-100)=(x−3)(9x

2

−100)

=(x-3)[(3x)^2-10^2]=(x−3)[(3x)

2

−10

2

]

Using the algebraic identity,

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

2

−b

2

=(a+b)(a−b)

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

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

3

−27x

2

−100x+300=(x−3)(3x+10)(3x−10) .