Question

Factorise 54x^2 + 42x^3 - 30x^4.

Answer 1

Given Equation is 54x^2 + 42x^3 - 30x^4.

It can be written as -30x^4 + 42x^3 + 54x^2.

                               = -6x^2(5x^2 - 7x -9).


Hope this helps!

Answer 2

To Do:

Factorise $54x^{2} +42 x^{3} -30x^{4}$

Step-by-step explanation:

[tex]Rearranging,\\ = -30x^{4}+42x^{3}+54x^{2} \\ Taking x^{2} common,\\ = x^{2} (-30x^{2} + 42x +54)\\ Factorising the term (-30x^{2} + 42x +54),\\ = (-30x^{2} + 42x +54)\\ =\frac{-b+\sqrt{b^{2} -4ac} }{2a} \\ =\frac{-42+\sqrt{42^{2} -4*-30*54} }{2*-30} \\ =\frac{42+\sqrt{1764+6480} }{60} \\\\ =\frac{42+\sqrt{8244} }{60} \\\\ =\frac{42+6\sqrt{687} }{60} \\\\\\ =6(\frac{7+\sqrt{687} }{10})\\ [/tex]

[tex]and moving t x^{2} ,\\ x^{2} =0\\ x=0[/tex]

$The solution of the factorization is x=0, x= 6(\frac{7+\sqrt{687} }{10} ) and x = 6(\frac{7-\sqrt{687} }{10} )$