Question

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

Answer 1

Answer:

The answer is $-6x^2(5x^2 - 7x -9)$ which can be factorised further to give $-30x^2(x - 2.213)(x + 0.813)$

Step-by-step explanation:

It is given to factorise $54x^2 + 42x^3 - 30x^4$.

To factorise we first take any common terms of the expression given.

So the expression becomes

$54x^2 + 42x^3 - 30x^4 = x^2( 54 + 42x - 30 x^2) = -6x^2(5x^2 - 7x -9)$

So we see the term left in brackets after taking out the common terms is quadratic in nature.

The quadratic equation cannot be factorised  further into terms with whole numbers as the roots of the quadratic equation are radical in nature. But we can continue to factorise.

Roots of the quadratic equation are x = $\frac{7 + \sqrt{49 + 180} }{10} = 2.213$

and $\frac{7 - \sqrt{49 + 180} }{10} = -0.813$

Therefore the complete factorisation is given by $-30x^2(x - 2.213)(x + 0.813)$

Answer 2

6x^2(−5x^2+7x+9) is the correct answer