Answer

Verified

406.5k+ views

**Hint:**In order to solve this question we will first put this equation equals to 0. After this, we will take all the commons and after it, the equation will be converted into the quadratic form then we will find the roots of that quadratic and after the transformation, we can find the factors.

**Complete step by step solution:**

For solving this we need to take all the possible commons:

$3{x^3} - 3{x^2} - 60x$

On taking all commons

$3x({x^2} - x - 20)$

Since one factor is already found the other we will find through the quadratic equations;

By putting the whole quadratic equation equals to 0.

${x^2} - x - 20 = 0$

On applying the dharacharya on this equation:

$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$

From the above equation putting the value of a=1, b=-1, c=-20 on this formula:

$x = 5, - 4$

Now transforming these on side of x the factors will be:

$(x - 5)$ and $(x + 4)$

Now putting all the factors together with:

**$(3x)(x - 5)(x + 4)$**

So this will be the final answer.

So this will be the final answer.

**Note:**

This can also be found through an alternate method:

After taking the common we will direct factorize the quadratic equation;

$3x({x^2} - x - 20)$

Now factoring the quadratic:

$3x({x^2} - 5x + 4x - 20)$

Now taking all the possible commons:

$3x\{ x(x - 5) + 4(x - 5)\} $

Now further taking the common:

$(3x)(x - 5)(x + 4)$

So by this method also we find the same as the factors.

All the time we cannot apply the factorization method because we cannot find the factor when there are no real roots so the first one is more comfortable for us.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

At which age domestication of animals started A Neolithic class 11 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE