
How do you factor $3{x^3} - 3{x^2} - 60x$
Answer
447.6k+ 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.
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.
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.
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
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
What did the military generals do How did their attitude class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

For Frost what do fire and ice stand for Here are some class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

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

Write a letter to the principal requesting him to grant class 10 english CBSE
