Question

What is the factorization of the trinomial below/ 3x^2-21x+30?

Answer 1

3*(x-5)*(x-2)

Explanation:

To factorize 3*x^2 - 21*x + 30 we can find the roots with the quadratic formula:

`x = (-b \pm √(b^2 - 4(a))(c))/(2(a))`

`x = (21 \pm √((-21)^2 - 4(3)(30)))/(2(3))`

`x = (21 \pm 9)/(6)`

`x_1 = (21 + 9)/(6)`

`x_1 = 5`

`x_2 = (21 - 9)/(6)`

`x_2 = 2`

The factorized form is
`a*(x - x_1)*(x - x_2)`, that is, 3*(x-5)*(x-2)

Answer 2

3(x-5)(x-2)

Explanation:

First you can take 3 as a common factor:

`3(x^(2) -7x+10)`

Then you can take two ways:

Use the resolver ecuation to get the roots, or think in two numbers that the sum is -7 and the product is 10.

The only two integers that we can choice are -5 and -2

(-5)*(-2)=10

-5+(-2)=-7

Then you can write the ecuation as a product of its roots:

3 * (x-5) * ( x-2)

And its the same expresion as:

3x^2-21x+30

To be sure you are doing well, solve the product of your solution and you will have the same expresion.