Question

What is the expression in factored form?

3x^2 + 18x + 24

a. 3(x+2)(x+4)
b. 3(x-2)(x+4)
c. 3(x-2)(x-4)
d. 3(x+2)(x-4)

Answer 1

`\boxed{a.\:\:3(x+2)(x+4)}`

Explanation:

The given expression is

`3x^2+18x+24`

We factor 3 to obtain;

`3(x^2+6x+8)`

We split the middle term to obtain;

`3(x^2+4x+2x+8)`

`=3[x(x+4)+2(x+4)]`

We factor further to get;

`=3(x+4)(x+2)`

Answer 2

Choice a is correct answer.

Explanation:

Given expression is :

3x²+18x+24

We have to represent above expression in factored form.

As we have noticed that the expression contains the multiples of 3.

taking 3 as common from given expression,we get

3(x²+6x+8)

Now, spit the middle term of above expression so that the product of two terms should be 8 and their sum be 6.

3(x²+4x+2x+8)

Making two groups and taking two terms as common,we get

3(x(x+4)+2(x+4))

Taking (x+4) as common,we get

3(x+4)(x+2) which is the factored form of 3x²+18x+24.