Question

Using the Distributive Property to factorize the equation 3x^2 + 24x = 0, you get _____The solution of the equation is _____A.) x(3x+8)=0B.) 3x(x^2+8)=0C.) 3x(x+8)=0D.) x(3x+24)=0A.) x=0, x=8B.) x=0, x=-8C.) x=0, x=24D.) x=0, x=-24

Answer 1

The equation to be solved is:

$3x^2+24x=0$

We can see that 3x is a common factor of both terms.

Knowing that we can proceed to the factorization:

$3x(x+8)=0$

This is obtained by dividing each term by the common factor, 3x.

Now, solving for x:

We have 2 factors whose multiplications equals 0. Then, either one factor or the other has to be 0. With the first factor as 0:

$\begin{gathered} 3x=0 \\ x=0 \end{gathered}$

With the second factor as 0:

$\begin{gathered} x+8=0 \\ x=-8 \end{gathered}$

Then, both x=0 and c=-8 satisfy the equation.

Answers will be C and B, respectively.

For the first question, D would also be correct if the factorization is performed with x as common factor. However it is more convenient to factor with 3x as common factor.