Solve 6x^6-9x^4=0: Common Factor Factoring Practice

Question

Solve the following by removing a common factor:

$6x^6-9x^4=0$

00:00 Solve the exercise by factoring out a common factor

00:04 Let's factor this number into these factors

00:14 And this number into these factors, so there will be a common factor

00:21 Mark the common factor in the same color

00:39 Take the common factor and factor it out of the parentheses

00:43 All other factors will remain inside the parentheses in the same order

00:49 To get 0, one of the factors in multiplication must equal 0

01:00 Therefore this is one solution

01:06 Now let's set the second factor to 0 and find another solution

01:13 Let's isolate X

01:20 This is the second solution, it can be either negative or positive

01:25 And this is the solution to the question

First, we take out the smallest power

$6x^6-9x^4=$

$6x^4\left(x^2-1.5\right)=0$

If possible, we reduce the numbers by a common factor

Finally, we will compare the two sections with: $0$

$6x^4=0$

We divide by: $6x^3$

$x=0$

$x^2-1.5=0$

$x^2=1.5$

$x=\pm\sqrt{\frac{3}{2}}$

$x=0,x=\pm\sqrt{\frac{3}{2}}$