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

Solve the following by removing a common factor:

6x6−9x4=0 6x^6-9x^4=0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve the problem by finding a common factor.
00:12 First, break down the number into its smaller parts.
00:22 Now, do the same with this number until you find a common part.
00:29 Highlight the common factor using the same color.
00:47 Next, take this common part and bring it outside the parentheses.
00:52 Keep all other parts inside the parentheses in their current order.
00:57 Remember, to make the result zero, at least one part must equal zero.
01:08 So, this gives us one possible answer.
01:14 Let's set the next part to zero to find another answer.
01:21 We need to get X by itself now.
01:28 Here's our second answer—it can be positive or negative.
01:33 And that's how we solve this question! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following by removing a common factor:

6x6−9x4=0 6x^6-9x^4=0

2

Step-by-step solution

First, we take out the smallest power

6x6−9x4= 6x^6-9x^4=

6x4(x2−1.5)=0 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 0

6x4=0 6x^4=0

We divide by: 6x3 6x^3

x=0 x=0

x2−1.5=0 x^2-1.5=0

x2=1.5 x^2=1.5

x=±32 x=\pm\sqrt{\frac{3}{2}}

3

Final Answer

x=0,x=±32 x=0,x=\pm\sqrt{\frac{3}{2}}

Practice Quiz

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\( 112^0=\text{?} \)

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