Solve each polynomial equation in Exercises 1–10 by factoring and...

Question

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle.

5x^4 - 20x^2 = 0

Accepted Answer

So this problem says that use factoring in the zero product principle to solve the given polynomial equation Where we have nine a to the 5th -81. It's the third equals zero. So let's try and take out some factors from this polynomial. You look here, you have a nine and an 81. We know 81 is divisible by nine. So let's go ahead and take a nine out first. You have none Times. It pays the fifth together nine from the 81. So we get a negative nine A to the 3rd, That's equal to zero. Now we can also look and we see there's an aide to the third on both of these terms we have eight to the third here and a to the fifth which should be broken down to eight to the third. So let's take out and it's the third everywhere. No, it's the third. Now it's the fifth. Taking out eight to the third gives us aid to the second And then -9, that's equal to zero. Now we can make use of what's called the difference of two squares theorem. So if you notice here we have an A squared minus nine, you make use of the difference of two squares. We have the formula A squared minus B squared equals a plus B. Times a minus B. As factors in this case our A is going to be a R B is going to be three because three squared equals nine. So go ahead and write this. You will have 9.8 to the third. A square minus nine by a difference of two squares is a plus three A minus three. This all equals zero. Now we have three factors we can set equal to zero and then solve for a 98 to the third equal zero, A plus three equals zero and a minus three equals zero. You saw this on this side. 559. You can taste the third equals zero. I'll be safe. The Cube root at the end of the 3rd. We will get a equals zero. Now over here we subtract three from both sets. We will get a equals negative three. And finally over here we add three to both sides to get a equals three. So the answers to our problems are a equals zero equals negative three and equals three worst corresponds to answer. Be okay. I hope they help you solve the problem. Thank you for watching. Goodbye. So this problem says that use factoring in the zero product principle to solve the given polynomial equation Where we have nine a to the 5th -81. It's the third equals zero. So let's try and take out some factors from this polynomial. You look here you have a nine and 81. We know 81 is divisible by nine. So let's go ahead and take a nine out first. You have none times it pays the fifth together. Nine from the 81. So we get a negative nine. 8 to the 3rd. That's equal to zero. Now we can also look and we see there's an aide to the third on both of these terms we have eight to the third here and A to the fifth which should be broken down to eight to the third. So let's take out an 8 to the third everywhere. Nine. It's the third. Now it's the fifth. Taking out eight to the third gives us aid to the second And then -9 that's equal to zero. Now we can make use of what's called the difference of two squares there. Um so if you notice here we have an a squared -9. We make use of the difference of two squares. We have the formula A squared minus B squared equals a plus B. Times a minus B. As factors in this case our A. Is going to be a R. B. Is going to be three because three squared equals nine. So go ahead and write this. You will have 9.8 to the third. A square minus nine by a difference of two squares is a plus three A minus three. This all equals zero. Now we have three factors we can set equal to zero and then solve for a 9. 8 to the 3rd equals zero. A plus three equals zero and a minus three equals zero. You solve this on this side 559. We can face the third equal zero. I'll be safe. The cube the third we will get A equals zero. Now, over here we subtract three from both sets we will get A equals negative three. And finally over here we add three to both sides to get A equals three. So the answers to our problems are equal zero equals negative three and equals three worst corresponds to answer. Be okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 5x^4 - 20x^2 = 0

Key Concepts

Factoring Polynomials

Zero-Product Principle

Polynomial Degree and Roots

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