Worked example: finding the missing monomial factor | High School Math | Khan Academy

TL;DR

By dividing both sides of the equation and simplifying, we find that F is equal to three x-squared.

Transcript

• [Voiceover] So we have negative 30x to the fifth is equal to negative 10x to the third, times F. And I encourage you to pause this video and see if you can figure out what F is going to be. Well, the way that we can tackle it, we could just isolate the F on the right-hand side here if we divide by negative 10x to the third. So we might say, well,... Read More

Key Insights

• 🙃 Isolating a variable in a polynomial equation often involves dividing both sides and simplifying the expression.
• 👻 Cancelling out common factors allows for easier manipulation of the equation.
• 🍉 Understanding exponent properties enables simplification by subtracting exponents or canceling out terms.

Questions & Answers

Q: How do we isolate the variable F in the equation?

To isolate F, we divide both sides of the equation by negative 10x to the third and cancel out the common factors.

Q: Why can we cancel out the multiplying and dividing actions on the right side of the equation?

Multiplying and dividing by the same term results in cancelation, as it is equivalent to multiplying by one. This simplification allows us to isolate F.

Q: How do we simplify the left side of the equation?

By dividing negative 30x to the fifth by negative 10x to the third, we get a coefficient of positive three. Dividing x to the fifth power by x to the third power results in x-squared.

Q: What can we conclude about the factors and divisibility of the equation?

We can say that negative 30x to the fifth is divisible by negative 10x to the third, three x-squared is a factor of negative 30x to the fifth, and negative 30x to the fifth is divisible by three x-squared.

Summary & Key Takeaways

• The video teaches how to solve an equation with a polynomial expression by isolating the variable F.

• Dividing both sides of the equation allows us to cancel out the common factors and simplify the expression.

• We find that F is equal to three x-squared.