Q26, polynomial division (long division)

TL;DR

Learn how to perform long division to divide a polynomial by a binomial.

Transcript

in this question we are going to divide this out and the way to do this is we are going to use the long division and the reason is because we have binomial in the denominator right and also this is 3x plus 2 this is not X plus a number or X minus the number so we cannot use the synthetic division don't division it's the way to go ok so let's go ahe... Read More

Key Insights

• ➗ Long division is used when dividing a polynomial by a binomial that is not in the form X plus/minus a number.
• 🍉 The first term of the quotient is always canceled out during long division.
• 🍉 Terms in the dividend and divisor can cancel each other out during the long division process.
• 🍉 Bringing down the correct terms during each step is crucial for accurate calculation in long division.
• 😑 The remainder after long division is the final part of the answer, represented as a fractional expression.
• 🪘 Long division is a common and important method in algebraic calculations.
• 😑 Long division helps in simplifying complex polynomial expressions.

Questions & Answers

Q: Why is long division used to divide a polynomial with a binomial?

Long division is used when the denominator is a binomial because synthetic division can only be used when the denominator is of the form X plus/minus a number. Long division is the appropriate method in this case.

Q: What should be done with the first term of the quotient in long division?

The first term of the quotient is always canceled out when performing long division. It does not need to be written down.

Q: How do you determine the next term in the quotient during long division?

To determine the next term in the quotient, divide the product of the previous quotient term and the divisor by the first term of the divisor.

Q: Can terms in the dividend and divisor cancel each other out during long division?

Yes, terms in the dividend and divisor can cancel each other out during long division. This happens when multiplying the quotient term with the divisor, resulting in the elimination of corresponding terms.

Summary & Key Takeaways

• Long division is used to divide a polynomial by a binomial when the binomial is not in the form X plus/minus a number.

• Start by writing the dividend and divisor, and divide the first term of the dividend by the first term of the divisor to determine the quotient.

• Multiply the quotient by the divisor and subtract it from the dividend, bringing down the next term. Repeat the process until all terms have been evaluated.