How To Factor Trinomials With Negative Exponents

TL;DR

Learn how to factor expressions with negative exponents by finding the greatest common factor and dividing the terms accordingly.

Transcript

let's say if you were to receive an expression like this 2x to the negative 2 plus 8 x to the negative 5. what would you do to factor this particular expression how can you take out the gcf or the greatest common factor well let's compare that example with this one what would you do to take out the gcf the greatest common factor would be three and ... Read More

Key Insights

• 😑 Factoring expressions with negative exponents involves finding the GCF and simplifying the terms by dividing.
• 🧑‍🏭 Expressions in quadratic form can be factored by substitution and then factoring the resulting quadratic equation.
• 🧑‍🏭 Trinomials in expressions with negative exponents can be factored by identifying factors that multiply to the constant term and add to the coefficient of the middle term.

Questions & Answers

Q: How do you factor expressions with negative exponents?

To factor expressions with negative exponents, find the GCF and divide each term by the GCF to simplify the expression.

Q: What is the GCF in factoring expressions with negative exponents?

The GCF is the term with the smaller exponent. Identify the term with the smaller exponent and divide each term by it.

Q: How do you factor expressions in quadratic form with negative exponents?

Use substitution to rewrite the expression in terms of a new variable, then factor the resulting quadratic equation.

Q: Can expressions with negative exponents be further factored?

Yes, if the expression is a trinomial, it can be further factored by identifying two numbers that multiply to a constant term and add to the coefficient of the middle term.

Summary & Key Takeaways

• When factoring expressions with negative exponents, start by finding the greatest common factor (GCF) of the terms.

• The GCF is the term with the smaller exponent. Divide each term by the GCF to simplify the expression.

• If the expression is in quadratic form, it can be factored by substitution.

• If the expression is not in quadratic form, factor out the GCF and, if possible, further factor the resulting trinomial.