How To Factor Completely | Math

TL;DR

Learn how to factor completely by taking out the greatest common factor and factoring trinomials with leading coefficients of 1 or greater.

Transcript

in this lesson we're going to talk about how to factor completely we're going to go over some challenging problems so that you can really master this topic so how can we factor this expression 3x squared plus 21x plus 30. feel free to try that problem when you get a chance the first thing we can do is take out the gcf notice that the coefficients a... Read More

Key Insights

• 🧑‍🏭 Start factoring by identifying and factoring out the greatest common factor (GCF) from all the terms in the expression.
• 🍉 Trinomials with a leading coefficient of 1 can be factored by finding two numbers that multiply to the constant term and add up to the coefficient of the middle term.
• 🥺 Trinomials with a leading coefficient greater than 1 require the additional step of multiplying the leading coefficient by the constant term before factoring by grouping.
• 😑 Expressions with negative exponents can be factored by rewriting the exponents as reciprocals.

Questions & Answers

Q: How do you factor a trinomial with leading coefficient of 1?

To factor a trinomial with leading coefficient of 1, find two numbers that multiply to the constant term and add up to the coefficient of the middle term. Then, rewrite the middle term as the sum of these two numbers and factor by grouping.

Q: What is the first step in factoring completely?

The first step in factoring completely is to identify and factor out the greatest common factor (GCF) from all the terms in the expression.

Q: How do you factor a trinomial with a leading coefficient greater than 1?

To factor a trinomial with a leading coefficient greater than 1, multiply the leading coefficient by the constant term. Then, find two numbers that multiply to this product and add up to the coefficient of the middle term. Rewrite the middle term using these numbers and factor by grouping.

Q: How do you factor expressions with negative exponents?

To factor expressions with negative exponents, rewrite the exponents as reciprocals. For example, x^(-2) becomes 1 / x^2.

Summary & Key Takeaways

• To factor expressions completely, start by identifying and factoring out the greatest common factor (GCF).

• For trinomials with a leading coefficient of 1, find two numbers that multiply to the constant term and add up to the coefficient of the middle term, then factor by grouping.

• For trinomials with a leading coefficient greater than 1, multiply the leading coefficient by the constant term, find two numbers that multiply to the product and add up to the coefficient of the middle term, then factor by grouping.