Factoring Trinomials & Polynomials, Basic Introduction - Algebra | Summary and Q&A

TL;DR

Learn how to factor equations by finding the greatest common factor (GCF) and using formulas for perfect squares, sums of cubes, and differences of squares.

Key Insights

• ❎ Factoring involves finding common factors and using formulas for perfect squares, sums of cubes, and differences of squares.
• 🧑‍🏭 The GCF is used to easily factor binomials by dividing each term by the GCF.
• 💯 Perfect square trinomials follow a specific formula for factoring.
• 🧑‍🏭 Sums and differences of cubes can be factored using their respective formulas.

Transcript

in this video we're gonna talk about factoring how to factor the greatest common factor the GCF so let's say if we have the expression 3x plus 15 what is the greatest common factor between 3x + 15 3x + 15 are both divisible by what number they're both divisible by 3 so therefore 3 is the GCF the greatest common factor 3x divided by 3 is simply x + ... Read More

Questions & Answers

Q: How do you factor a binomial?

To factor a binomial, find the GCF of the terms and divide each term by the GCF. The resulting expression will have the GCF outside the parentheses and the quotient inside.

Q: How do you factor a perfect square trinomial?

A perfect square trinomial can be factored using the formula a^2 + 2ab + b^2 = (a + b)^2. Identify the values of a and b, which are the square roots of the first and third terms, and then square the sum of a and b.

Q: What is the formula for factoring sums of cubes?

The formula for factoring sums of cubes is a^3 + b^3 = (a + b)(a^2 - ab + b^2). Note that the first term and cube root of the second term are in parentheses, followed by the second term and the factors of the resulting squared expression.

Q: How can you solve equations by factoring?

To solve equations by factoring, set the factored expression equal to zero and solve each portion separately. The solutions will be the values of x that make the equation true.

Summary & Key Takeaways

• Factoring involves finding the GCF of terms in an expression to simplify it.

• For binomials, the GCF can be found by identifying the common factors and dividing each term by the GCF.

• Perfect square trinomials can be factored using the formula a^2 + 2ab + b^2 = (a + b)^2.

• For sums and differences of cubes, the respective formulas are a^3 + b^3 = (a + b)(a^2 - ab + b^2) and a^3 - b^3 = (a - b)(a^2 + ab + b^2).

• Equations can be solved by factoring the expression to find the roots or values of x.