Solving Polynomial Equations By Factoring and Using Synthetic Division  Algebra 2 & Precalculus  Summary and Q&A
TL;DR
Learn how to solve polynomial equations by factoring using techniques such as difference of perfect squares and factoring by grouping.
Questions & Answers
Q: How can you factor an expression in the form a^2  b^2 using the difference of perfect squares technique?
To factor expressions in the form a^2  b^2, where a and b are numbers, you express it as (a + b)(a  b). For example, x^2  25 can be factored as (x + 5)(x  5).
Q: How do you solve polynomial equations with a number in front of x squared, such as 9x^2  16?
To solve equations with a number in front of x squared, you can factor out the greatest common factor (GCF). In this example, the GCF is 2, so you can factor it as 2(4x^2  9). Then, you can further factor the expression using techniques like the difference of perfect squares.
Q: What can you do when factoring by grouping is not possible?
When factoring by grouping is not possible, you can use synthetic division. This method involves dividing the polynomial by a possible rational root to find the factors.
Q: How can the quadratic formula be used to find the solutions of a quadratic equation?
The quadratic formula, x = (b ± √(b^2  4ac)) / (2a), can be used to find the solutions of a quadratic equation in the form ax^2 + bx + c = 0. By substituting the values of a, b, and c into the formula, you can calculate the solutions.
Summary & Key Takeaways

Factoring is a method used to solve polynomial equations by breaking them down into their factors.

Difference of perfect squares technique can be used to factor expressions in the form a^2  b^2.

Factoring by grouping is used to factor expressions with four terms.

Synthetic division is used when factoring by grouping is not possible.

The quadratic formula can be used to find the solutions of quadratic equations.