# Solving Polynomial Equations By Factoring and Using Synthetic Division - Algebra 2 & Precalculus | Summary and Q&A

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January 11, 2017
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The Organic Chemistry Tutor
Solving Polynomial Equations By Factoring and Using Synthetic Division - Algebra 2 & Precalculus

## 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.

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