Factor Quadratics - Day 2

This section focuses on more advanced factoring techniques, combining the Greatest Common Factor (GCF) method with the X-method.

The process involves two main steps:

1. Factor out the GCF if possible.
2. Use the X-method to factor the remaining quadratic expression.

Example: For 5m² - 10m - 15, first factor out the GCF of 5: 5$m² - 2m - 3$. Then use the X-method on $m² - 2m - 3$ to get 5m+1$$m-3.

Several practice problems are provided, including:

• 24n² + 16n - 48
• 5m² + 5m - 100
• 28k² + 28k

Highlight: Remember to always check for a GCF before applying the X-method when solving quadratic equations by factoring.

Solve Quadratics by Factoring (GCF, X-method)

This page outlines the complete process for solving quadratic equations by factoring, combining all the techniques learned.

The steps for solving are:

1. Make the equation equal to zero (add the opposite if necessary).
2. Factor out the GCF, if possible.
3. Use the X-method to factor further, if possible.
4. Set each factor to zero and solve for x.

Vocabulary: The solutions to a quadratic equation are also called roots, zeros, or x-intercepts.

Example: For x² - 10x + 16 = 0, we factor to get x-2$$x-8 = 0, leading to solutions x = 2 or x = 8.

The guide provides several practice problems with detailed solutions, including:

• 3x² + 25n + 20 = 0
• x² + 16x + 60 = 0
• 2x² + 13x + 42 = 0

Highlight: When solving quadratic equations, always remember to set the equation to zero before factoring.

This comprehensive guide provides students with the tools and practice needed to master solving quadratic equations by factoring.

Factor Quadratics: X-method

The X-method is a powerful technique for factoring quadratic equations. This method involves finding two numbers that multiply to give a·c and add to give b in the standard form ax² + bx + c.

Definition: The standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

To use the X-method:

1. Identify the values of a, b, and c in the quadratic expression.
2. Find two numbers that multiply to give a·c and add to give b.
3. Rewrite the middle term using these two numbers.
4. Factor by grouping.

Example: For x² + 16x + 60, we have a=1, b=16, and c=60. The factors of 60 that add up to 16 are 6 and 10. So, the factored form is x+6$$x+10.

The guide also introduces the concept of converting between standard form and intercept form of quadratic equations.

Vocabulary: Intercept form of a quadratic equation is ax-p$$x-q, where p and q are the x-intercepts.

Highlight: Practice problems are provided, including 3x² - 9x - 10 and 3x² + 14x - 80, to help students master the X-method.