Review factoring quadratics. (Review quickly: this is not new material!)

x^2+8x+12

x^2-15x-16

16x^2-x

2x^2-4x-30

Here’s a quick review of factoring quadratics.

1. **Factoring \(x^2 + 8x + 12\)**:
   - Look for two numbers that multiply to \(12\) (the constant term) and add up to \(8\) (the coefficient of \(x\)).
   - These numbers are \(6\) and \(2\).
   - So, \(x^2 + 8x + 12 = (x + 6)(x + 2)\).

2. **Factoring \(x^2 - 15x - 16\)**:
   - Find two numbers that multiply to \(-16\) and add to \(-15\).
   - These numbers are \(-16\) and \(1\).
   - So, \(x^2 - 15x - 16 = (x - 16)(x + 1)\).

3. **Factoring \(16x^2 - x\)**:
   - First, factor out the greatest common factor (GCF), which is \(x\).
   - \(16x^2 - x = x(16x - 1)\).

4. **Factoring \(2x^2 - 4x - 30\)**:
   - First, factor out the GCF, which is \(2\).
   - \(2x^2 - 4x - 30 = 2(x^2 - 2x - 15)\).
   - Now, factor \(x^2 - 2x - 15\) by finding two numbers that multiply to \(-15\) and add to \(-2\). These numbers are \(-5\) and \(3\).
   - So, \(2x^2 - 4x - 30 = 2(x - 5)(x + 3)\).

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Would you like more details or have any questions? Here are some related questions:

1. Can you factor quadratics with larger coefficients, such as \(3x^2 + 17x + 10\)?
2. How do you factor quadratics that do not have real-number solutions?
3. Can you solve quadratic equations by factoring and finding the roots?
4. What if there is a negative coefficient in front of \(x^2\)? How would you factor \( -x^2 + 4x + 12 \)?
5. How does factoring quadratics help in solving word problems?

**Tip:** Always check for a greatest common factor (GCF) before factoring the rest of the quadratic.

Review factoring quadratics. (Review quickly: this is not new material!)
x^2+8x+12
x^2-15x-16
16x^2-x
2x^2-4x-30

Quickly review how to factor quadratic equations such as x^2+8x+12 and x^2-15x-16. This step-by-step guide covers essential algebraic techniques, including factoring trinomials and applying the GCF. Perfect for students in Grades 8-10.

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