a. x + 5x + 6

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. a,b,e

2. c,d,f

and 3.

**Let's Factor!**

1. **Factor Each Quadratic Expression:**
   - Try to write each quadratic expression as a product of two linear expressions. That is, write each expression in factored form.

   a) \( x^2 + 5x + 6 \)

   b) \( x^2 + 2x - 15 \)

   c) \( x^2 + 6x + 10 \)

   d) \( x^2 - 9x + 8 \)

   e) \( x^2 - 16 \)

   f) \( x^2 - 10x + 6 \)

2. **Find the x-intercepts:**
   - Find the \( x \)-intercepts, if any, for each quadratic function. For functions that have \( x \)-intercepts, sketch a graph using the intercepts and one or two other points that satisfy the equation.

   a) \( y = x^2 + 5x + 6 \)

   b) \( y = x^2 + 2x - 15 \)

   c) \( y = x^2 + 6x + 10 \)

   d) \( y = x^2 - 9x + 8 \)

   e) \( y = x^2 - 16 \)

   f) \( y = x^2 - 10x + 6 \)

3. **Sketch and Analyze Graphs:**
   - Find the \( x \)-intercepts of each function. Sketch a graph of the function using the \( x \)-intercepts and one or two other points that satisfy the equation.

   a) \( y = (x - 3)(x + 3)(x + 1) \)

   b) \( y = (x - 3)(x + 3)(x - 1) \)

   c) \( y = (x - 2)(x^2 - 9) \)

   d) \( y = x(x + 2)(x - 2) \)

**Illustrations:**
- The page includes diagrams of musicians and artists, where the equations are creatively displayed as props in their activities. For example, musicians playing instruments labeled with \( x \) or \( x^2 \), and an artist painting equations on a canvas. These visuals are engaging aids to make the mathematical concepts more relatable
Transcribed Image Text:**Let's Factor!** 1. **Factor Each Quadratic Expression:** - Try to write each quadratic expression as a product of two linear expressions. That is, write each expression in factored form. a) \( x^2 + 5x + 6 \) b) \( x^2 + 2x - 15 \) c) \( x^2 + 6x + 10 \) d) \( x^2 - 9x + 8 \) e) \( x^2 - 16 \) f) \( x^2 - 10x + 6 \) 2. **Find the x-intercepts:** - Find the \( x \)-intercepts, if any, for each quadratic function. For functions that have \( x \)-intercepts, sketch a graph using the intercepts and one or two other points that satisfy the equation. a) \( y = x^2 + 5x + 6 \) b) \( y = x^2 + 2x - 15 \) c) \( y = x^2 + 6x + 10 \) d) \( y = x^2 - 9x + 8 \) e) \( y = x^2 - 16 \) f) \( y = x^2 - 10x + 6 \) 3. **Sketch and Analyze Graphs:** - Find the \( x \)-intercepts of each function. Sketch a graph of the function using the \( x \)-intercepts and one or two other points that satisfy the equation. a) \( y = (x - 3)(x + 3)(x + 1) \) b) \( y = (x - 3)(x + 3)(x - 1) \) c) \( y = (x - 2)(x^2 - 9) \) d) \( y = x(x + 2)(x - 2) \) **Illustrations:** - The page includes diagrams of musicians and artists, where the equations are creatively displayed as props in their activities. For example, musicians playing instruments labeled with \( x \) or \( x^2 \), and an artist painting equations on a canvas. These visuals are engaging aids to make the mathematical concepts more relatable
Expert Solution
Step 1 factorization is a process of breaking of higher degree expression into lower degree exp.

here the first question is 

a) x2+5x+6

we have to write above expression as a product of two linear expression.

 

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