Polynomial Factoring Techniques and Examples
Learn how to solve polynomials by factoring, find x-intercepts, and understand the concept of x-intercepts in quadratic equations. Explore examples of factoring quadratic equations and solving polynomial equations step by step.
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Presentation Transcript
Complete the review problems: 1. Simplify: ( 3 x ) ( ) 6 + 2 2 4 9 4 5 x x x 2. Factor: 6 x + x + 2 9 3 3. Factor: 2 x + 15 50 x
What does x-intercept mean? Find the x-intercepts of the graph The x-intercepts are (-1, 0) and (2, 0). **Remember: x-intercepts are also called the solutions to the quadratic
On Day 2 (Page 4 in packet) we found the zeros of polynomials by graphing or by setting the factors equal to 0. Solve by graphing: Find the x-intercepts 2ndTrace, 2:Zero, left bound, right, bound, guess Refer to this video to see how to find the solutions by graphing: https://www.youtube.com/watch?v=RxA 8YMRF4M4
If the polynomial is in factored form, set each factor equal to 0 and solve: Ex 1. y = (x-3)(x+15)(x-6)3 Since this polynomial is in factored form, we set each factor = 0. x 3 = 0 +3 +3 X = 3 The solutions (or zeros) are 3, -15, and 6. x + 15 = 0 - 15 - 15 + 6 +6 x = -15 x 6 = 0 x = 6
Complete this example: ( ) ( ) 2 = + ) 3 2 5 ( y x x x
Factoring a quadratic is a way of finding the x-intercepts, or solutions. 1. Put the equation in standard form 2. Set the whole equation equal to ZERO 3. FACTOR 4. Set ALL individual factors = ZERO 5. SOLVE for x in each factor
Example 1: SOLVE: x2+ 3x + 2 = 0 1. Factor: (x+2)(x+1) = 0 2. Set each factor equal to zero. 3. x + 2 = 0 4. Solve each x + 1 = 0 x = -2 and x = -1
Example 2: SOLVE: 2x2+ 3x 2 = 0 1. Factor: (2x 1)(x+2) = 0 2. Set each factor equal to zero. 3. 2x 1 = 0 4. Solve each x = and x = -2 x + 2 = 0
Example 3: SOLVE: 3n4+ 3n3= 18n2 1. We need put in standard form before we can factor. 3n4+ 3n3- 18n2= 0 2. Now we can factor out the GCF: 3n2(n2+ n 6) = 0 3. Now we can factor the quadratic: 3n2(n + 3)(n 2) = 0 4. Set each factor (including the GCF equal to zero and solve. 3n2= 0 n + 3 = 0 n = 0 n = -3 The solutions are 0, -3, and 2 n 2 = 0 n = 2
Solve the rest by factoring. Make sure to SHOW YOUR WORK TO RECEIVE CREDIT! 4. x2- 8x 48 = 0
5. 4x2+ 12x + 9 = 0
6. 4x2+ 12x + 9 = 0
7. x3+ 6x2+ 8x = 0
8. 5x3+ 10x2+ 20x = 0
9. 2x2+ 3x 9 = 0
10. 7x2+ 53x + 28 = 0
11. x2+ 8x + 7 = 0
12. X2+ 11x + 18 = 0
All problems must have work shown and be completed by the end of class. If you need additional help with solving by factoring refer to the video: https://www.youtube.com/watch?v=SDe- 1lGeS0U You can also go to KHAN academy and watch videos from their site. Homework is ALL of page 16 in your packet.
