1. Problem of the Day Factor the following: x2 – 16 x2 + 7x + 12

2. Problem of the Day Factor AND Solve: 3x2 – 28x – 20
How can you solve a quadratic equation if it cannot be factored?
Problem of the Day

3. Section 5-5a Solving Polynomial Equations

4. Then Now Objectives You solved quadratic functions by factoring.
Factor polynomials using the sum and difference of cubes.
Factor polynomials by grouping.
Solve polynomial equations by factoring.

5. Common Core State Standards
Content Standards
A.CED.1 – Create equations and inequalities in one variable and use them to solve problems.
Mathematical Practices
4) Model with mathematics.
Common Core State Standards

6. Sum and Difference of Cubes

7. Factor each polynomial: 5𝑦 4 − 320𝑦𝑧 3 −54 𝑤 4 −250𝑤 𝑧 3
Example 1

8. Factor each polynomial: 24𝑥 5 +3 𝑥 2 𝑦 3 12𝑞 𝑤 3 −12 𝑞 4
Example 1

9. Factor each polynomial: 𝑎 3 𝑥 2 − 𝑏 3 𝑥 2 16𝑔 3 +2 ℎ 3
Example 1

10. PACKAGING A small cubed box is placed inside a larger cubed box
PACKAGING A small cubed box is placed inside a larger cubed box. If the smaller cube is half the length of the larger cube, and the volume remaining in the larger cube is 𝑐𝑚 3 , what should be the dimensions of the two cubes?
Real-World Example 4

11. PACKAGING A small cubed box is placed inside a larger cubed box
PACKAGING A small cubed box is placed inside a larger cubed box. If the smaller cube is one third the length of the larger cube, and the volume remaining in the larger cube is 𝑐𝑚 3 , what should be the dimensions of the two cubes? 3x 3x
Real-World Example 4 3x

12. PACKAGING A small cubed box is placed inside a larger cubed box
PACKAGING A small cubed box is placed inside a larger cubed box. If the smaller cube is half the length of the larger cube, and the volume remaining in the larger cube is 23,625 𝑐𝑚 3 , what should be the dimensions of the two cubes?
Real-World Example 4

13. Factor the polynomial: 𝑥 3 +5 𝑥 2 −2𝑥−10
Example 2

14. Factor the polynomial: 𝑎 2 +3𝑎𝑦+2𝑎 𝑦 2 +6 𝑦 3
Example 2

15. Factor the polynomial: 𝑦 2 +𝑦𝑧−2𝑦−2𝑧
Example 2

16. Section 5-5a Worksheet
Homework