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Subtracting Polynomials: Understanding and Application

In this lesson, we will focus on subtracting polynomials using organized methods. The key strategy involves changing subtraction into addition by altering the signs of each term. We will practice using both vertical and horizontal methods for subtraction, ensuring clarity in operations. As a review, remember the process of subtracting integers as a basis. Exercises will include problems to solve on your own, with an emphasis on documenting your work to receive credit. Prepare your notebooks and let's get started!

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Subtracting Polynomials: Understanding and Application

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  1. MJ2A Ch 13.3 – Subtracting Polynomials

  2. Bellwork • Add using either the vertical or horizontal method • (r2 + 9) + (-4r2 + 6r + 10) • (4x2 – 7x) + (8x + 5) • (c + 4) + (c2 – c + 6) Solutions -3r2 + 6r + 19 4x2 + x + 5 C2 + 10

  3. Assignment Review • Text p. 676 # 11 – 22

  4. Before we begin… • Please take out your notebook and get ready to work… • In the last lesson we work with adding polynomials… • In today’s lesson we will work with subtracting polynomials…. • Again…this is easy…the key is being organized!

  5. Objective 13.3 • Students will subtract polynomials

  6. Quick Review • Remember way back when…we discussed subtracting integers and we said that you don’t subtract integers you add the opposite… • We will use this strategy in today’s lesson to subtract polynomials… • What that means is you have to change the signs of each term before you add them…

  7. Subtracting Polynomials • When subtracting polynomials you will use the vertical method… • That is because you have to change the subtraction to addition and change the signs of each term… • It is easier to see what you have done using the vertical method… • Let’s look at an example…

  8. Example #1 • Subtract (5x + 9) – (3x + 6) • Set up the problem vertically 5x + 9 • Change to an addition problem by changing the signs of each term on the bottom row only! + – – 3x + 6 • Then add the like terms 8x + 3

  9. Example #2 • Subtract (4a2 + 7a + 4) – (3a2 + 2) • Set up the problem vertically 4a2 + 7a + 4 + – • Change to an addition problem by changing the signs of each term on the bottom row only! – 3a2 + 2 a2 + 7a + 2 • Then add the like terms

  10. Your Turn • In the notes section of your notebook subtract the following polynomials • (9x + 5) – (4x + 3) • (2x + 4) – (-x + 5) • (3x2 + x) – (8 – 2x) Solutions 5x + 2 3x - 1 3x2 + 3x – 8

  11. Summary • In the notes section of your notebook summarize the key concepts covered in today’s lesson • Today we discussed • Subtracting Polynomials • What strategy will you use? • When changing the signs of the terms which ones will you change?

  12. Assignment • Text p. 680 # 10 – 25 Reminder • This assignment is due tomorrow • I do not accept late assignments • You must show how you got your answer (no work = no credit)

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