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Agenda Wednesday 08/29

Learn about synthetic division, dividing polynomials, and sketching negative versions of graphs in this lesson. Simplify expressions and solve problems using synthetic division rules.

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Agenda Wednesday 08/29

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  1. Agenda Wednesday 08/29 • NTK Bellwork • Recapping End Behavior • EQ 4: Synthetic Division • Exit Ticket

  2. NTK Bellwork 08/29

  3. Agenda Wednesday 08/29 • NTK Bellwork • Recapping End Behavior • EQ 4: Synthetic Division • Exit Ticket

  4. What would happen if made these graphs negative? Sketch the negative version of each graph

  5. Concave up Concave down

  6. Revisit NTK Bellwork 08/29

  7. Dividing PolynomialsUsing Synthetic Division

  8. What are polynomials? ¿Qué son polinomios? You do not have to write this! ¡No tienes que escribir esto!

  9. Synthetic Division (división sintética) Important Vocabulary, write down this example and each of the terms that are labelled. (Vocabulario importante, anote este ejemplo y cada uno de los términos que están etiquetados.) Dividend Divisor Quotient

  10. Synthetic Division Rules (Reglas de división sintética) • The degree of your quotient will be the difference of what you divide. (El grado de su cociente será la diferencia de lo que divide.) • Ex: • Make sure ALL exponents are represented. Absent terms are “0” terms. (Asegúrate de que TODOS los exponentes estén representados. Los términos ausentes son "0".) • Ex:

  11. Make sure all exponents are represented (add in “0s” if not) • Use the OPPOSITE of the one you’re dividing by Simplify for all x≠ 2.

  12. Synthetic Division Ex. 2

  13. Synthetic Division Ex. 3

  14. Synthetic division ex. 4 • Sometimes the questions is worded differently.

  15. Synthetic Division Ex. 4

  16. Bring first number down below line Multiply these and put answer above line in next column Multiply these and put answer above line in next column Multiply these and put answer above line in next column Let's try a problem where we factor the polynomial completely given one of its factors. You want to divide the factor into the polynomial so set divisor = 0 and solve for first number. - 2 4 8 -25 -50 - 8 Add these up 0 50 Add these up Add these up No remainder so x + 2 IS a factor because it divided in evenly 4 x2 + x 0 - 25 0 Put variables back in (one x was divided out in process so first number is one less power than original problem). So the answer is the divisor times the quotient: List all coefficients (numbers in front of x's) and the constant along the top. If a term is missing, put in a 0. You could check this by multiplying them out and getting original polynomial

  17. 3. Simplify for all x ≠ 4 • If p(x)(x – 2) = x2 + 3x – 10, what is p(x) for all x ≠ 2?

  18. Exit Ticket 1. Simplify for all x ≠ -1

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