Polynomial Function and Synthetic Division
- 6. The term 5x2+8x-3 where 5 is the leading coefficient 5x2 is the leading term -3 is the constant
- 9. Example: Identify if the ff. is a function. If yes, identify its kind, leading coefficient, and the constant
- 10. 8x17-7x18+6x4-5x+216 ANSWER: Yes, 18th degree polynomial function, -7, 216
- 11. 4x3-3x5 ANSWER: Yes, Quintic Function, -3, 0
- 13. synthetic division is an easy process of dividing polynomials by a binomial with the degree of 1 and has a 1 as leading coefficient
- 14. example: we can use synthetic division if 3X^2+20X+3 / X-2 or 10X^6+3X^4+20X-3 / X+4
- 15. Steps: Let's take (3X^2+20X+3)/ (X-2) Then write the coefficients of the dividend 2 | 3 20 3 ___| _____________________ the sign of the constant in the divisor and put it in the box 2 | ___|
- 16. Then write the coefficients of the dividend 2 | 3 20 3 __| _____________________
- 17. Bring the 1st no. down 2 | 3 20 3 __| _____________________
- 18. Multiply it to the no. in the box and add it 2 | 3 20 3 __| +6 _____________________ 3 26
- 19. Do step 5 until you get to the last no. 2 | 3 20 3 __| +6 +52 _____________________ 3 26 55
- 20. Then get the degree of the divisor and subtract 1 2-1 = 1 The degree of the quotient is 1 so .. 3X+26.. .then the last no. 55 is the remainder
- 21. EXAMPLES
- 22. (𝑥4 +3𝑥3 − 7𝑥2 + 13 𝑥 − 5 ) ÷ (𝑥 − 2) 2 1 3 -7 -9 6 2 10 6 -6 1 5 3 -3 0 𝐹𝑖𝑛𝑎𝑙 𝐴𝑛𝑠𝑤𝑒𝑟 ∶ 𝑥3 +5 𝑥2 + 3x - 3
- 23. ( 2 𝑥3 + 4 x - 8) ÷ (𝑥 + 1 ) -1 2 0 4 -8 -1 1 -5 2 -1 5 13 Final Answer : 2 𝑥2 - 1 x + 5 - 13 𝑥+1
- 24. Find the remainder when the polynomial 𝑥2 -2x -4 is divided by x-3 using synthetic division 3 3 -2 4 9 21 3 7 17 The remainder is 17
- 25. ( 4 𝑥3 - 12 𝑥2 + 17 𝑥 − 12 ) ÷ (2𝑥 − 3 ) 𝟑 𝟐 2 6 17 2 -6 3 9 2 6 2 - 3 4 0 Final answer : 2 𝑥2 -3x+ 4 4 𝑥3 − 12 𝑥2 + 17 𝑥 −12 2𝑥 −3 = 4𝑥3 −12 𝑥2 17 𝑥 −12 ÷2 2𝑥−3 ÷2 = 2𝑥3 −6 𝑥2+ 17 2 𝑥 −6 𝑥− 3 2
- 26. (𝑥4 − 3𝑥3 + 11 𝑥2 − 3x + 10) ÷ (𝑥2 + 1 ) 0, -1 1 - 3 11 -3 10 1 -3 10 0 0 Final answer : 𝑥2 − 3𝑥 + 10 0 -1 0 3 0 - 10
- 27. Members: Blancas, Laidez Iglesia, Mijs Cardillo, Jay Lei Pacheco, Dara Jeanette Rivera, Harriet