Unit 3A: Polynomials, Part 2
151419157185543A.1 – 3A.3003A.1 – 3A.3center4500452120Unit 3A: Polynomials, Part 211540067000Unit 3A: Polynomials, Part 2center790007945755pebblebrook high schoolAlgbra 21154000pebblebrook high schoolAlgbra 2right230023114020177600980020173A.1 Dividing PolynomialsRecall how to do long division: Let’s see to divide with polynomials using long division’s try: (5x2 + 3x – 2) ÷ (x + 1)Example #1: Divide polynomials using long division Synthetic Division: Let’s watch a video… Example #2: Divide using synthetic division400259814605000You try: Divide using both methodsPurpose – find values to the output of the function, P(x).Example #3: Evaluate the polynomial using Synthetic DivisionYou Try…FACTS: If P(a) = 0, the x – a is linear factor of the polynomial.Example #4: Determine which is a factor of x + 1b) x + 2c) x + 3d) x – 3Section 3A.1 Homework3A.2 Theorems of PolynomialsSteps for finding rational roots:1st- identify ALL factors a (coefficient of leading term of the polynomial2nd – identify ALL factors of c (constant of polynomial)3rd – find ALL answers to ac4th – Plug the possible solutions into the original problem to see if the solution = 0.Example #1: Find the rational roots. x3 + x2 – 3x – 3 = 0 2x2 – x2 + 2x – 1 = 0You Try….Example #2: Finding Irrational Roots1 + 3–11Examples #3: Finding Imaginary Roots 3 – i 2iYou Try….Section 3A.2 Homework 3A.3 Roots of a polynomialsRoots ? Solutions? Zeros (x – values when y = 0)Example #1: Find the zeros when in factored form. Y = (x – 2) (x + 1) ( x – 3)You Try…Example #2: Find the zeros by factoringYou Try….Example #3: Solve the polynomialYou Try…. Example #3: Write the polynomial in standard given the zeros. x = -2, 3, 3 x = -1, 3iYou Try…Section 3A.3 Homework1, -2i ................
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