Long and Synthetic Division Long Division β’ Polynomial long division can be used to divide a polynomial d(x), producing a quotient polynomial q(x) and a remainder polynomial r(x) Question 1 β’ Make sure the powers are in descending order! β’ Divide Using Long Division 3 2 (π₯ β 7π₯ β 19π₯ + 17) ÷ (π₯ β 9) Question 2 β’ Divide Using Long Division (x Question 3 β’ Divide Using Long Division (β20π + 5 β 28π2 + 6π 5 + 29π 4 + 19π 3 ) ÷ (6π β 1) Question 4 β’ Divide Using long Division 5 2 4 3 (42 + 8π¦ + 4π¦ β 69π¦ + 8π¦ β 54π¦) ÷ (β5 + 8π£) Question 5 β’ Use the Remainder Theorem to evaluate each function at the given value. f(x) = 2π₯ 4 + 11π₯ 3 β 10π₯ 2 β 23π₯ β 4 ππ‘ π₯ = β6 Question 6 β’ Use the Remainder Theorem to evaluate each function at the given value. 5 4 3 2 f(m) = π β 8π + π + 36π + 46π β at x=7 161 6 Question 7 β’ Find all the zeros. One zero has been given. 3 2 f(x)= π₯ + 4π₯ + 4π₯ + 16; π₯ = β4 Question 8 Find all the zeros. One zero has been given. β’ f(x)= 4π₯ 3 β 8π₯ 2 β 25π₯ + 50; π₯ = 2 Question 9 Find all the zeros. One zero has been given. β’ f(x)= π₯ 3 β π₯ 2 β 4π₯ + 4; π₯ = 1 Question 10 Find all the zeros. One zero has been given. β’ f(x)= 6π₯ 3 β 4π₯ 2 β 66π₯ β 56; π₯ = 4 Question 11 Find all the zeros. One zero has been given. β’ f(x)= 9π₯ 3 + 9π₯ 2 + 16π₯ + 16; π₯ = -1 Question 12 β’ State the possible rational zeros for each function. Then find all rational zeros. f(x)=π₯ 3 β 2π₯ 2 β π₯ + 2 Question 13 β’ State the possible rational zeros for each function. Then find all rational zeros. f(x)=2π₯ 3 + π₯ 2 β 8π₯ β4 Question 14 β’ State the possible rational zeros for each function. Then find all rational zeros. f(x)=π₯ 3 β 3π₯ 2 β π₯ + 3 Question 15 β’ Just list the possible rational zeros. f(x)=5π₯ 3 + 2π₯ 2 β 45π₯ β 18 Question 16 β’ What are rational and irrational numbers? Question 17 β’ What type of zeros will not be included in the possible rational numbers list? Question 18 β’ What are the two important things that the Remainder Theorem says? Question 19 β’ What does it mean to have multiplicity of zeros? Question 20 β’ How can you verify zeros of a polynomial using a graphing calculator?
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