Polynomial Supplements

# Polynomial Supplements - AP CALCULUS POLYNOMIAL...

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AP CALCULUS POLYNOMIAL SUPPLEMENTARY Problems : 1) When completely factored, what is one of the factors of 51 05 42 x x −+ ? A) x x 21 B) x 2 1 C) x 2 1 + D) x + E) x 2) One factor of x x x 32 31 6 4 8 +−− is x + 4 . What are the remaining two factors? A) () x + 3 and x + 4 B) x + x C) x 4 and x 1 D) x x + E) x x + 3) The expression 243 1 0 3 xxx x +− + is equal to A) 0 2 7 91 3 2 xx x ++ B) 28 2 9 23 3 2 x −++ C) 0 2 7 91 3 2 x + D) 0 2 7 32 3 2 x E) none of the above 4) Which of the following is the graph of ( ) ( ) fx a x x n =+ 12 2 where a n > 0 ? A) B) C) D) E)

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5) Find the polynomial function, () fx of least degree that passes through ( ) 18 , and has the following roots: x = − 3 , x =− 1 (multiplicity 2), x = 0 (multiplicity 3) and x = 2 . Also, find when ( ) < 0 . 6) Find the values of A and B such that x x 2 23 is a factor of the polynomial ( ) x A x x x B =+− + 21 4 5 43 2 . 7) When x A x x =+ ++ 75 35 is divided by x + 3 , the remainder is 3163 . Prove that has a root in the interval [] x ∈− 10 , . State all theorems used in your proof.
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Polynomial Supplements - AP CALCULUS POLYNOMIAL...

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