Numeric CAS - Part 3: Synthetic Division

Synthetic Division

Goal: Divide the polynomial p(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_0 by (x - r).

p(x) ÷ (x - r) = q_n x^n + q_(n-1) x^(n-1) + ... + q_0 with remainder E

Input: A list of coefficients {a_n, a_(n-1), a_(n-2), ... , a_0} (List 1)

Output: Resulting coefficients {q_n, q_(n-1), ... , q_0, E} (List 2)

Example: (2x^3 + x - 3) ÷ (x - 3) = 2x^2 + 6x + 19 + 54 ÷ (x - 3)

List 1: {2, 0, 1, -3}, R = 3
List 2: {2, 6, 19, 54}

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Casio Prizm

POLYSYN
Synthetic Division - 160 bytes

"P(X) ÷ (X-R)"
"{AnX^n,...,A0}"
"LIST:"?→List 1
"R"?→R
List 1 → List 2
For 1→K To Dim List 1 - 1
R × List 2[K] + List 1[K+1] → List 2[K+1]
Next
"LAST TERM = REMAINDER" ◢
List 2

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TI-84+

POLYSYN
Synthetic Division - 143 bytes

: Disp "P(X)/(X-R)"
: Disp "{AnX^n,...,A0}"
: Input "LIST:", L1
: Input "R:", R
: L1->L2
: For(K,1,dim(L1)-1)
: R*L2(K)+L1(K+1)->L2(K+1)
: End
: Disp "LAST TERM=", "REMAINDER"
: Pause L2

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HP 39gii

POLYSYN
Synthetic Division
11/23/2012

L1 and A are prompted. The resulting is a list of coefficients, with the last term the remainder

Example: (21x^2 + 42x + 144)/(x - 12) = 21x + 294 + 3672/(x-12)
Output List: {21, 294, 3672}

EXPORT POLYSYN()
BEGIN
LOCAL K,S,T;
EDITLIST(L1);
INPUT(R,"P(X)/(X-R)");
L1 → L2;
SIZE(L1)→ S;
S-1 → T;
FOR K FROM 1 TO T DO
R * L2(K) + L1(K+1) → L2(K+1);
END;
MSGBOX("LAST TERM=REMAINDER");
RETURN L2;
END;

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This blog is property of Edward Shore. 2012