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Polynomials: Remainder Theorem
y3 – 9 y2 + 15 y + a when divided by y – 4 has a remainder of –7
=>a =

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Worked Solution:

The Remainder Theorem:
When a polynomial P(y) is divided by y – a the remainder is P(a)
The divisor is y – 4 so we substitute y = 4 into y3 – 9 y2 + 15 y + a:
=>the remainder is (4)3 – 9 (4)2 + 15 (4) + a = –20 + a
But we know the remainder is –7:
=> –20 + a = –7
<=>a = 13

© MEI Produced by Dr Ron Knott, 3 September 2004
tom . button [AT] mei . org . uk 		Test reference: PolyRemThm.html?ref=38134