Question

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RK F 16 ton Attempt 1 of 1 F 17 purif F 18 with Use the remainder theorem to find P(-2) for P(x)=1? +3x2+7. Specifically, give the quotient and the remainder for the associated division and the value of P(-3). 26.9 F F 19 20 Quotient = 0 21 Remainder = 0 DO x 6 ?

Answer 1

some basic fact a Rem ainder theorem : suppose P(x) - be. polynomial, then Remainder when PCX) divided by (x-2) obtained is equal pla) i.e of Dividend - PIX) and Divisior = x-a then Remainder a Pla) P(X) = Now From question : x3+3x²+7 for P(-3) , when we divide Pla) by ( 2-1-3)) then remainder obtained is equal to P(-3) To obtain. remainder P(-3) we have divide by (x+3) Dividend = x2 +372+7, Division - 243 suppose quotient = Q(x) so, P(-3) At first we P(x) P1-3) P(-3) P1-3) will find remainder = x3+3x2+7 (-393 + 3x630277 { put a = -3; - 27 +27 + 7 7 Answer Remainder a 7 a3+3x2+7-7 Dividenda Divisior x quotient + Remainder x² + 3x²+7 . (x+3) (qcx) + 7 (20)(2+3) (910) (2+3) a37392 (2000))(2+37 x2 2 (0+3) a +370 P(x) quotient Remainder a 7 Answer P(-3) . 22 Hence x2 CSScanned with CamScanner