if p(x) is polynomial of degree 4 with leading coefficient as three such that p(1)=2,p(2)=8,P(3)=18,p(4)=32,then the value of p(5) is

If p(x) is the polynomial of degree 4 with leading coefficient as three such that P(1) = 2,p(2) = 8, P(3) = 18 P(4) = 32, then how do you find the value of P(5)?AnswerRequestFollow5Have this question too? Request Answers:Request From QuoraWe will distribute this question to writers, and notify you about new answers.Bernard LeakBernard Leak, Firmware Developer (2008-present)208 Answers in AlgebraSubrato RoySubrato Roy, studied at Holy Cross School (2015)14 Answers in AlgebraKunwar PratyushKunwar Pratyush4 Answers in AlgebraRavi Ranjan Kumar SinghSandeep VijayShaswat BisiView More or Search8 ANSWERSRobin ReddyRobin Reddy, Maths buffAnswered Jun 9Assume the given equation to be 33x4+Bx3+Cx2+Dx+E=P(x)x4+Bx3+Cx2+Dx+E=P(x) Given p(1) =2 which implies 3+B+C+D+E = 2 this is our first equation.Given p(2) =8 which implies 48+8B+4C+2D+E=8 this is our second equation.Given p(3) =18 which implies 243+27B+9C+3D+E=18 this is our third equation.Given p(4) =32 which implies 768+64B+16C+4D+E=32 this is our fourth equation.Rearranging the terms in all four equation gives us B+C+D+E= -18B+4C+2D+E=-4027B+9C+3D+E=-22564B+16C+4D+E=-736We have four unknown terms in the equations and we have four such equations so these equation can be easily solved to give us the value of B,C,D,E.Hence, the values are B= -30 , C= 107 ,D= -150 ,E= 72.Hence, the polynomial is 33x4−30x3+107x2−150x+72=P(x)x4−30x3+107x2−150x+72=P(x)Therefore , P(5) = 3(625) -30(125)+107(25)-150(5)+72 = 122.