the Expression 4x^2-p(x)+7 leaves a remainder of -2 when divided by (x-3) find the value of pA) 11B)-2C)15D)40​

Answer:(c)  For p = 15,  [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).Step-by-step explanation:Here,  The dividend expression is  [tex]4x^2-p(x)+7[/tex] = E(x)The Divisor = (x-3)Remainder  = -2Now, by REMAINDER THEOREM:Dividend  = (Divisor x Quotient)  + RemainderIf ( x -3 ) divides the given polynomial with a remainder -2.⇒  x = 3  is a  solution of given polynomial E(x)  - (-2) =  [tex]E(x)  - (-2)  = 4x^2-p(x)+7 -(-2)  = 4x^2-p(x)+9[/tex] =  S(x)Now, S(3) = 0⇒[tex]4x^2-p(x)+9 = 4(3)^2 - p(3) + 9 = 0\\\implies 36 - 3p + 9 = 0\\\implies 45= 3p , \\or p  =15[/tex]or, p =1 5Hence, for p = 15,  [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).