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 = -2
Now, by REMAINDER THEOREM:
Dividend = (Divisor x Quotient) + Remainder
If ( 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 5
Hence, for p = 15, [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).
