Use the Remainder Theorem (Just substitute the value given below if i Zero then the tx) is a factor of the polynomial function) Identify also which of the following is the factor of f(x) See EXAMPLE for guide to your SOLUTION Using the Remainder Theorem: PX) = x - 6x + 5x + 12 At x = 4 P141 - 1411-614) + 5[4) + 12 Substitute x by 4 P14) = 64 - 6116) + 20 + 12 Simplify P141 = 64 - 96 + 20 + 12 P14) = 0 Perform the indicated operations The remainder is 0. Problem: f(x) = 2x3 - 14x2 + x -7 at f(x) = 7, at f(x) = -7, at f(x) = 3, and f(x)=-3 show your solution each f(x) Write your solution below:
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Step-by-step explanation:
Proof of Remainder Theorem
You know that Dividend = (Divisor × Quotient) + Remainder.
If r(x) is the constant then, p(x) = (x-c)·q(x) + r.
Let us put x=c
p(c) = (c-c)·q(c) + r
p(c) = (0)·q(c) + r
p(c) = r
Hence,
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