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  • 03-11-2022
  • Mathematics
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Use the Remainder Theorem to explain whether or not (x − 2) is a factor of F(x) = x4 − 2x3 + 3x2 − ax+ 3

Use the Remainder Theorem to explain whether or not x 2 is a factor of Fx x4 2x3 3x2 ax 3 class=

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MeeahN705258 MeeahN705258
  • 03-11-2022
Explanation

The remainder theorem states that when a polynomial P(x) is divided by (x - a), for some number a, the remainder r is equal to P(a). Also states that when P(a) = 0, then (x - a) is a factor of P(x).

Then, let us see the result of evaluating the given polynomial when x = 2.

[tex]\begin{gathered} x=2 \\ F\lparen x)=x^4−2x^3+3x^2−ax+3 \\ F(2)=2^4−2(2)^3+3(2)^2−a(2)+3 \end{gathered}[/tex]

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