Question
Find the remainder when the polynomial $f(x) = 2x^4- 6x^3 + 2x^2 - x + 2$ is divided by $x + 2.$
✓
Answer
If $x + 2 = 0$
$x = -2$
$f(x) = 2x^4 - 6x^3 + 2x^2 - x + 2, ..$.[By remainder theorem]
$f(-2) = 2(-2)^4 - 6(-2)^3 + 2(-2)^2 - (-2) + 2$
$= 2(16) -6(-8) + 2(4) + 2 + 2$
$= 32 + 48 + 8 + 2 + 2 = 92$
Hence, required remainder $= 92.$
$x = -2$
$f(x) = 2x^4 - 6x^3 + 2x^2 - x + 2, ..$.[By remainder theorem]
$f(-2) = 2(-2)^4 - 6(-2)^3 + 2(-2)^2 - (-2) + 2$
$= 2(16) -6(-8) + 2(4) + 2 + 2$
$= 32 + 48 + 8 + 2 + 2 = 92$
Hence, required remainder $= 92.$
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