Find the value of p(x) = x 4 -2x 3 + 3x 2 px +3p -7 when divided by (x+1) leaves the remainder 19 . also find the remainder when p(x) is divided by (x+2).
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Given p(x) = x⁴ - 2 x³ + 3 x² + p x + 3 p - 7
Given P(-1) = 19 = (-1)⁴ - 2 (-1)³ + 3 (-1)² - p + 3 p - 7
= 2p - 1
=> p = 10
=> P(x) = x⁴ - 2 x ³ + 3 x² + 10 x + 23
Remainder when divided by x+2 :
P(-2) = 16 - 2 (-8) + 3 * 4 - 20 + 23
= 47
Given P(-1) = 19 = (-1)⁴ - 2 (-1)³ + 3 (-1)² - p + 3 p - 7
= 2p - 1
=> p = 10
=> P(x) = x⁴ - 2 x ³ + 3 x² + 10 x + 23
Remainder when divided by x+2 :
P(-2) = 16 - 2 (-8) + 3 * 4 - 20 + 23
= 47
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