Question

By Remainder Theorem, find the remainder when p(x) = 2x3 + x2 - 4x + 5 is divided by 2x + 1 .​

Answer 1

According to remainder theorem,

• 2x + 1 = 0
• 2x = -1
• x = -1/2

So, put x = -1/2 in p(x)

• p(x) = 2x³ + x² - 4x + 5
• p(-1/2) = 2×(-1/2)³ + (-1/2)² - 4×(-1/2) + 5
• p(-1/2) = 2× -1/8 + 1/4 - (-2) + 5
• p(-1/2) = -1/4 + 1/4 +2 + 5
• p(-1/2) = 7

Thus, the remainder through remainder theoram is 7.

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