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P(x) = 2x3 – x2 + 4x + 5 is divided by x + 2. Choose the correct option from each drop-down menu.

When P(x) is divided by x + 2, the remainder is [ ] P(–2) = [ ]. The Remainder Theorem is [verfied/not verified] ]

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Answer: When P(x) is divided by x + 2, the remainder is [-23 ] P(–2) = [9]. The Remainder Theorem is [not verified]

Step-by-step explanation:

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The remainder of the division of polynomial, P(x) = 2x3 – x2 + 4x + 5 by (x + 2) is; -23

The remainder of the division of the polynomial, P(x) = 2x3 – x2 + 4x + 5 by (x + 2) can be evaluated by the remainder theorem.

This involves adding evaluating the value of the polynomial at, x = -2.

  • Since, (x +2) is the Divisor, we evaluate, P(x) at x = -2

Therefore, we have;

  • P(-2) = 2 ×(-2)³ -(-2)² + 4(-2) + 5

  • P(-2) = -16 -4 -8 +5

  • P(-2) = -23.

Therefore, the remainder when P(x) = 2x3 – x2 + 4x + 5 is divided by (x + 2) is; -23

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