Question

Use the remainder theorem to find P(1) for P(x) = -x³+4x²+6.

Specifically, give the quotient and the remainder for the associated division and the value of P(1).
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Answer 1

To find P(1) using the remainder theorem, divide P(x) by (x - 1) to obtain the quotient and remainder. P(1) is equal to the remainder.

Step-by-step explanation:

To use the remainder theorem to find P(1) for P(x) = -x³+4x²+6, we divide P(x) by (x - 1). The quotient will be the result of the division, and the remainder will be the value of P(1). Let's perform the division:

-x³ + 4x² + 6 ÷ (x - 1)

Using long division, we get a quotient of -x² - 3x - 1 and a remainder of 7. Therefore, P(1) = 7.

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