Solve Polynomial Division: Find K Given Remainder of 3

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Homework Help Overview

The problem involves finding the value of k in the polynomial 4x^2 + 9x + k, given that the remainder is 3 when this polynomial is divided by x-1. The context is polynomial division and the properties of remainders.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster expresses confusion about how to utilize the given remainder in the context of polynomial division. Some participants suggest performing the division process while others propose using the remainder theorem, which states that the remainder can be found by evaluating the polynomial at the divisor's root.

Discussion Status

Participants are exploring different methods to approach the problem, with some guidance provided on how to find k. There is no explicit consensus on a single method, as multiple interpretations of the problem are being discussed.

Contextual Notes

The original poster's confusion highlights the challenge of applying the remainder theorem in this context. There may be assumptions about prior knowledge of polynomial division and the properties of remainders that are not explicitly stated.

HelloMotto
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Homework Statement


The remainder is 3 when 4x^2 + 9x + k is divided by x-1
Im suppose to find the K. I am just confused because this question they give me the remainder..so what am i suppose to do with it?
 
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Perform the usual operation, continue bringing k down and then at the end just solve for k by setting it equal to what your remainder should be.
 
thank you
 
You could also use the fact that when a polynomial, P(x), is divided by x- a, the remainder is exactly P(a). You don't need to do any division at all.
 

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