Polynomials - Factor and Remainder Theorem

[Bob Jones]

Q16) A and B

(a) When a polynomial is divided by (2x+1)(x-3), the remainder is 3x-1. What is the remainder when the polynomial is divided by 2x+1?

(b) When x^5 + 3x^3 + ax + b is divided by x^2 - 1, the remainder is 2x - 7. Find a and b.

(c) When a polynomial P(x) is divided by x^2 - 5, the remainder is x + 4. Find the remainder when P(x) + P(-x) is divided by x^2 - 5. (Hint: Write down the division identity.)

Please help I am stuck, thank you

 

[BigBeachBanana]

Q16) A and B

Please help I am stuck, thank you

a) Seems incomplete or I'm missing something.
b) Perform long division to get the remainder in terms of a and b then equate that to the given remainder.

 

[blamocur]

Seems incomplete or I'm missing something.

Looks to me like you are missing something. Which of the three problems looks incomplete to you?

 

[blamocur]

One problem at a time. For 16.a: if [imath]P(x)[/imath] is the polynomial in question how can you express [imath]P[/imath] through [imath](2x+1)(x-3)[/imath] and [imath]3x-1[/imath] ?

 

[Dr.Peterson]

Q16) A and B

Please help I am stuck, thank you

Please show us where you are stuck, by showing what work you have done and what went wrong. As it is, we don't know what sort of help you need, or what you know that you can use to solve this.

One key idea will be that the remainder has to have a degree less than that of the divisor. What does that imply for this problem?

 

[BigBeachBanana]

Looks to me like you are missing something. Which of the three problems looks incomplete to you?

I was referring to a) but I was being silly.