A couple of hard questions about the Factor and Remainder Thoerem that I'm having a hard time with.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

18) f(x) = 2x3 + x2 – 5x + c, where c is a constant.

Given that f(1) = 0,

(a) find the value of c

(b) factorise f(x) completely,

(c) find the remainder when f(x) is divided by (2x – 3).

19) f(x) = x3 – 2x2 + ax + b, where a and b are constants.

When f(x) is divided by (x – 2), the remainder is 1.

When f(x) is divided by (x + 1), the remainder is 28.

(a) Find the value of a and the value of b.

(b) Show that (x – 3) is a factor of f(x).

2. Relevant equations

None

3. The attempt at a solution

These are the last two questions of the homework, and the only ones I am having some difficulty with. The other 17 questions I have finished and am happy with. I reckon I can do 18) a) though;

f(1) = 2(1)^3 + 1² - 5(1) + c

= 2 + 1 -5 + c

c = 2

Right? Any help with the other questions is very welcome! Thanks for your time.

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# Homework Help: Factor and Remainder Thoerem

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