# Polynomial Division + Other question help (1 Viewer)

#### Danneo

##### Member
1. When the polynomial P(x) is divided by (x+1)(x-2) its remainder is 18x+17. What is the remainder when P(x) is divided by (x-2)?
Ans = 51

2. If a>0 and the function f(x) = ax^3 + bx^2 + cx + d is always increasing, what is the condition on a, b and c?
a)(b^2)-ac<0
b)(b^2)-2ac<0
c)(b^2)-3ac<0
d)(b^2)-4ac<0

For question 2, how do you go about solving it

3. What is the number of solutions of the equation ln|(x^2)-1| (Absolute value)

EDIT:
3. What is the number of solutions of the equation ln|(x^2)-1| = 0 (Absolute value) I done goofed lol

Last edited:

#### integral95

##### Well-Known Member
1. You have to find P(2), assuming you know your remainder theorem.

$\bg_white P(x) = Q(x)(x+1)(x-2) + 18x+17$

Sub x = 2 to get your answer

2. You have to see that f'(x) >0 and therefore you use the discriminate on f'(x) and make that negative. $\bg_white \Delta <0$

3. That's not even an equation

#### Danneo

##### Member
Yikes, my bad, fixed it, Q3 should of been equal to 0
For question 2, i derived it but not sure how to get an answer out of it
Thx

#### HoldingOn

##### Active Member
Yikes, my bad, fixed it, Q3 should of been equal to 0
For question 2, i derived it but not sure how to get an answer out of it
Thx
It should be b^2 -3ac<0 just factor out 4

#### integral95

##### Well-Known Member
Yikes, my bad, fixed it, Q3 should of been equal to 0
For question 2, i derived it but not sure how to get an answer out of it
Thx
Well the answer is 3

since

$\bg_white ln(1) = 0 \\ |x^2-1| = 1 \Rightarrow x^2-1 = 1, \ \ \ x^2 -1 = -1$

First equation has 2 solutions, second equation has one.