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Math Challenge I-C Handout 9

 
 
Picture of Wanyang Zhou
Math Challenge I-C Handout 9
by Wanyang Zhou - Sunday, November 12, 2017, 6:07 PM
 

I am getting stuck on the following questions. Can anyone help me?

Question 9.23:

Solve the equation x3−2x2−9x+18=0x3−2x2−9x+18=0 if you are given that x=±3x=±3 are both roots.


Question 9.25:

Consider P(x)=x3+ax2+bx+1P(x)=x3+ax2+bx+1. Suppose P(1)=3P(1)=3 and P(2)=17P(2)=17. What is the remainder when P(x)P(x) is divided by (x+2)(x+2)?


Question 9.29:

Solve the equation

xx2−5x+6=x−2x2−x−6.



 
Picture of David Reynoso
Re: Math Challenge I-C Handout 9
by David Reynoso - Monday, November 13, 2017, 11:24 AM
 

For question 23, remember that the Factor Theorem tells you that if $a$ is a solution of $P(x) = 0$, then $(x-a)$ is a factor of $P(x)$.

Question 25 is telling you the values you would get by plugging in $1$ and $2$ in the polynomial. That information should help you find what $a$ and $b$ should be.

For question 29 it is important to remember that we can treat rational expressions in a similar way we do regular fractions. Try factoring the denominators to simplify the expression.

 
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