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Hi, so I posted my questions but they didn't get answered yesterday, and I would really like some help with them, so I am going to repost them. :)

 

1. Let f(x)=x+5 and let g(x)=x^2+1. Let p(x)=g(x)+f(x) and let q(x)=g(x)-f(x). Find p(x) * q(x).

 

2. Consider the polynomials f(x)=4x^3+3x^2+2x+1 and g(x)=3-4x+5x^2-6x^3. Find c such that the polynomial f(x)+cg(x) has degree 2.

 Sep 9, 2016

Best Answer 

 #1
avatar+118608 
+5

((G(x)+f(x))((g(x)-f(x))

 

=( g(x))^2  -   (f(x))^2

 

= (x^2+1)^2.  -   (x+5)^2

 

= (x^4+2x^2+1)  -  (x^2+10x+25)

 

=    x^4  +x^2.  -10x.    -24

 Sep 10, 2016
 #1
avatar+118608 
+5
Best Answer

((G(x)+f(x))((g(x)-f(x))

 

=( g(x))^2  -   (f(x))^2

 

= (x^2+1)^2.  -   (x+5)^2

 

= (x^4+2x^2+1)  -  (x^2+10x+25)

 

=    x^4  +x^2.  -10x.    -24

Melody Sep 10, 2016
 #2
avatar+118608 
+5

In f(x) the coefficient of x^3. is  4

In g(x) it is -6

 

-6×(4/6)=-4

So the coefficient is   2/3

 Sep 10, 2016

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