"We write (x^2)/(x^+5x+3) = F(x) - (G(x))/(x^2+5x+3) where deg G(x) < 2. Then..."

[zozobear18]

Please help me understand this problem!

 

[stapel]

View attachment 36409Please help me understand this problem!

This is asking you to convert the fraction to mixed-number form. So do the long division of [imath]x^2[/imath] by [imath]x^2 + 5x + 3[/imath], and see what you get.

 

[khansaheb]

View attachment 36409Please help me understand this problem!

From your text book (or classnotes or Google), please explain what is meant by

deg G(x) < 2

 

[blamocur]

From your text book (or classnotes or Google), please explain what is meant by

deg G(x) < 2

I am guessing they mean the degree of polynomial [imath]G(x)[/imath]. I.e., [imath]G(x)[/imath] is a first degree polynomial.

 

[Dr.Peterson]

View attachment 36409Please help me understand this problem!

Presumably they either stated or implied that F and G are meant to be polynomials (which is suggested by the choices anyway). The restriction on the degree of G makes the fraction a proper fraction, which tells us that G is the remainder of the division, and F is the quotient. So, as @stapel said, use polynomial long division to divide [imath]x^2[/imath] by [imath]x^2+5x+3[/imath].

 

[khansaheb]

As I see it:

NONE of the 4 choices presented as "answers" is viable.
.

 

[Harry_the_cat]

As I see it:

NONE of the 4 choices presented as "answers" is viable.
.

If you start the long division process, it becomes clear that F(x)=1.

If the last option is meant to be correct, then there is a typo. G(x) should be 5x + 3 rather than 3x + 5.

Note that:

\(\displaystyle 1 - \frac{5x+3}{x^2+5x+3} = \frac{x^2+5x+3}{x^2+5x+3} - \frac{5x+3}{x^2+5x+3} = \frac{x^2}{x^2+5x+3}\)