Question

Use polynomial division to solve application problem.
Picture attached for question.

Answer 1

Hello,

We need to divide polynomials, I will try to specify each step

First of all, we need to divide

$63x^3-37x^2+77x+65$

by

9x+5

First focus on the highest degree term, we need to multiply (9x+5) by $7x^2$

so that we get $63x^3+35x^2$ this is to eliminate the term in highest degree

and then subtract to the first polynomial we got

$63x^3-37x^2+77x+65-63x^3-35x^2=-72x^2+77x+65$

and then we need to divide this one by (9x+5) again

$(9x+5)*(-8x)=-72x^2-40x$

and then

$-72x^2+77x+65-(-72x^2-40x)=117x+65$

finally

$(9x+5)*(13)=117x+13*5=117x+65$

so the rest is 0

Finally it comes

$63x^3-37x^2+77x+65=(9x+5)(7x^2-8x+13) \ So\\\\\dfrac{63x^3-37x^2+77x+65}{9x+5}=7x^2-8x+13$

hope this helps