Question

Let a(x)=3x^4-2x^2+x+5a(x)=3x
4
−2x
2
+x+5a, left parenthesis, x, right parenthesis, equals, 3, x, start superscript, 4, end superscript, minus, 2, x, squared, plus, x, plus, 5, and b(x)=x^4+x^2+x+1b(x)=x
4
+x
2
+x+1b, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, plus, x, squared, plus, x, plus, 1.
When dividing aaa by bbb, we can find the unique quotient polynomial qqq and remainder polynomial rrr that satisfy the following equation:
\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}
b(x)
a(x)
​
=q(x)+
b(x)
r(x)
​
start fraction, a, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction, equals, q, left parenthesis, x, right parenthesis, plus, start fraction, r, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction,
where the degree of r(x)r(x)r, left parenthesis, x, right parenthesis is less than the degree of b(x)b(x)b, left parenthesis, x, right parenthesis.
What is the quotient, q(x)q(x)q, left parenthesis, x, right parenthesis?
q(x)=q(x)=q, left parenthesis, x, right parenthesis, equals
What is the remainder, r(x)r(x)r, left parenthesis, x, right parenthesis?
r(x)=r(x)=r, left parenthesis, x, right parenthesis, equals

Answer 1

Let a(x)=3x^4-2x^2+x+5a(x)=3x
4
−2x
2
+x+5a, left parenthesis, x, right parenthesis, equals, 3, x, start superscript, 4, end superscript, minus, 2, x, squared, plus, x, plus, 5, and b(x)=x^4+x^2+x+1b(x)=x
4
+x
2
+x+1b, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, plus, x, squared, plus, x, plus, 1.
When dividing aaa by bbb, we can find the unique quotient polynomial qqq and remainder polynomial rrr that satisfy the following equation:
\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}
b(x)
a(x)

=q(x)+
b(x)
r(x)

start fraction, a, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction, equals, q, left parenthesis, x, right parenthesis, plus, start fraction, r, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction,
where the degree of r(x)r(x)r, left parenthesis, x, right parenthesis is less than the degree of b(x)b(x)b, left parenthesis, x, right parenthesis.
What is the quotient, q(x)q(x)q, left parenthesis, x, right parenthesis?
q(x)=q(x)=q, left parenthesis, x, right parenthesis, equals
What is the remainder, r(x)r(x)r, left parenthesis, x, right parenthesis?
r(x)=r(x)=r, left parenthesis, x, right parenthesis, equals

Answer 2

Answer:

Step-by-step explanation: