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Math Problems
Precalculus
Divide polynomials using synthetic division
Your answer should be in the form
p
(
x
)
+
k
x
+
3
p(x)+\frac{k}{x+3}
p
(
x
)
+
x
+
3
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
x
2
+
5
x
+
5
x
+
3
\frac{x^2+5x+5}{x+3}
x
+
3
x
2
+
5
x
+
5
Get tutor help
Use synthetic division to find
(
2
x
2
+
16
x
+
30
)
÷
(
x
+
5
)
(2x^2 + 16x + 30) \div (x + 5)
(
2
x
2
+
16
x
+
30
)
÷
(
x
+
5
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
______
Get tutor help
Use synthetic division to find
(
x
2
+
8
x
−
3
)
÷
(
x
−
2
)
(x^2 + 8x - 3) \div (x - 2)
(
x
2
+
8
x
−
3
)
÷
(
x
−
2
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
______
Get tutor help
Use synthetic division to find
(
x
2
+
3
x
+
2
)
÷
(
x
+
2
)
(x^2 + 3x + 2) \div (x + 2)
(
x
2
+
3
x
+
2
)
÷
(
x
+
2
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
______
Get tutor help
Use synthetic division to find
(
x
2
+
6
x
−
28
)
÷
(
x
+
5
)
(x^2 + 6x - 28) \div (x + 5)
(
x
2
+
6
x
−
28
)
÷
(
x
+
5
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
______
Get tutor help
Use synthetic division to find
(
7
x
2
+
3
x
−
10
)
÷
(
x
−
1
)
(7x^2 + 3x - 10) \div (x - 1)
(
7
x
2
+
3
x
−
10
)
÷
(
x
−
1
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
______
Get tutor help
Use synthetic division to find
(
x
2
+
7
x
+
32
)
÷
(
x
+
5
)
(x^2 + 7x + 32) \div (x + 5)
(
x
2
+
7
x
+
32
)
÷
(
x
+
5
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
______
Get tutor help
Use synthetic division to find
(
x
2
+
12
x
+
11
)
÷
(
x
+
1
)
(x^2 + 12x + 11) \div (x + 1)
(
x
2
+
12
x
+
11
)
÷
(
x
+
1
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
8
x
2
+
24
x
+
16
)
÷
(
x
+
2
)
(8x^2 + 24x + 16) \div (x + 2)
(
8
x
2
+
24
x
+
16
)
÷
(
x
+
2
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
5
x
2
−
14
x
+
27
)
÷
(
x
−
3
)
(5x^2 - 14x + 27) \div (x - 3)
(
5
x
2
−
14
x
+
27
)
÷
(
x
−
3
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
−
9
x
+
14
)
÷
(
x
−
2
)
(x^2 - 9x + 14) \div (x - 2)
(
x
2
−
9
x
+
14
)
÷
(
x
−
2
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
6
x
2
−
29
x
+
20
)
÷
(
x
−
4
)
(6x^2 - 29x + 20) \div (x - 4)
(
6
x
2
−
29
x
+
20
)
÷
(
x
−
4
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
3
x
2
−
x
−
24
)
÷
(
x
−
3
)
(3x^2 - x - 24) \div (x - 3)
(
3
x
2
−
x
−
24
)
÷
(
x
−
3
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
−
18
x
+
17
)
÷
(
x
−
1
)
(x^2 - 18x + 17) \div (x - 1)
(
x
2
−
18
x
+
17
)
÷
(
x
−
1
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
+
6
x
−
18
)
÷
(
x
−
3
)
(x^2 + 6x - 18) \div (x - 3)
(
x
2
+
6
x
−
18
)
÷
(
x
−
3
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
−
7
x
+
12
)
÷
(
x
−
4
)
(x^2 - 7x + 12) \div (x - 4)
(
x
2
−
7
x
+
12
)
÷
(
x
−
4
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
+
x
−
2
)
÷
(
x
+
2
)
(x^2 + x - 2) \div (x + 2)
(
x
2
+
x
−
2
)
÷
(
x
+
2
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
−
4
x
+
34
)
÷
(
x
−
1
)
(x^2 - 4x + 34) \div (x - 1)
(
x
2
−
4
x
+
34
)
÷
(
x
−
1
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
9
x
2
−
29
x
−
28
)
÷
(
x
−
4
)
(9x^2 - 29x - 28) \div (x - 4)
(
9
x
2
−
29
x
−
28
)
÷
(
x
−
4
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
+
8
x
−
7
)
÷
(
x
−
1
)
(x^2 + 8x - 7) \div (x - 1)
(
x
2
+
8
x
−
7
)
÷
(
x
−
1
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_________
Get tutor help
Use synthetic division to find
(
x
2
+
2
x
+
7
)
÷
(
x
+
5
)
(x^2 + 2x + 7) \div (x + 5)
(
x
2
+
2
x
+
7
)
÷
(
x
+
5
)
.
\newline
Write your answer in the form
q
(
x
)
+
r
d
(
x
)
q(x) + \frac{r}{d(x)}
q
(
x
)
+
d
(
x
)
r
, where
q
(
x
)
q(x)
q
(
x
)
is a polynomial,
r
r
r
is an integer, and
d
(
x
)
d(x)
d
(
x
)
is a linear polynomial. Simplify any fractions.
\newline
_______
Get tutor help
Divide using synthetic division.
\newline
x
5
+
3
x
4
+
2
x
3
+
4
x
2
+
5
x
−
5
x
+
2
x
5
+
3
x
4
+
2
x
3
+
4
x
2
+
5
x
−
5
x
+
2
=
\begin{array}{l} \frac{x^{5}+3 x^{4}+2 x^{3}+4 x^{2}+5 x-5}{x+2} \\ \frac{x^{5}+3 x^{4}+2 x^{3}+4 x^{2}+5 x-5}{x+2}= \\ \end{array}
x
+
2
x
5
+
3
x
4
+
2
x
3
+
4
x
2
+
5
x
−
5
x
+
2
x
5
+
3
x
4
+
2
x
3
+
4
x
2
+
5
x
−
5
=
\newline
(Simplify your answer. Use integers or fractions for any numbers in the expression. Do not factor.)
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