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Let’s check out your problem:
Divide. If the polynomial does not divide evenly, include the remainder as a
fraction
.
\newline
(
5
w
2
+
24
w
+
21
)
÷
(
w
+
3
)
(5w^2 + 24w + 21) \div (w + 3)
(
5
w
2
+
24
w
+
21
)
÷
(
w
+
3
)
\newline
_____
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Math Problems
Algebra 2
Add, subtract, multiply, and divide polynomials
Full solution
Q.
Divide. If the polynomial does not divide evenly, include the remainder as a fraction.
\newline
(
5
w
2
+
24
w
+
21
)
÷
(
w
+
3
)
(5w^2 + 24w + 21) \div (w + 3)
(
5
w
2
+
24
w
+
21
)
÷
(
w
+
3
)
\newline
_____
Divide First Term:
Divide the first term of the dividend by the first term of the divisor:
5
w
2
÷
w
=
5
w
5w^2 \div w = 5w
5
w
2
÷
w
=
5
w
.
Multiply by
5
w
5w
5
w
:
Multiply the divisor by
5
w
5w
5
w
:
(
w
+
3
)
(
5
w
)
=
5
w
2
+
15
w
(w + 3)(5w) = 5w^2 + 15w
(
w
+
3
)
(
5
w
)
=
5
w
2
+
15
w
.
Subtract Result:
Subtract the result from the dividend:
5
w
2
+
24
w
+
21
5w^2 + 24w + 21
5
w
2
+
24
w
+
21
-
5
w
2
+
15
w
5w^2 + 15w
5
w
2
+
15
w
= (9\)w +
21
21
21
\
Divide New First Term:
Divide the new first term of the remainder by the first term of the divisor:
9
w
÷
w
=
9
9w \div w = 9
9
w
÷
w
=
9
.
Multiply by
9
9
9
:
Multiply the divisor by
9
9
9
:
(
w
+
3
)
(
9
)
=
9
w
+
27
(w + 3)(9) = 9w + 27
(
w
+
3
)
(
9
)
=
9
w
+
27
.
Subtract Result:
Subtract the result from the remainder:
(
9
w
+
21
)
−
(
9
w
+
27
)
=
−
6
(9w + 21) - (9w + 27) = -6
(
9
w
+
21
)
−
(
9
w
+
27
)
=
−
6
.
Include Remainder:
Since
−
6
-6
−
6
is less than the degree of the divisor
(
w
+
3
)
(w + 3)
(
w
+
3
)
, we include the remainder as a fraction:
−
6
÷
(
w
+
3
)
-6 \div (w + 3)
−
6
÷
(
w
+
3
)
.
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\newline
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\newline
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\newline
(
24
t
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+
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(
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Question
Is the function
q
(
x
)
=
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−
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q
(
x
)
=
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−
9
even, odd, or neither?
\newline
Choices:
\newline
[[even][odd][neither]]
\text{[[even][odd][neither]]}
[[even][odd][neither]]
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Question
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)
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\newline
(
r
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(
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r
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)
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(
r
+
3
)
(
4
r
+
2
)
\newline
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Question
Find the roots of the factored polynomial.
\newline
(
x
+
7
)
(
x
+
4
)
(x + 7)(x + 4)
(
x
+
7
)
(
x
+
4
)
\newline
Write your answer as a list of values separated by commas.
\newline
x
=
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