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Math Problems
Algebra 2
Factor using a quadratic pattern
The polynomial
p
(
x
)
=
x
3
−
19
x
−
30
p(x) = x^3 - 19x - 30
p
(
x
)
=
x
3
−
19
x
−
30
has a known factor of
(
x
+
2
)
(x + 2)
(
x
+
2
)
. Rewrite
p
(
x
)
p(x)
p
(
x
)
as a product of linear factors.
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Divide out all common factors
\newline
x
+
4
x
−
4
−
x
−
4
x
+
5
\frac{x+4}{x-4}-\frac{x-4}{x+5}
x
−
4
x
+
4
−
x
+
5
x
−
4
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SB
−
3
-3
−
3
\newline
Q
1
1
1
.
1
1
1
Identify their terms and their factors.
\newline
4
a
2
b
2
−
4
a
2
b
2
c
2
+
c
2
4a^{2}b^{2}-4a^{2}b^{2}c^{2}+c^{2}
4
a
2
b
2
−
4
a
2
b
2
c
2
+
c
2
,
4
a
2
b
2
−
4
a
2
b
2
c
2
+
c
2
−
4
a
2
b
2
c
2
−
2
×
2
×
4
×
×
×
x
+
b
4a^{2}b^{2}-4a^{2}b^{2}c^{2}+c^{2}-4a^{2}b^{2}c^{2}-2\times 2\times 4\times \times \times x+b
4
a
2
b
2
−
4
a
2
b
2
c
2
+
c
2
−
4
a
2
b
2
c
2
−
2
×
2
×
4
×
×
×
x
+
b
,
4
a
2
b
2
c
2
=
c
×
c
4a^{2}b^{2}\quad c^{2}=c \times c
4
a
2
b
2
c
2
=
c
×
c
,
2
×
2
×
a
×
a
×
b
×
b
2\times 2\times a \times a \times b \times b \quad
2
×
2
×
a
×
a
×
b
×
b
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Consider the expression
\newline
4
x
2
+
x
+
3
.
4 x^{2}+x+3 \text {. }
4
x
2
+
x
+
3
.
\newline
Complete
2
2
2
descriptions of the parts of the expression.
\newline
1
1
1
. The entire expression is a sum with
□
\square
□
.
\newline
2
2
2
. The coefficients are
□
\square
□
.
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Factor
x
4
+
8
x
2
+
16
x^4 + 8x^2 + 16
x
4
+
8
x
2
+
16
completely.
\newline
All factors in your answer should have integer coefficients.
\newline
______
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