degree and the standard form of the polynomials (x³- 1) (x³- 4), (y³- 2) (y³+ 11), (a³- 3/8) (a³- 16/17), (a + 3/4) (a + 4/3)
pls answer
Answers
Answer:
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
The first polynomial he looks at is
x
3
−
8
. So the first step is to put it into the form of something cubed
±
something else cubed. Since this problem has a minus we use minus. First put down the skeleton:
(
)
3
−
(
)
3
Next we find what term cubed gives us
x
3
. Obviously the answer is
x
, so we put that in the first slot.
(
x
)
3
−
(
)
3
Then we find what cubed gives us
8
. The answer is
2
because
2
∗
2
∗
2
=
8
.
(
x
)
3
−
(
2
)
3
Then we factor into the form given by the equation above. In this problem
a
=
x
and
b
=
2
. So we factor this polynomial into:
(
x
−
2
)
(
x
2
+
2
x
+
4
)
Note that when using these formulas the quadratic term will not be able to factored any further. In other words, we can't factor
(
x
2
+
2
x
+
4
)
anymore.
The second example he goes through is
343
x
3
+
64
y
3
. See if you can solve this one on your own and then watch the video to see if your answer is correct