What number should be placed in the box to help complete the division calculation 3426 divided by 16
1 answer:
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Answer:
see explanation
Step-by-step explanation:
This is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
16 = ( 4
)² ⇒ a = 4
1 = 1² ⇒ b = 1
Hence
16 - 1
= (4 )² - 1²
= (4 - 1)(4
+ 1)
4 - 1 ← is also a difference of squares and factors as
(2x² - 1)(2x² + 1)
Thus
16 - 1
= (2x² - 1)(2x² + 1)(4 + 1 )
Answer:
Step-by-step explanation:
We want to find a third degree polynomial with zeros <em>x </em>= 2 and <em>x</em> = 2i and f(-1) = 30.
First, note that by the Complex Root Theorem, since <em>x</em> = 2i is a root, <em>x</em> = -2i must also be a root.
Hence, we will have the three factors:
Where <em>a</em> is the leading coefficient.
Expand and simplify the second and third factors:
Hence:
Since f(-1) = 30:
In conclusion, third degree polynomial function is: