x^2 = the first integer
(x - 1)^2 = the second integer.
x^2 - (x - 1)^2 = ?
First, let's plug a number into our equation for x.
(2)^2 - (2 - 1)^2 = ?
4 - (1)^2 = ?
4 - 1 = 3
As we can see the difference is odd but it's also the sum of the two consecutive integers.
2 + 1 = 3.
This works for all numbers. Let's plug another number into our equation for x.
(4)^2 - (4 - 1)^2 = ?
16 - (3)^2 = ?
16 - 9 = 7
4 + 3 = 7
Try any number and it will always be odd.
Answer:
60 penguins
Step-by-step explanation:
We need to find out how many times 9, the number of polar bears for every 20 penguins, was multiplied by, so that we can multiply 20 penguins by the same amount.
27/9 = 3
20*3 = 60
Answer:
265
Step-by-step explanation: Used a Calculator
Find the possible rational roots and use synthetic division to find the first zero.
I chose x=1 (which represents the factor "x-1")
1║2 -7 -13 63 -45
║ 2 -5 -18 45
2 -5 -18 45 0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.
Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")
3║2 -5 -18 45
║ 6 3 -45
2 1 -15 0
Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors. Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.
Final Answer: (x-1)(x-3)(x+3)(2x-5)
