1.
(Create a table then plot the points)
X | 0 | 1 | 2 | 3 |
-------------------------
Y | -1 | 3 | 7 | 11 |
4 (0) -1 => 0 - 1 = -1
4 (1) -1 => 4 - 1 = 3
4 (2) -1 => 8 - 1 = 7
4 (3) -1 => 12 - 1 = 11
Just apply the table method to the others and you should be fine! :)
A) Ang 1 + Ang 2 = 90
B) Ang 1 = Ang 2 + 20
B) Ang 1 -Ang 2 = 20 then adding this to equation A produces
2 Ang1= 110
Ang 1 = 55 degrees
Ang 2 =35 degrees
The zeroes are
0, -5, 3 + i (and its conjugate)
The factors are
x (x + 5) (x - (3 + i)) (x - (3 - i))
Expanding...
(x² + 5x)((x - 3) - i) ((x - 3) + i)
(x² + 5x)((x - 3)² - i²)
(x² + 5x)(x² - 6x + 9 - (-1))
(x² + 5x)(x² - 6x + 10)
x⁴ - 6x³ + 10x² + 5x³ - 30x² + 50x
x⁴ - x³ - 20x² + 50x
You can treat x and 2x+1 just as though they are real numbers.
So f(2x+1) = 3(2x+1) - 5 = 6x + 3 - 5 = 6x - 2
In the above, I made use of something called the distributive law which says that if a,b and c are real numbers, then a(b+c) = ab + ac.
