(x + 2)^5 = (x + 2) (x + 2) (x + 2)(x + 2)(x + 2) =
(x2 + 4x + 4)(x2+4x+4)(x+2) = ( x4 + 4x3 + 4x2 + 4x3 + 16x2 + 16x + 4x2 +16x + 16)(x+2) = ( x4 + 8x3 + 24x2 + 32x + 16)(x+2) = ( x5 + 8x4 + 24x3 + 32x2 + 16x + 2x4 + 16x3 + 48x2 + 64x + 32) =
x5 + 10x4 + 40x3 + 80x2 + 80x + 32
Answer D
Answer: x=3 and y=−2
Step-by-step explanation:
x=−2y−1;4x−4y=20
Step: Solve x=−2y−1 for x:
Step: Substitute−2y−1 for x in 4x−4y=20:
4x−4y=20
4(−2y−1)−4y=20
−12y−4=20(Simplify both sides of the equation)
−12y−4+4=20+4(Add 4 to both sides)
−12y=24
−12y
−12
=
24
−12
(Divide both sides by -12)
y=−2
Step: Substitute−2 for y x=−2y−1:
x=−2y−1
x=(−2)(−2)−1
x=3(Simplify both sides of the equation)
(-5,9) because -6—1=-6+1 which equals -5 and 7—2=7+2 which equals 9
Answer:
a. a = 1, b = -5, c = -14
b. a = 1, b = -6, c = 9
c. a = -1, b = -1, c = -3
d. a = 1, b = 0, c = -1
e. a = 1, b = 0, c = -3
Step-by-step explanation:
a. x-ints at 7 and -2
this means that our quadratic equation must factor to:
FOIL:
Simplify:
a = 1, b = -5, c = -14
b. one x-int at 3
this means that the equation will factor to:
FOIL:
Simplify:
a = 1, b = -6, c = 9
c. no x-int and negative y must be less than 0
This means that our vertex must be below the x-axis and our parabola must point down
There are many equations for this, but one could be:
a = -1, b = -1, c = -3
d. one positive x-int, one negative x-int
We can use any x-intercepts, so let's just use -1 and 1
The equation will factor to:
This is a perfect square
FOIL:
a = 1, b = 0, c = -1
e. x-int at
our equation will factor to:
This is also a perfect square
FOIL and you will get:
a = 1, b = 0, c = -3