Group and factor
undistribute then undistribute again
remember
ab+ac=a(b+c)
this is important
6d^4+4d^3-6d^2-4d
undistribute 2d
2d(3d^3+2d^2-3d-2)
group insides
2d[(3d^3+2d^2)+(-3d-2)]
undistribute
2d[(d^2)(3d+2)+(-1)(3d+2)]
undistribute the (3d+2) part
(2d)(d^2-1)(3d+2)
factor that difference of 2 perfect squares
(2d)(d-1)(d+1)(3d+2)
77.
group
(45z^3+20z^2)+(9z+4)
factor
(5z^2)(9z+4)+(1)(9z+4)
undistribuet (9z+4)
(5z^2+1)(9z+4)
Answer:
The function is increasing for all real values of x where
x < –4.
Step-by-step explanation:
we have

This is a vertical parabola open downward (the leading coefficient is negative)
The vertex (h,k) represent a maximum
The roots of the function (or x-intercepts) are x=-6 and x=-2
The x-coordinate of the vertex is the midpoint of the roots
so

The y-coordinate of the vertex is
substitute the x-coordinate of the vertex in the quadratic equation



The vertex is the point (-4,4)
The function is increasing in the interval (-∞,-4)
The function is decreasing in the interval (-4,∞)
Answer:
First, distribute the -2 to each value in the parentheses.
-2x + 4 = 10
(The 4 is positive because a negative multiplied by a negative is a positive)
Then, subtract 4 from both sides to get rid of it.
-2x = 6
Divide by -2 to get x by itself
x = -3