I didn't get all the part with the tiles, but here's the general answer:
given a polynomial
we have that 
is a factor of 
if and only if k is a root of , i.e. if
So, given the polynomial
We can check if 
is a factor by evaluating 
:
So, is not a factor.
Similarly, we can evaluate 
to check if 
are factors:
So, only 
is a factor of 
The vertex of this parabola is at (3,-2). When the x-value is 4, the y-value is 3: (4,3) is a point on the parabola. Let's use the standard equation of a parabola in vertex form:
y-k = a(x-h)^2, where (h,k) is the vertex (here (3,-2)) and (x,y): (4,3) is another point on the parabola. Since (3,-2) is the lowest point of the parabola, and (4,3) is thus higher up, we know that the parabola opens up.
Substituting the given info into the equation y-k = a(x-h)^2, we get:
3-[-2] = a(4-3)^2, or 5 = a(1)^2. Thus, a = 5, and the equation of the parabola is
y+2 = 5(x-3)^2 The coefficient of the x^2 term is thus 5.
Answer:
x^3 + 10x^2 + 21x - 12
Step-by-step explanation:
(x + 4)(x^2 + 6x - 3)
you can separate to make it easier for u
x(x^2 + 6x - 3) + 4(x^2 + 6x - 3), this is optional u don't have to do this part
x^3 + 6x^2 - 3x + 4x^2 + 24x - 12
add like terms together
x^3 + 10x^2 + 21x - 12
Answer:
6 2/6 in fractions or 6.3333.
