9000101608
Level:
B
Expand \(\left (3x + y\right )\left (9x^{2} - 3xy + y^{2}\right )\).
\(27x^{3} + y^{3}\)
\(27x^{3} - y^{3}\)
\((3x + y)^{3}\)
\(27x^{3} + 3y^{3}\)
B
9000101710
Level:
B
Factor the following polynomial.
\[
x^{2}y - x^{2}z - 4xyz + 4xy^{2} + 4y^{3} - 4y^{2}z
\]
\(\left (y - z\right )\left (x + 2y\right )^{2}\)
\(\left (y - z\right )\left (x - 2y\right )^{2}\)
\(\left (y - z\right )\left (x^{2} + 4y + 4y^{2}\right )\)
\(\left (y + z\right )\left (x - 2y\right )^{2}\)
9000101704
Level:
B
Factor the following polynomial.
\[
16x^{2}y^{4} - 25x^{4}y^{2}
\]
\(\left (4xy^{2} - 5x^{2}y\right )\left (4xy^{2} + 5x^{2}y\right )\)
\(\left (4xy - 5x^{2}y\right )\left (4xy^{2} + 5xy\right )\)
\(\left (4x^{2}y^{2} - 5xy\right )\left (4x^{2}y^{2} + 5xy\right )\)
\(\left (4xy^{2} - 5x^{2}y\right )^{2}\)
9000100707
Level:
B
Consider points \(A = [-2;-1]\),
\(B = [1;y]\),
\(C = [3;-4]\). Find the coordinate
\(y\) which ensures
that the vectors \(\overrightarrow{AB } \)
and \(\overrightarrow{AC } \)
are perpendicular.
\(y = 4\)
\(y = -4\)
\(y = 0.8\)
\(y = -0.8\)
9000101706
Level:
B
Factor the following polynomial.
\[
8x^{4} - 48x^{3} + 72x^{2}
\]
\(8x^{2}\left (x - 3\right )^{2}\)
\(- 8x^{2}\left (3 - x\right )^{2}\)
\(8\left (x^{2} - 3\right )^{2}\)
\(8x\left (x^{2} - 3\right )^{2}\)
9000100708
Level:
B
Given points \(A = [-2;-1]\),
\(B = [x;-3]\),
\(C = [4;-4]\), find the coordinate
\(x\) which ensures
that the vectors \(\overrightarrow{AB } \)
and \(\overrightarrow{AC } \)
are parallel.
\(x = 2\)
\(x = 7\)
\(x = -3\)
\(x = 3\)
9000101702
Level:
B
Factor the following polynomial.
\[
3x^{3} + 3x^{2}y + 4xy + 4y^{2}
\]
\(\left (3x^{2} + 4y\right )\left (x + y\right )\)
\(\left (3x + y\right )\left (x^{2} + y^{2}\right )\)
\(\left (3x^{2} + 4\right )\left (x + y^{2}\right )\)
\(\left (3x + y^{2}\right )\left (x + y\right )\)
9000101101
Level:
B
Find the distance from the point \(A = [0;1;-3]\)
to the point \(B = [-1;3;0]\).
\(\sqrt{14}\)
\(3\)
\(4\)
\(\sqrt{26}\)
9000101703
Level:
B
Factor the following polynomial.
\[
\left (5x - y\right )^{2} -\left (x - y\right )^{2}
\]
\(4x\left (6x - 2y\right )\)
\(x\left (5x - y\right )\)
\(6x\left (6x - 2y\right )\)
\(- 32x^{2}\)
9000097006
Level:
B
Consider the parabola \((y - 1)^{2} = 12(x - 1)\).
Find the focus of this parabola.
\([4;1]\)
\([1;6]\)
\([3;1]\)
\([1;1]\)