9000146709
Level:
C
Divide the following two polynomials using long division.
\[
\left (4x^{2} - 10x - 1\right ) : (x - 2)
\]
\(4x - 2 - \frac{5}
{x-2}\)
\(4x - 2 + \frac{3}
{x-2}\)
\(4x + 2 - \frac{5}
{x-2}\)
\(4x + 2 + \frac{3}
{x-2}\)
Polynomials and Rational Expressions
9000146710
Level:
C
Divide the following two polynomials using long division.
\[
\left (x^{3} + 3x^{2} - x + 4\right ) : \left (x^{2} - x + 1\right )
\]
\(x + 4 + \frac{2x}
{x^{2}-x+1}\)
\(x + 4 + \frac{2x+8}
{x^{2}-x+1}\)
\(x + 2 + \frac{6-2x}
{x^{2}-x+1}\)
\(x + 2 + \frac{2x+2}
{x^{2}-x+1}\)
9000146209
Level:
C
Factor the following expression.
\[
27a^{3} - 8b^{9}
\]
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 6ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 6ab^{3} + 4b^{6}\right )\)
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 12ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 12ab^{3} + 4b^{6}\right )\)
9000146210
Level:
C
Factor the following expression.
\[
64x^{6} + 125
\]
\(\left (4x^{2} + 5\right )\left (16x^{4} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{4} + 20x^{2} + 25\right )\)
\(\left (4x^{2} + 5\right )\left (16x^{3} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{3} + 20x^{2} + 25\right )\)
9000146701
Level:
A
Expand the following polynomial.
\[
2 - (2x + 1) + x(5 - 2x) - 3(x - 2)
\]
\(- 2x^{2} + 7\)
\(- 2x^{2} + 9\)
\(- 2x^{2} - 3\)
\(- 2x^{2} - 5\)
9000146702
Level:
A
Expand the following expression.
\[
a - 4(2 - a) - a(5a + 1) + 2a(3 - 2a)
\]
\(- 9a^{2} + 10a - 8\)
\(- 9a^{2} + 12a - 8\)
\(- 9a^{2} + 2a - 8\)
\(- 9a^{2} + 4a - 8\)
9000146201
Level:
B
Expand the following expression.
\[
\left (2x^{3} - y^{2}\right )^{3}
\]
\(8x^{9} - 12x^{6}y^{2} + 6x^{3}y^{4} - y^{6}\)
\(8x^{9} - 4x^{6}y^{2} + 2x^{3}y^{4} - y^{6}\)
\(8x^{6} - 12x^{5}y^{2} + 6x^{3}y^{4} - y^{5}\)
\(8x^{6} - 4x^{5}y^{2} + 2x^{3}y^{4} - y^{5}\)
9000146202
Level:
B
Expand the following expression.
\[
\left (a^{2} + \sqrt{3}b\right )^{3}
\]
\(a^{6} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{6} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)
9000146203
Level:
A
Expand the following expression.
\[
\left (x^{5} -\sqrt{2}y\right )^{2}
\]
\(x^{10} - 2\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y + 2y^{2}\)
\(x^{10} - 2\sqrt{2}x^{5}y - 2y^{2}\)
\(x^{10} -\sqrt{2}x^{5}y - 2y^{2}\)
9000146204
Level:
A
Expand the following expression.
\[
\left (\frac{a}
{2} + 4b^{3}\right )^{2}
\]
\(\frac{a^{2}}
{4} + 4ab^{3} + 16b^{6}\)
\(\frac{a^{2}}
{4} + 2ab^{3} + 16b^{6}\)
\(\frac{a^{2}}
{4} + 4ab^{3} + 16b^{5}\)
\(\frac{a^{2}}
{4} + 2ab^{3} + 16b^{5}\)