9000146703
Level:
A
Expand the following expression.
\[
(a - 2)(5a + 3) - (2a + 1)(3 - a)
\]
\(7a^{2} - 12a - 9\)
\(3a^{2} - 12a - 9\)
\(7a^{2} - 2a - 9\)
\(3a^{2} - 2a - 9\)
Polynomials and Rational Expressions
9000146207
Level:
B
Factor the following expression.
\[
4a^{2} -\left (a - 1\right )^{2}
\]
\(\left (a + 1\right )\left (3a - 1\right )\)
\(\left (a - 1\right )\left (3a - 1\right )\)
\(\left (a + 1\right )\left (3a + 1\right )\)
\(\left (a - 1\right )\left (3a + 1\right )\)
9000146208
Level:
B
Factor the following expression.
\[
\left (2x - 1\right )^{2} -\left (x + 3\right )^{2}
\]
\(\left (x - 4\right )\left (3x + 2\right )\)
\(\left (x - 4\right )\left (3x - 2\right )\)
\(\left (x + 4\right )\left (3x + 2\right )\)
\(\left (x + 4\right )\left (3x - 2\right )\)
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.
\[
2 - (2x + 1) + x(5 - 2x) - 3(x - 2)
\]
\(- 2x^{2} + 7\)
\(- 2x^{2} + 9\)
\(- 2x^{2} - 3\)
\(- 2x^{2} - 5\)
9000101706
Level:
B
Factor the following polynomial.
\[
8x^{4} - 48x^{3} + 72x^{2}
\]
\(8x^{2}\left (x - 3\right )^{2}\)
\(- 8x^{2}\left (3 - x\right )^{2}\)
\(8\left (x^{2} - 3\right )^{2}\)
\(8x\left (x^{2} - 3\right )^{2}\)
9000101708
Level:
C
Factor the following polynomial.
\[
8x^{3} - 27
\]
\(\left (2x - 3\right )\left (4x^{2} + 6x + 9\right )\)
\(\left (2x - 3\right )\left (4x^{2} - 6x + 9\right )\)
\(\left (2x + 9\right )\left (4x^{2} - 6x + 9\right )\)
\(\left (2x - 3\right )\left (4x^{2} + 6x - 9\right )\)
9000101709
Level:
C
Factor the following polynomial.
\[
27x^{6}z - 8y^{3}z
\]
\(z\left (3x^{2} - 2y\right )\left (9x^{4} + 6x^{2}y + 4y^{2}\right )\)
\(z\left (3x^{2} + 2y\right )\left (9x^{4} + 6x^{2}y - 4y^{2}\right )\)
\(z\left (3x^{2} + 2y\right )\left (9x^{4} - 6x^{2}y + 4y^{2}\right )\)
\(z\left (3x^{2} - 2y\right )\left (9x^{4} + 6x^{2}y^{2} + 4y\right )\)
9000101702
Level:
B
Factor the following polynomial.
\[
3x^{3} + 3x^{2}y + 4xy + 4y^{2}
\]
\(\left (3x^{2} + 4y\right )\left (x + y\right )\)
\(\left (3x + y\right )\left (x^{2} + y^{2}\right )\)
\(\left (3x^{2} + 4\right )\left (x + y^{2}\right )\)
\(\left (3x + y^{2}\right )\left (x + y\right )\)