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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


\(y = 8 b^{9} - 27 y^{18}\)

\(y = - 9 a^{8} + 16 x^{4}\)

\(y = 64 c^{3} - 1\)

\(y = - 16 b^{8} + 9 c^{4}\)

\(y = 64 a^{6} - 27 x^{12}\)

\(y = 8 a^{9} + 27\)

\(y = - 4 x^{12} + y^{6}\)

\(y = - 8 a^{18} + b^{9}\)

\(y = 8 a^{3} - 27\)

\(y = 27 a^{9} - 8\)

\(y = 9 c^{6} - 16\)

\(y = - c^{8} + y^{4}\)

\(y = 8 a^{6} - 27 x^{12}\)

\(y = 8 b^{9} + 27 y^{18}\)

\(y = - c^{6} + y^{3}\)

\(y = 27 y^{6} + 8\)

\(y = y^{6} + 1\)

\(y = 27 a^{6} + 8\)

\(y = 16 c^{4} - 9\)

\(y = 8 b^{3} + 27\)

\(y = b^{12} + 8 c^{6}\)

\(y = - 64 a^{18} + y^{9}\)

\(y = 4 a^{4} - 9 x^{8}\)

\(y = c^{6} + 8\)

\(y = c^{18} + 8 y^{9}\)

\(y = b^{9} - 64 x^{18}\)

\(y = y^{4} - 16\)

\(y = 16 b^{4} - 1\)

Answers


\(y = 8 b^{9} - 27 y^{18} \) ⇒
\(\left(2 b^{3} - 3 y^{6}\right) \left(4 b^{6} + 6 b^{3} y^{6} + 9 y^{12}\right)\)

\(y = - 9 a^{8} + 16 x^{4} \) ⇒
\(\left(- 3 a^{4} + 4 x^{2}\right) \left(3 a^{4} + 4 x^{2}\right)\)

\(y = 64 c^{3} - 1 \) ⇒
\(\left(4 c - 1\right) \left(16 c^{2} + 4 c + 1\right)\)

\(y = - 16 b^{8} + 9 c^{4} \) ⇒
\(\left(- 4 b^{4} + 3 c^{2}\right) \left(4 b^{4} + 3 c^{2}\right)\)

\(y = 64 a^{6} - 27 x^{12} \) ⇒
\(\left(4 a^{2} - 3 x^{4}\right) \left(16 a^{4} + 12 a^{2} x^{4} + 9 x^{8}\right)\)

\(y = 8 a^{9} + 27 \) ⇒
\(\left(2 a^{3} + 3\right) \left(4 a^{6} - 6 a^{3} + 9\right)\)

\(y = - 4 x^{12} + y^{6} \) ⇒
\(\left(- 2 x^{6} + y^{3}\right) \left(2 x^{6} + y^{3}\right)\)

\(y = - 8 a^{18} + b^{9} \) ⇒
\(\left(- 2 a^{6} + b^{3}\right) \left(4 a^{12} + 2 a^{6} b^{3} + b^{6}\right)\)

\(y = 8 a^{3} - 27 \) ⇒
\(\left(2 a - 3\right) \left(4 a^{2} + 6 a + 9\right)\)

\(y = 27 a^{9} - 8 \) ⇒
\(\left(3 a^{3} - 2\right) \left(9 a^{6} + 6 a^{3} + 4\right)\)

\(y = 9 c^{6} - 16 \) ⇒
\(\left(3 c^{3} - 4\right) \left(3 c^{3} + 4\right)\)

\(y = - c^{8} + y^{4} \) ⇒
\(\left(- c^{4} + y^{2}\right) \left(c^{4} + y^{2}\right)\)

\(y = 8 a^{6} - 27 x^{12} \) ⇒
\(\left(2 a^{2} - 3 x^{4}\right) \left(4 a^{4} + 6 a^{2} x^{4} + 9 x^{8}\right)\)

\(y = 8 b^{9} + 27 y^{18} \) ⇒
\(\left(2 b^{3} + 3 y^{6}\right) \left(4 b^{6} - 6 b^{3} y^{6} + 9 y^{12}\right)\)

\(y = - c^{6} + y^{3} \) ⇒
\(\left(- c^{2} + y\right) \left(c^{4} + c^{2} y + y^{2}\right)\)

\(y = 27 y^{6} + 8 \) ⇒
\(\left(3 y^{2} + 2\right) \left(9 y^{4} - 6 y^{2} + 4\right)\)

\(y = y^{6} + 1 \) ⇒
\(\left(y^{2} + 1\right) \left(y^{4} - y^{2} + 1\right)\)

\(y = 27 a^{6} + 8 \) ⇒
\(\left(3 a^{2} + 2\right) \left(9 a^{4} - 6 a^{2} + 4\right)\)

\(y = 16 c^{4} - 9 \) ⇒
\(\left(4 c^{2} - 3\right) \left(4 c^{2} + 3\right)\)

\(y = 8 b^{3} + 27 \) ⇒
\(\left(2 b + 3\right) \left(4 b^{2} - 6 b + 9\right)\)

\(y = b^{12} + 8 c^{6} \) ⇒
\(\left(b^{4} + 2 c^{2}\right) \left(b^{8} - 2 b^{4} c^{2} + 4 c^{4}\right)\)

\(y = - 64 a^{18} + y^{9} \) ⇒
\(\left(- 4 a^{6} + y^{3}\right) \left(16 a^{12} + 4 a^{6} y^{3} + y^{6}\right)\)

\(y = 4 a^{4} - 9 x^{8} \) ⇒
\(\left(2 a^{2} - 3 x^{4}\right) \left(2 a^{2} + 3 x^{4}\right)\)

\(y = c^{6} + 8 \) ⇒
\(\left(c^{2} + 2\right) \left(c^{4} - 2 c^{2} + 4\right)\)

\(y = c^{18} + 8 y^{9} \) ⇒
\(\left(c^{6} + 2 y^{3}\right) \left(c^{12} - 2 c^{6} y^{3} + 4 y^{6}\right)\)

\(y = b^{9} - 64 x^{18} \) ⇒
\(\left(b^{3} - 4 x^{6}\right) \left(b^{6} + 4 b^{3} x^{6} + 16 x^{12}\right)\)

\(y = y^{4} - 16 \) ⇒
\(\left(y^{2} - 4\right) \left(y^{2} + 4\right)\)

\(y = 16 b^{4} - 1 \) ⇒
\(\left(4 b^{2} - 1\right) \left(4 b^{2} + 1\right)\)
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