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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


\(y = 64 x^{3} - 27\)

\(y = 16 c^{2} - 9 x^{4}\)

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

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

\(y = c^{9} - 27\)

\(y = 64 a^{3} - 27 x^{6}\)

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

\(y = y^{9} + 64\)

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

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

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

\(y = b^{6} - 9 x^{12}\)

\(y = c^{4} - 1\)

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

\(y = b^{6} - 1\)

\(y = - 16 a^{12} + y^{6}\)

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

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

\(y = 64 b^{6} + 27 c^{3}\)

\(y = 4 y^{6} - 1\)

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

\(y = 4 c^{4} - 1\)

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

\(y = 16 a^{2} - 9 x^{4}\)

\(y = 27 b^{6} + 1\)

\(y = 4 x^{6} - 9 y^{12}\)

\(y = 27 x^{9} - 1\)

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

Answers


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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(y = b^{6} - 1 \) ⇒
\(\left(b^{3} - 1\right) \left(b^{3} + 1\right)\)

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

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

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

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

\(y = 4 y^{6} - 1 \) ⇒
\(\left(2 y^{3} - 1\right) \left(2 y^{3} + 1\right)\)

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

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

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

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

\(y = 27 b^{6} + 1 \) ⇒
\(\left(3 b^{2} + 1\right) \left(9 b^{4} - 3 b^{2} + 1\right)\)

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

\(y = 27 x^{9} - 1 \) ⇒
\(\left(3 x^{3} - 1\right) \left(9 x^{6} + 3 x^{3} + 1\right)\)

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