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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


\(y = 16 y^{6} - 1\)

\(y = 8 b^{6} - 1\)

\(y = - 8 a^{6} + b^{3}\)

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

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

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

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

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

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

\(y = 27 x^{12} + y^{6}\)

\(y = x^{3} - 8\)

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

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

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

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

\(y = 64 a^{9} - 27\)

\(y = c^{3} - 8\)

\(y = 27 y^{6} - 1\)

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

\(y = a^{6} + 8 b^{3}\)

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

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

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

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

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

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

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

\(y = 27 y^{6} - 1\)

Answers


\(y = 16 y^{6} - 1 \) ⇒
\(\left(4 y^{3} - 1\right) \left(4 y^{3} + 1\right)\)

\(y = 8 b^{6} - 1 \) ⇒
\(\left(2 b^{2} - 1\right) \left(4 b^{4} + 2 b^{2} + 1\right)\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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