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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


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

\(y = 64 x^{6} - 1\)

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

\(y = 64 b^{6} - y^{12}\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(y = 64 x^{9} + 27\)

\(y = 64 b^{6} + y^{12}\)

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

\(y = 27 b^{6} + 64 y^{12}\)

Answers


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

\(y = 64 x^{6} - 1 \) ⇒
\(\left(4 x^{2} - 1\right) \left(16 x^{4} + 4 x^{2} + 1\right)\)

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

\(y = 64 b^{6} - y^{12} \) ⇒
\(\left(4 b^{2} - y^{4}\right) \left(16 b^{4} + 4 b^{2} y^{4} + y^{8}\right)\)

\(y = y^{6} + 64 \) ⇒
\(\left(y^{2} + 4\right) \left(y^{4} - 4 y^{2} + 16\right)\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(y = 64 b^{6} + y^{12} \) ⇒
\(\left(4 b^{2} + y^{4}\right) \left(16 b^{4} - 4 b^{2} y^{4} + y^{8}\right)\)

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

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