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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


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

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

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

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

\(y = 64 x^{9} + 1\)

\(y = 64 b^{9} - 1\)

\(y = 64 c^{9} + 27 x^{18}\)

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

\(y = 4 c^{2} - 1\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answers


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

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

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

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

\(y = 64 x^{9} + 1 \) ⇒
\(\left(4 x^{3} + 1\right) \left(16 x^{6} - 4 x^{3} + 1\right)\)

\(y = 64 b^{9} - 1 \) ⇒
\(\left(4 b^{3} - 1\right) \left(16 b^{6} + 4 b^{3} + 1\right)\)

\(y = 64 c^{9} + 27 x^{18} \) ⇒
\(\left(4 c^{3} + 3 x^{6}\right) \left(16 c^{6} - 12 c^{3} x^{6} + 9 x^{12}\right)\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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