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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(y = 8 a^{6} + 1\)

\(y = 8 y^{6} + 1\)

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

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

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

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

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

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

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

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

\(y = 8 x^{3} + 27 y^{6}\)

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

Answers


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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