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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answers


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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