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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


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

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

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

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

\(y = 4 b^{6} - 9 y^{12}\)

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

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

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

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

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

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

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

\(y = - 9 a^{12} + 4 y^{6}\)

\(y = a^{2} - 1\)

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

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

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

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

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

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

\(y = 16 x^{2} - 1\)

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

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

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

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

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

\(y = 8 b^{9} - 27\)

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

Answers


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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