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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


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

\(y = 27 b^{3} + 1\)

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

\(y = 8 y^{9} - 1\)

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

\(y = c^{9} - 1\)

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

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

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

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

\(y = 4 a^{6} - 1\)

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

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

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

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

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

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

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

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

\(y = - a^{8} + 16 c^{4}\)

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

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

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

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

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

\(y = - 16 b^{12} + 9 c^{6}\)

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

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

Answers


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

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

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

\(y = 8 y^{9} - 1 \) ⇒
\(\left(2 y^{3} - 1\right) \left(4 y^{6} + 2 y^{3} + 1\right)\)

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

\(y = c^{9} - 1 \) ⇒
\(\left(c^{3} - 1\right) \left(c^{6} + c^{3} + 1\right)\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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