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MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Instructions for problem set  Factor the polynomial

Questions


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

\(y = 9 x^{4} - 1\)

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

\(y = 27 c^{9} + 8 x^{18}\)

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

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

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

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

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

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

\(y = b^{12} + 64 x^{6}\)

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

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

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

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

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

\(y = 9 c^{4} - 1\)

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

\(y = 9 a^{4} - 1\)

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

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

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

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

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

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

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

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

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

Answers


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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