Math Problems

MathematicsPrecalculusCubic Equations → Finding Factors of Basic Polynomials

Factor the polynomial

## Questions

 $$y = b^{6} + 64$$ $$y = x^{4} - 9$$ $$y = 16 x^{6} - 9$$ $$y = 27 a^{6} - 64$$ $$y = 64 a^{9} + 27$$ $$y = - 27 x^{12} + y^{6}$$ $$y = b^{4} - 16 x^{8}$$ $$y = - 64 c^{12} + 27 y^{6}$$ $$y = 8 a^{9} + b^{18}$$ $$y = 16 a^{4} - 9$$ $$y = 8 b^{6} - 27$$ $$y = c^{6} + 27$$ $$y = b^{6} + 27 x^{12}$$ $$y = 64 a^{3} - 27$$ $$y = 8 x^{9} + 1$$ $$y = 27 c^{6} - 8$$ $$y = 27 a^{9} - 8 b^{18}$$ $$y = c^{4} - 4$$ $$y = a^{9} - 64$$ $$y = 8 a^{6} + 27 x^{12}$$ $$y = - 4 a^{8} + b^{4}$$ $$y = c^{6} + 1$$ $$y = 9 x^{6} - y^{12}$$ $$y = 16 b^{6} - y^{12}$$ $$y = 8 x^{6} + 27$$ $$y = - 9 c^{8} + x^{4}$$ $$y = y^{4} - 16$$ $$y = 27 b^{6} + 64 y^{12}$$

 $$y = b^{6} + 64$$ ⇒ $$\left(b^{2} + 4\right) \left(b^{4} - 4 b^{2} + 16\right)$$ $$y = x^{4} - 9$$ ⇒ $$\left(x^{2} - 3\right) \left(x^{2} + 3\right)$$ $$y = 16 x^{6} - 9$$ ⇒ $$\left(4 x^{3} - 3\right) \left(4 x^{3} + 3\right)$$ $$y = 27 a^{6} - 64$$ ⇒ $$\left(3 a^{2} - 4\right) \left(9 a^{4} + 12 a^{2} + 16\right)$$ $$y = 64 a^{9} + 27$$ ⇒ $$\left(4 a^{3} + 3\right) \left(16 a^{6} - 12 a^{3} + 9\right)$$ $$y = - 27 x^{12} + y^{6}$$ ⇒ $$\left(- 3 x^{4} + y^{2}\right) \left(9 x^{8} + 3 x^{4} y^{2} + y^{4}\right)$$ $$y = b^{4} - 16 x^{8}$$ ⇒ $$\left(b^{2} - 4 x^{4}\right) \left(b^{2} + 4 x^{4}\right)$$ $$y = - 64 c^{12} + 27 y^{6}$$ ⇒ $$\left(- 4 c^{4} + 3 y^{2}\right) \left(16 c^{8} + 12 c^{4} y^{2} + 9 y^{4}\right)$$ $$y = 8 a^{9} + b^{18}$$ ⇒ $$\left(2 a^{3} + b^{6}\right) \left(4 a^{6} - 2 a^{3} b^{6} + b^{12}\right)$$ $$y = 16 a^{4} - 9$$ ⇒ $$\left(4 a^{2} - 3\right) \left(4 a^{2} + 3\right)$$ $$y = 8 b^{6} - 27$$ ⇒ $$\left(2 b^{2} - 3\right) \left(4 b^{4} + 6 b^{2} + 9\right)$$ $$y = c^{6} + 27$$ ⇒ $$\left(c^{2} + 3\right) \left(c^{4} - 3 c^{2} + 9\right)$$ $$y = b^{6} + 27 x^{12}$$ ⇒ $$\left(b^{2} + 3 x^{4}\right) \left(b^{4} - 3 b^{2} x^{4} + 9 x^{8}\right)$$ $$y = 64 a^{3} - 27$$ ⇒ $$\left(4 a - 3\right) \left(16 a^{2} + 12 a + 9\right)$$ $$y = 8 x^{9} + 1$$ ⇒ $$\left(2 x^{3} + 1\right) \left(4 x^{6} - 2 x^{3} + 1\right)$$ $$y = 27 c^{6} - 8$$ ⇒ $$\left(3 c^{2} - 2\right) \left(9 c^{4} + 6 c^{2} + 4\right)$$ $$y = 27 a^{9} - 8 b^{18}$$ ⇒ $$\left(3 a^{3} - 2 b^{6}\right) \left(9 a^{6} + 6 a^{3} b^{6} + 4 b^{12}\right)$$ $$y = c^{4} - 4$$ ⇒ $$\left(c^{2} - 2\right) \left(c^{2} + 2\right)$$ $$y = a^{9} - 64$$ ⇒ $$\left(a^{3} - 4\right) \left(a^{6} + 4 a^{3} + 16\right)$$ $$y = 8 a^{6} + 27 x^{12}$$ ⇒ $$\left(2 a^{2} + 3 x^{4}\right) \left(4 a^{4} - 6 a^{2} x^{4} + 9 x^{8}\right)$$ $$y = - 4 a^{8} + b^{4}$$ ⇒ $$\left(- 2 a^{4} + b^{2}\right) \left(2 a^{4} + b^{2}\right)$$ $$y = c^{6} + 1$$ ⇒ $$\left(c^{2} + 1\right) \left(c^{4} - c^{2} + 1\right)$$ $$y = 9 x^{6} - y^{12}$$ ⇒ $$\left(3 x^{3} - y^{6}\right) \left(3 x^{3} + y^{6}\right)$$ $$y = 16 b^{6} - y^{12}$$ ⇒ $$\left(4 b^{3} - y^{6}\right) \left(4 b^{3} + y^{6}\right)$$ $$y = 8 x^{6} + 27$$ ⇒ $$\left(2 x^{2} + 3\right) \left(4 x^{4} - 6 x^{2} + 9\right)$$ $$y = - 9 c^{8} + x^{4}$$ ⇒ $$\left(- 3 c^{4} + x^{2}\right) \left(3 c^{4} + x^{2}\right)$$ $$y = y^{4} - 16$$ ⇒ $$\left(y^{2} - 4\right) \left(y^{2} + 4\right)$$ $$y = 27 b^{6} + 64 y^{12}$$ ⇒ $$\left(3 b^{2} + 4 y^{4}\right) \left(9 b^{4} - 12 b^{2} y^{4} + 16 y^{8}\right)$$
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