In Exercises factoringexfirst - factoringexlast, factor completely over the integers. Check your answer by multiplication.
\(2x - 10x^2\)

\(2x(1 - 5x)\)
\(12t^5 - 8t^3= 4t^3\left (\answer {3t^2-2}\right )\)
\(16xy^2 - 12x^2y\)

\(4xy(4y-3x)\)
\(5(m+3)^2- 4(m+3)^3\)

\((m+3)^2(-4m-7) = -(m+3)^2(4m+7)\)

\((2x-1)(x+3) - 4(2x-1) = (2x-1)\left (\answer {x-1}\right )\)
\(t^2(t-5) + t - 5\)

\((t-5)(t^2+1)\)
\(w^2 - 121 = (w-11) \left (\answer {w+11}\right )\)
\(49 - 4t^2\)

\((7-2t)(7+2t) = - (2t-7)(2t+7)\)
\(81t^4 - 16\)

\((3t-2)(3t+2)(9t^2+4)\)
\(9z^2 - 64y^4 = (3z-8y^2)\left (\answer {3z+8y^2}\right )\)
\((y+3)^2 - 4y^2\)

\(3(-y+3)(y+1) = -3(y - 3)(y+1)\)
\((x+h)^3 - (x+h)\)

\((x+h)(x+h-1)(x+h+1)\)
\(y^2 - 24y + 144 = \left (\answer {y-12}\right )^2\)
\(25t^2 + 10t + 1\)

\((5t+1)^2\)
\(12x^3 - 36x^2 + 27x\)

\(3x(2x-3)^2\)
\(m^4 + 10m^2 + 25 = \left (\answer {m^2+5}\right )^2\)
\(27 - 8x^3\)

\((3-2x)(9 + 6x + 4x^2) = -(2x-3)(4x^2+6x+9)\)
\(t^6 +t^3\)

\(t^3(t+1)(t^2 - t + 1)\)
\(x^2 - 5x - 14 = (x-7)\left (\answer {x+2}\right )\)
\(y^2 - 12y + 27\)

\((y-9)(y-3)\)
\(3t^2 + 16t + 5 = \left (\answer {3t+1}\right )(t+5)\)
\(6x^2 - 23x + 20\)

\((2x-5)(3x-4)\)
\(35+2m - m^2\)

\((7-m)(5+m) = -(m-7)(m+5)\)
\(7w - 2w^2 - 3\)

\((-2w+1)(w-3) = -(2w-1)(w-3)\)
\(3m^3 + 9m^2 - 12m = 3m(m-1)\left (\answer {m+4}\right )\)
\(x^4 + x^2 - 20\)

\((x-2)(x+2)(x^2+5)\)
\(4(t^2-1)^2 +3(t^2-1) - 10\)

\((2t-3)(2t+3)(t^2+1)\)
\(x^3 - 5x^2 - 9x + 45 = (x-3)(x+3)\left (\answer {x-5}\right )\)
\(3t^2 + t - 3 - t^3\)

\((t-3)(1-t)(1+t) = -(t-3)(t-1)(t+1)\)
\(y^4 + 5y^2 + 9\)

\(y^4 + 5y^2 + 9 = (y^4 + 6y^2 + 9) - y^2\)

\((y^2-y+3)(y^2+y+3)\)
In Exercises solvebyfactorfirst - solvebyfactorlast, find all rational number solutions. Check your answers.
\((7x+3)(x-5) = 0\)

\(x = -\frac {3}{7}\) or \(x = 5\)
\((2t-1)^2 (t+4) = 0\)

\(t = \answer {-4}\) (smaller solution)

\(t = \answer {\frac {1}{2}}\) (larger solution)

\((y^2 + 4)(3y^2 +y - 10) = 0\)

\(y = \frac {5}{3}\) or \(y = -2\)
\(4t = t^2\)

\(t = \answer {0}\) (smaller solution)

\(t = \answer {4}\) (larger solution)

\(y+3 = 2y^2\)

\(y = -1\) or \(y = \frac {3}{2}\)
\(26x = 8x^2 + 21\)

\(x = \answer {\frac {3}{2}}\) (smaller solution)

\(x = \answer {\frac {7}{4}}\) (larger solution)

\(16x^4 = 9x^2\)

\(x = 0\) or \(x = \pm \frac {3}{4}\)
\(w(6w+11) = 10\)

\(w = \answer {-\frac {5}{2}}\) (smaller solution)

\(w = \answer {\frac {2}{3}}\) (larger solution)

\(2w^2 + 5w + 2 = - 3(2w+1)\)

\(w=-5\) or \(w = -\frac {1}{2}\)
\(x^2(x-3) = 16(x-3)\)

\(x=3\) or \(x = \pm 4\)
\((2t+1)^3 = (2t+1)\)

\(t = -1\), \(t= -\frac {1}{2}\), or \(t = 0\)
\(a^4 + 4 = 6 - a^2\)

\(a = \pm 1\)
\(\frac {8t^2}{3} = 2t+3\)

\(t = \answer {-\frac {3}{4}}\) (smaller solution)

\(t = \answer {\frac {3}{2}}\) (larger solution)

\(\frac {x^3+x}{2} = \frac {x^2+1}{3}\)

\(x = \answer {\frac {2}{3}}\)

\(\frac {y^4}{3} - y^2 = \frac {3}{2} (y^2 + 3)\)

\(y = \pm 3\)
With help from your classmates, factor \(4x^4 + 8x^2 + 9\).
With help from your classmates, find an equation which has \(3\), \(-\frac {1}{2}\), and \(117\) as solutions.