 the first derivative of 0*p**2 - 16/35*p**5 - 2/7*p**6 + 1/7*p**4 - 53 + 0*p + 8/21*p**3. Factor a(g).
-4*g**2*(g + 1)**2*(3*g - 2)/7
Let m(l) be the second derivative of -l**9/3024 - l**8/336 - l**7/420 + l**6/45 - 5*l**3 - l**2 + 144*l. Let b(c) be the second derivative of m(c). Factor b(k).
-k**2*(k - 1)*(k + 2)*(k + 4)
Let p be (-18)/4*1 + 13 + (-3311)/(-154). Let 675 + 1/3*y**2 + p*y = 0. Calculate y.
-45
Let k be 51/(22 + 3045/(-140)). Let 3/2*w**4 + 10404*w**2 + 2004504 - 235824*w - k*w**3 = 0. Calculate w.
34
Let x(n) be the first derivative of 3*n**5/5 - 405*n**4/4 + 4623*n**3 - 13467*n**2/2 + 1031. Factor x(u).
3*u*(u - 67)**2*(u - 1)
Let i(v) be the third derivative of 32*v**5/45 - 479*v**4/54 - 10*v**3/27 + 10244*v**2. Factor i(t).
4*(t - 5)*(96*t + 1)/9
Factor 25*t**2 + 9*t**4 + 321*t**2 - 61*t + 253*t + 84*t**3 - 106*t**2.
3*t*(t + 4)**2*(3*t + 4)
Let a(w) = -6*w - 19 + 11*w**3 - 5*w - 2*w + 21*w**2 + 0*w - 9*w**3. Let m be a(-11). Determine x, given that -4/3 - 5/3*x**m + x**2 + 1/3*x**4 + 5/3*x = 0.
-1, 1, 4
Let r(f) be the second derivative of -f**4/18 + 20*f**3/9 - 19*f**2/3 - 45*f + 4. Factor r(c).
-2*(c - 19)*(c - 1)/3
Let d(w) = -2*w**2 + 4*w + 1 + 2*w - 5*w. Let m(n) = -5*n**2 + 8*n - 7. Let u = -35 - -29. Let s(b) = u*d(b) + 3*m(b). Find k such that s(k) = 0.
3
Let o(s) = s**2 + s + 3. Let c(w) = -25*w**2 - 199*w - 66. Suppose -12*p + 25 = 13. Let h(i) = p*c(i) + 4*o(i). Factor h(k).
-3*(k + 9)*(7*k + 2)
Solve -2/3*v**2 - 80/3 - 26/3*v = 0.
-8, -5
Let j be 8 - 1*(-208)/8. Suppose -j*u + 7*u = -54. Suppose 8/3*b - 16/3 + 7/3*b**u + 1/3*b**3 = 0. Calculate b.
-4, 1
Let l(m) be the first derivative of 2*m**5/35 - m**4/14 - 10*m**3/21 - 3*m**2/7 + 537. Factor l(x).
2*x*(x - 3)*(x + 1)**2/7
Let y be 144/(-126)*21/(-32). Factor 1/4*c**4 + 15/4*c + 9/2 - 7/4*c**2 - y*c**3.
(c - 3)**2*(c + 1)*(c + 2)/4
Let w(q) = 8*q**2 - 955*q - 45. Let o(f) = -12*f**2 + 1432*f + 72. Let a(u) = 5*o(u) + 8*w(u). Let a(b) = 0. What is b?
0, 120
Let w(m) = -m**2 - m - 1. Let r(a) = -9*a**2 + 41*a + 106. Let z = -345 + 344. Let f(k) = z*r(k) + 4*w(k). Factor f(t).
5*(t - 11)*(t + 2)
What is p in -2/9*p**2 - 112/9 + 4*p = 0?
4, 14
Let a = -838 + 842. Suppose 5*n = j - 3, a*j + 16*n - 12 = 21*n. Factor 4/3*m**2 + 0 + 1/3*m**4 + 4/3*m**j + 0*m.
m**2*(m + 2)**2/3
Let o(d) be the second derivative of -169*d**6/225 - 429*d**5/50 - 1789*d**4/45 - 284*d**3/3 - 120*d**2 + 320*d + 1. Determine m, given that o(m) = 0.
-30/13, -2, -1
Suppose -281 = -4*p - 89. Factor -p*o**2 + 15*o**3 + 14*o - 4 + 49*o**4 + 16*o**3 - 45*o**3 + 3.
(o - 1)*(o + 1)*(7*o - 1)**2
Let p = 15115 - 15110. Let i(h) be the first derivative of -4/11*h**2 + 3/22*h**4 - 2/55*h**p + 0*h + 23 + 0*h**3. Factor i(o).
-2*o*(o - 2)**2*(o + 1)/11
Suppose 43*n - 47*n = -20. Suppose -4*v = 5*i - 38, 2 + 1 = -v + n*i. Factor 16*p**2 - 5 - 11*p + 9 - 3 - v*p**3 + 1.
-(p - 1)**2*(7*p - 2)
Suppose 97 = -3*c + t, 3*c + 69 = -t - 32. Let v = c + 37. Let 52*l**3 - 34*l - 10 - 21*l - 17*l**3 + 65*l**v + 20*l**5 - 55*l**2 = 0. What is l?
-2, -1, -1/4, 1
Let y = -83 - -97. Suppose -13*o + y*o = -4. Let d(l) = 3*l**2 - 7*l. Let s(z) = -2*z**2 + 6*z. Let n(f) = o*d(f) - 5*s(f). Suppose n(u) = 0. What is u?
-1, 0
Let q(s) be the first derivative of -s + 1/16*s**4 + 80 - 1/6*s**3 - 7/8*s**2. Factor q(o).
(o - 4)*(o + 1)**2/4
Let h be (114/(-18))/19 - (-318)/9. Let c(k) be the first derivative of h - 8*k + 1/4*k**4 - 7/3*k**3 + 7*k**2. Factor c(v).
(v - 4)*(v - 2)*(v - 1)
Let q(u) be the first derivative of u**7/42 - u**6/10 + u**5/10 - 29*u + 61. Let m(a) be the first derivative of q(a). Find k such that m(k) = 0.
0, 1, 2
Suppose -1326*f = -1342*f - 16208. Let x = f - -1017. Factor 1/9*t**x + 1/9*t**2 + 1/3*t**3 - 1/3*t - 2/9.
(t - 1)*(t + 1)**2*(t + 2)/9
Let g = -841 + 881. Suppose 2*z + 1 - 5 = 0. Factor 0*j**2 + 3*j**z + g*j + 4*j**2 + 35 - 2*j**2.
5*(j + 1)*(j + 7)
Let i(f) be the second derivative of f**6/10 - 219*f**5/10 - 295*f**4/4 - 74*f**3 + 2609*f. Determine x so that i(x) = 0.
-1, 0, 148
Suppose 2*y - 4 = 3*o, 11*y - 8*y = -3*o + 6. Factor -16*f + 15*f**5 + 18*f**5 + 2*f**4 - 8 - y*f**2 + 6*f**3 + 4*f**3 - 35*f**5.
-2*(f - 2)**2*(f + 1)**3
Solve -4/11*o**3 - 49/11*o**2 + 3/11*o**4 + 0 - 30/11*o = 0.
-3, -2/3, 0, 5
Let y = -167819 + 3524327/21. Determine a, given that y - 2/21*a**3 + 32/21*a - 8/21*a**2 = 0.
-4, 4
Suppose -3*a = -3*w - 3084, 0 = -3*w - 5*a - 4621 + 1529. Let y = 1167 + w. Suppose -162*v**2 - 36*v - y*v**3 + 0 - 130/3*v**4 - 14/3*v**5 = 0. Calculate v.
-3, -2/7, 0
Let h(z) be the third derivative of -1/15*z**5 - 41*z**2 + 13/12*z**4 - 2*z**3 + 0*z + 0. Suppose h(q) = 0. Calculate q.
1/2, 6
Let m = 17 + -11. Let b(g) = 2*g**2 + 9*g**2 - 3*g**2 + 6 + 0*g**2 - 12*g. Let n(s) = s**2 - s + 1. Let f(o) = m*n(o) - b(o). Find h, given that f(h) = 0.
0, 3
Let i be (174/116)/(170/(-13564)). Let j = i - -599/5. Factor -j*z - 4/17*z**2 + 2/17*z**3 + 4/17.
2*(z - 2)*(z - 1)*(z + 1)/17
Let b = -7764 + 7764. Let u(x) be the third derivative of -3/80*x**5 + 1/80*x**6 + 0*x**4 + 0 + 1/280*x**7 + 0*x**3 + x**2 + b*x. Find m such that u(m) = 0.
-3, 0, 1
Solve 1/9*x**2 + 41/3*x + 114 = 0 for x.
-114, -9
Let o(u) be the third derivative of 2*u**2 - 1/1260*u**6 + 0 - 3/28*u**4 + 0*u - 1/70*u**5 - 17/6*u**3. Let g(q) be the first derivative of o(q). Factor g(p).
-2*(p + 3)**2/7
Let g(h) = -5*h - 77. Let c be g(-16). Suppose -13*y**3 + 4*y**2 + 4*y**3 + 7*y**c + y**4 + 6*y**3 = 0. Calculate y.
-2, 0
Let z(m) be the second derivative of -2*m**6/45 + 4*m**4/9 + 814*m + 1. Find v, given that z(v) = 0.
-2, 0, 2
Factor 106/5 - 1/10*j**2 - 52/5*j.
-(j - 2)*(j + 106)/10
Let h = 1017639/5 + -203525. Suppose 2/5 - 18/5*s**3 + 18/5*s + h*s**2 - 16/5*s**4 = 0. What is s?
-1, -1/8, 1
Factor 58/5*a - 1/5*a**2 + 59/5.
-(a - 59)*(a + 1)/5
Find m, given that -8*m**2 + 3*m**2 + 248*m - 2*m**2 + 6*m**2 - m**2 = 0.
0, 124
Let x(b) be the first derivative of 13*b**4/2 - 152*b**3/3 + 148*b**2 - 192*b + 1954. What is m in x(m) = 0?
24/13, 2
Factor 320 + 1008*v + 3969/5*v**2.
(63*v + 40)**2/5
Factor 3/2*n**2 + 1905/2 - 198*n.
3*(n - 127)*(n - 5)/2
Find d, given that 368/5*d**2 + 8/5*d**4 - 368/5*d + 4/5*d**5 - 28*d**3 + 128/5 = 0.
-8, 1, 2
Factor 4902*z + 4139*z - 2338 - 4*z**2 + 2783*z - 3236*z - 6246.
-4*(z - 2146)*(z - 1)
Suppose 20 = 3*t + 2*w, -3*t = 2*t - 4*w + 18. Factor -3/7*g + 0 + 3/7*g**3 + 0*g**t.
3*g*(g - 1)*(g + 1)/7
Factor 3*a**3 - 495*a + 433*a + 105*a**2 + 38*a**2 - 237*a**2 - 5*a**3 + 28830.
-2*(a - 15)*(a + 31)**2
Find h, given that 33*h**3 - 3*h**2 - 177*h - 100*h**2 - 26*h**2 - 15 = 0.
-1, -1/11, 5
Let u be (-7916)/(-18600)*5 - 2. Let s = u - -6/155. Let s*i**2 + 0 - 1/6*i = 0. Calculate i.
0, 1
Let h(c) be the second derivative of c**6/6 + 75*c**5/4 - 490*c**4/3 + 530*c**3 - 800*c**2 + 3677*c. Factor h(p).
5*(p - 2)**2*(p - 1)*(p + 80)
Find a, given that -13/2*a**4 - 12 - 5*a + 1/2*a**5 + 37/2*a**2 + 9/2*a**3 = 0.
-1, 1, 2, 12
Let g be (-3 - (-220)/12)/(2/3). Suppose h + 8 = g. Factor -h*p**3 - 5*p**2 - 4*p**5 + 12*p**4 + 11*p**2 + p**5.
-3*p**2*(p - 2)*(p - 1)**2
Let h(p) be the third derivative of 5*p**8/336 - 4*p**7/21 - 15*p**6/4 - 18*p**5 - 225*p**4/8 - 1026*p**2. Suppose h(s) = 0. Calculate s.
-3, -1, 0, 15
Suppose -97 = -3*u - 88. Factor 7 - 8 + 4*c - 22*c**2 - 9*c**3 + u + 22 + c**5 + 2*c**4.
(c - 3)*(c - 1)*(c + 2)**3
Let f(h) = 13*h - 115. Let p be f(-14). Let o be 9/(p/(-1106)) + 12/(-66). Factor o*n + 40/3 + 125/6*n**2.
5*(5*n + 4)**2/6
Determine y, given that -1096*y**2 + 5*y**3 + 376*y**2 + 1781638*y + 720 - 1781643*y = 0.
-1, 1, 144
Let w(l) be the third derivative of -l**8/126 - 83*l**7/105 - 617*l**6/90 - 237*l**5/10 - 343*l**4/9 - 76*l**3/3 + 3499*l**2. Suppose w(r) = 0. What is r?
-57, -2, -1, -1/4
Let v(t) be the first derivative of -t**4/2 + 116*t**3/3 + 309*t**2 + 756*t - 857. Factor v(r).
-2*(r - 63)*(r + 2)*(r + 3)
Let m(q) be the first derivative of 6*q**5/35 - 39*q**4/14 + 10*q**3 + 39*q**2/7 - 216*q/7 - 890. Let m(r) = 0. Calculate r.
-1, 1, 4, 9
Let u(g) = g**4 - 12*g**3 + 69*g**2 - 48*g + 2. Let o(w) = -3*w**4 + 19*w**3 - 136*w**2 + 95*w - 5. Let d(v) = 4*o(v) + 10*u(v). Suppose d(c) = 0. What is c?
-25, 0, 1, 2
Let g(i) be the second derivative of -i**7/2520 - 17*i**3/6 + 69*