f -x**7/420 + 7*x**6/90 - 5*x**5/12 + x**4 + 40*x**3/3 - 27*x**2 + x. Let v(c) be the first derivative of o(c). Factor v(r).
-2*(r - 12)*(r - 1)**2
Let x(b) be the third derivative of b**5/180 - 44*b**4/3 + 15488*b**3 - b**2 - 4*b + 75. What is s in x(s) = 0?
528
Let u be (7904/(-342))/(-52) - (-2)/(-18). Suppose 8/3*a + u*a**3 + 4/3 + 5/3*a**2 = 0. Calculate a.
-2, -1
Let n(x) be the third derivative of 0*x**4 + x + 6*x**2 + 1/80*x**6 + 0*x**3 - 23/20*x**5 + 0. Factor n(c).
3*c**2*(c - 46)/2
Let m = 25222612688 + -1227609782304506/48671. Let b = 2/6953 - m. Determine c, given that -4/7*c**2 - 20/7*c + b = 0.
-6, 1
Let l(f) be the third derivative of f**8/7560 + 2*f**7/945 + 7*f**3 + 6*f**2. Let s(h) be the first derivative of l(h). Factor s(y).
2*y**3*(y + 8)/9
Let o(i) be the first derivative of i**4/26 + 46*i**3/39 + 80*i**2/13 + 152*i/13 - 1372. Suppose o(k) = 0. What is k?
-19, -2
Let a = 2018559 - 2018557. Factor -18/7*s + 2/7*s**4 + 0 - a*s**3 + 30/7*s**2.
2*s*(s - 3)**2*(s - 1)/7
Let a(h) be the third derivative of h**5/50 - 17*h**4/60 - 46*h**3/15 + 168*h**2. Factor a(r).
2*(r + 2)*(3*r - 23)/5
Let h(i) = -i - 2. Let n be h(-2). Suppose n*x + 4*c = -3*x + 9, 0 = -3*x - 2*c + 9. Factor -47*j**5 + 49*j**5 - 3*j**3 + j**x.
2*j**3*(j - 1)*(j + 1)
Suppose o = -2*h + 2417 + 249, 0 = h - 5*o - 1355. Let 909*b**2 - 79 + 154*b**3 + 136*b**3 + 57*b**4 - 71 + 229*b**3 - h*b = 0. What is b?
-5, -2/19, 1
Factor 0 - 734/13*p**4 + 67712/13*p**2 + 0*p + 2/13*p**5 + 5152*p**3.
2*p**2*(p - 184)**2*(p + 1)/13
Let f(l) be the second derivative of -l**6/30 - 109*l**5/20 + 199*l**4/3 - 922*l**3/3 + 696*l**2 + 1384*l. Let f(s) = 0. What is s?
-116, 2, 3
Let t(m) be the third derivative of m**8/1176 + 2*m**7/735 - 29*m**6/420 + m**5/5 + 312*m**2 - 2. Find w, given that t(w) = 0.
-7, 0, 2, 3
Let i(g) = -g**4 + 55*g**3 - 445*g**2 - 6783*g - 6306. Let h(v) = 2*v**4 - 111*v**3 + 896*v**2 + 13567*v + 12614. Let s(b) = -3*h(b) - 7*i(b). Solve s(p) = 0.
-7, -1, 30
Let x(p) = 11*p**2 + 577*p - 3090. Let l(r) = -72*r**2 - 3750*r + 20090. Let d(c) = -14*l(c) - 92*x(c). Determine q so that d(q) = 0.
-151, 5
Let s = -631/14 + 333/7. Suppose -21*z + 173 - 47 = 0. Factor 9/2*v**4 - 2 + 6*v - z*v**3 - s*v**2.
(v - 1)*(v + 1)*(3*v - 2)**2/2
Factor -1858*q**3 + 39855*q**2 + 93787436965 + 1853*q**3 + 22072519*q - 127967254*q.
-5*(q - 2657)**3
Let c = -1559/52 - -406/13. Let 0 - c*u + 1/4*u**2 = 0. Calculate u.
0, 5
Suppose 6 = 9*u - 12. Let n(k) = 3*k**2 - 6*k + 2. Let l be n(u). Determine g so that 14 + 4*g**3 - 54*g + 9*g**l + 40 + 9*g**2 - 6*g**3 = 0.
3
Factor -248*i**2 + 484*i - 19912 + i**3 + 3*i**3 + 19672.
4*(i - 60)*(i - 1)**2
Let j be (-18 - (17 - 34))*0. Let w(z) be the second derivative of 0 - 1/45*z**3 - 1/90*z**4 + 29*z + j*z**2. Suppose w(g) = 0. Calculate g.
-1, 0
Let g(w) = -2*w**3 - 13*w**2 + 25*w + 12. Let c be g(-8). Factor 38*v**4 - 2*v**3 - 85*v**c + 45*v**4 - 8*v**2 - 8*v**3.
-2*v**2*(v + 1)*(v + 4)
Solve 33/5*l**3 + 11/5*l**4 - 14/5*l**5 + 0 - 4/5*l + 4/5*l**2 = 0.
-1, -1/2, 0, 2/7, 2
Let u(g) be the second derivative of -5*g - 1/6*g**4 - g**2 - 2/3*g**3 + 0. Determine c so that u(c) = 0.
-1
Let q(r) be the first derivative of 1/6*r**4 - 12*r**2 + 2/3*r**3 + 0*r + 9 + 1/60*r**5. Let d(h) be the second derivative of q(h). Factor d(k).
(k + 2)**2
Let u(x) be the first derivative of 2*x**5/85 + 226*x**4/17 - 2*x**3/51 - 452*x**2/17 + 2550. Solve u(o) = 0.
-452, -1, 0, 1
Suppose 0 = -4*j + 7 - 103. Let d(o) = -o**3 + 27*o**2 + 86*o + 48. Let x(a) = -4*a**3 + 136*a**2 + 428*a + 240. Let n(m) = j*d(m) + 5*x(m). Factor n(l).
4*(l + 1)*(l + 3)*(l + 4)
Let w(q) be the first derivative of q**4/2 + q + 111. Let a(i) = 24*i**4 + 88*i**3 + 104*i**2 + 28*i - 10. Let d(v) = -a(v) - 2*w(v). Solve d(c) = 0.
-2, -1, 1/6
Let a(t) be the first derivative of -t**5/5 - 5*t**4 - 28*t**3/3 + 242*t + 31. Let i(z) be the first derivative of a(z). Factor i(k).
-4*k*(k + 1)*(k + 14)
Let f be (3 - -1)/(3/21). What is z in 57*z + 40*z - 92*z**3 + 50*z**5 - 55*z + 18 - f*z**2 + 10*z**4 = 0?
-1, -3/5, 1
Let m(p) be the third derivative of p**7/1008 + p**6/80 - p**5/12 - 7*p**4/36 - 115*p**3/6 - 7*p**2 - p. Let u(g) be the first derivative of m(g). Factor u(x).
(x - 2)*(x + 7)*(5*x + 2)/6
Determine d, given that -5*d - 3*d**2 + 528 - 68*d - 78*d - 75*d - 32*d = 0.
-88, 2
Suppose 8256 = 3689*d - 6500. Solve 24/7*l**2 - 4/7*l**d + 0 - 4/7*l**3 + 0*l = 0.
-3, 0, 2
Let k = 7796 + -54564/7. Factor 0 + 2/7*y**5 - 6/7*y**3 - 4/7*y**4 + 8/7*y**2 + k*y.
2*y*(y - 2)**2*(y + 1)**2/7
Let p be 6*(230/(-20) + 10) - -9. Let k(b) be the second derivative of -42*b + p + 5/114*b**4 - 2/57*b**3 - 3/19*b**2. Suppose k(m) = 0. Calculate m.
-3/5, 1
What is y in -247/4*y + 1/4*y**5 - 1/2*y**2 - 123/4 + 125/4*y**4 + 123/2*y**3 = 0?
-123, -1, 1
Suppose -1133815 - 6154*t - 4*t**2 + 555558 + 1138*t - 994259 = 0. What is t?
-627
Let m(q) be the first derivative of q**5/10 + 3*q**4 - q**3/6 - 6*q**2 + 967. Determine y, given that m(y) = 0.
-24, -1, 0, 1
Let u(z) be the first derivative of 11/4*z**4 + 9*z**2 + 7/6*z**6 + 23*z**3 + 0*z + 86 - 33/5*z**5. Factor u(k).
k*(k - 3)**2*(k + 1)*(7*k + 2)
Let g(z) be the first derivative of -12*z + 21/2*z**2 + 84 + 45/4*z**4 + 62*z**3. Suppose g(a) = 0. What is a?
-4, -1/3, 1/5
Let s = -22 + 24. Suppose -s*o - 8 + 80 = 0. Determine a, given that -4*a**2 - 128*a + 128 - 18*a**2 + o*a**3 - 2*a**2 = 0.
-2, 4/3
Let y(i) be the third derivative of i**7/840 + 7*i**6/120 - 3*i**5/8 + 89*i**4/24 + 15*i**2. Let c(p) be the second derivative of y(p). Factor c(g).
3*(g - 1)*(g + 15)
Let c(x) be the third derivative of 0*x + 2645/3*x**3 + 0 + 1/24*x**5 - 123*x**2 - 115/12*x**4. Factor c(u).
5*(u - 46)**2/2
Let l(r) = r**3 + 117*r**2 - 1139*r - 627. Let b be l(-126). Let 4*m**2 - 1/3*m**b - 15*m + 50/3 = 0. Calculate m.
2, 5
Let r(t) = -2*t - 2. Let y(h) = -23*h + 4. Let l(d) = -6*r(d) - 2*y(d). Let p(m) = m**2 + 290*m + 22. Let x(j) = -22*l(j) + 4*p(j). Factor x(z).
4*z*(z - 29)
Let s = -2689 + 2693. Let o(z) be the first derivative of 10 + 0*z**2 - 1/6*z**3 + 0*z - 1/8*z**s. Determine q so that o(q) = 0.
-1, 0
Let w(y) be the third derivative of -1/3*y**3 + 0*y + 1/360*y**6 - 13/72*y**4 - 7/180*y**5 + 0 + 1/630*y**7 + 2*y**2. Suppose w(z) = 0. What is z?
-2, -1, 3
Suppose -10*q + 5*q + 22*q = -41*q. Let h(j) be the second derivative of 1/3*j**6 + q*j**3 - 1/6*j**4 + 0 - 2*j - 2/5*j**5 + 0*j**2. Factor h(d).
2*d**2*(d - 1)*(5*d + 1)
Factor 6142*r**2 - 388/3*r**3 + 38024/3*r + 2/3*r**4 + 19208/3.
2*(r - 98)**2*(r + 1)**2/3
Solve 289/6*d + 2/3*d**5 + 0 + 143/2*d**3 + 38/3*d**4 + 323/3*d**2 = 0.
-17/2, -1, 0
Let i(x) be the second derivative of -x**5/20 + 11*x**4/12 - 6*x**3 + 18*x**2 + 682*x. Factor i(p).
-(p - 6)*(p - 3)*(p - 2)
Let a(c) = c**2 + 31*c - 77. Let k be a(-34). Let n = k + -23. Factor 6*b + 4/3 + 8/3*b**n.
2*(b + 2)*(4*b + 1)/3
Factor 1039771202 + 1208*o**3 + 173662*o**2 + 99950*o**2 - 325*o**4 + 27543608*o + 327*o**4.
2*(o + 151)**4
Factor 0 - 19/4*u**2 - 11/2*u**3 - 1/4*u**4 + 21/2*u.
-u*(u - 1)*(u + 2)*(u + 21)/4
Let y(a) be the first derivative of 29*a**6/4 + 39*a**5/5 - 9*a**4/8 + 965. Factor y(r).
3*r**3*(r + 1)*(29*r - 3)/2
Let o = 97209 - 97204. Let -16/13 + 22/13*w**3 + 4/13*w**2 - 24/13*w + 12/13*w**4 + 2/13*w**o = 0. What is w?
-2, -1, 1
Suppose 22298 = -26*y - 2038. Let f = y - -939. Determine w so that 1/2*w**5 - 1/2 + w**2 + 1/2*w - w**f - 1/2*w**4 = 0.
-1, 1
Let d be 2 - ((-78)/45 + 2). Let y = 4096487/15 - 273099. Solve -y*x**2 - 8/5 + d*x = 0 for x.
1, 12
Suppose -2*z = 2*t - 42, t - 3*z + 152 = 97. Factor 106/5*k**t - 2/5*k**3 - 106/5 + 2/5*k.
-2*(k - 53)*(k - 1)*(k + 1)/5
Suppose 4*o = -o + 3*t + 91, 5*o = -5*t + 75. Let c = 29 - o. Factor 12*d**2 - 3*d**5 + c*d**4 - 2*d - 27*d**3 + 9*d**3 - d.
-3*d*(d - 1)**4
Let n be 724*-5*(-2)/5. Factor 78*k**2 + 131 + 2815 + 2*k**3 + n + 1014*k.
2*(k + 13)**3
Let q(t) be the first derivative of -147*t**4/20 - 1603*t**3/15 + 81*t**2/5 + 88*t/5 - 1398. Solve q(z) = 0 for z.
-11, -4/21, 2/7
Let l(d) = 15 + 6*d - 2*d - 5. Let w be l(-2). Factor 0*v**2 - 9*v + 2*v**w + 98 - 11*v - 8*v.
2*(v - 7)**2
Determine b, given that -53*b - 7*b + b**5 - 37*b**3 + 13*b**4 + 1035230*b**2 - 1035339*b**2 = 0.
-15, -1, 0, 4
Suppose 5