et b = -105054 - -105056. Determine a so that 2/3*a**5 - 2*a + 4/3*a**2 + 4/3*a**3 + 2/3 - b*a**4 = 0.
-1, 1
Determine l, given that -15*l**2 + 17120 - 17120 + 115*l = 0.
0, 23/3
Let v be 200/(-450) - (2 + (-2863)/63). Let m(z) be the first derivative of -1/4*z**4 - 19/2*z**2 + 9*z + 11/3*z**3 - v. Factor m(u).
-(u - 9)*(u - 1)**2
Suppose 4299 = 2124*z - 8003 + 3806. Factor -3/2 + 31/4*a - 9/4*a**3 - z*a**2.
-(a - 1)*(a + 3)*(9*a - 2)/4
Let v = 807088 + -3228349/4. Let f = 22/35 + 1067/140. Suppose f*b + 0 - v*b**2 = 0. Calculate b.
0, 11
Let c = 125349 + -125347. Let -4/5*v**4 - 2*v**3 + 42/5*v**2 + c - 38/5*v = 0. Calculate v.
-5, 1/2, 1
Suppose 9 = -3*r + 18. Suppose 19 = m - l - 2*l, -4*m - r*l = -1. Factor o - o**5 - 6*o + 5*o - o**m.
-o**4*(o + 1)
Let r = -73 + 75. Factor -6*u**r + 2*u**4 + 1 + 22*u - 3 - 6*u**3 - 10.
2*(u - 3)*(u - 1)**2*(u + 2)
Let m(h) be the third derivative of -h**7/315 + 11*h**6/60 + 8*h**5/5 + 37*h**4/9 - 6*h**2 - 2*h + 195. Suppose m(g) = 0. Calculate g.
-2, 0, 37
Determine n, given that 18/5*n - 52/5*n**2 + 468/5 - 2/5*n**3 = 0.
-26, -3, 3
Solve -328*f + 448 - 19/2*f**3 - 441/4*f**2 - 1/4*f**4 = 0.
-16, -7, 1
Let j be ((-6)/(-12))/((-3)/(-9)). Let t = 28939 + -28935. Factor -1/4*z**t - 1/4 - j*z**2 - z - z**3.
-(z + 1)**4/4
Suppose b + b - 6*b = b. Let k(r) be the first derivative of -5 + b*r - 2/15*r**3 - 2/5*r**2. Suppose k(c) = 0. What is c?
-2, 0
Let j(u) be the third derivative of u**8/26880 - 19*u**7/3360 + 361*u**6/960 + u**5/5 + 86*u**2 - 2*u. Let v(r) be the third derivative of j(r). Factor v(n).
3*(n - 19)**2/4
Let j(q) be the third derivative of 1/280*q**6 + 0*q**4 + 0 + 1/784*q**8 + 0*q**5 + 46*q**2 + 0*q**3 + 0*q - 1/245*q**7. What is n in j(n) = 0?
0, 1
Suppose -2*j - 8 = 5*r + 2, -5*r = 4*j. Let b(n) = 13*n**2 + 96*n. Let l(i) = 19*i**2 + 144*i. Let a(x) = j*l(x) - 7*b(x). Factor a(t).
4*t*(t + 12)
Let k = 832 - 814. Let w be 3/(-12)*(-24)/k. Find x, given that -1/3*x**2 + 0*x - 1/3*x**3 + w*x**5 + 1/3*x**4 + 0 = 0.
-1, 0, 1
Find n, given that -1046/5*n + 86/5*n**3 - 2/5*n**4 - 164 - 138/5*n**2 = 0.
-2, -1, 5, 41
Let b = -448 - -495. Suppose -9*v**3 + 84*v**5 + 7*v**4 - 25*v**4 + 46*v**4 + 6*v**4 - 6*v**2 + b*v**4 = 0. What is v?
-1, -1/4, 0, 2/7
Determine a, given that -41/3*a + 1/3*a**5 + 40/3*a**3 - 30*a**2 + 22 + 8*a**4 = 0.
-22, -3, -1, 1
Let r(j) = 55*j**3 - 168*j**2 + 5*j. Let t(h) = -h**4 - 55*h**3 + 181*h**2 - 5*h. Let i(d) = 10*r(d) + 9*t(d). Let i(b) = 0. Calculate b.
0, 1/9, 1, 5
Let v(d) = -34*d - 1190. Let i be v(-35). Let m(y) be the second derivative of -1/18*y**4 + 1/15*y**5 - 2/9*y**3 + 1/2*y**2 - 27*y - 1/90*y**6 + i. Factor m(s).
-(s - 3)*(s - 1)**2*(s + 1)/3
Let x(f) be the third derivative of -f**6/140 - 59*f**5/70 - 3019*f**2. Let x(q) = 0. Calculate q.
-59, 0
Let q be (3/(-16))/(17/(-68))*(39984/288)/49. Factor 1/8*a**4 + 18 - q*a**3 - 57/2*a + 25/2*a**2.
(a - 6)**2*(a - 4)*(a - 1)/8
Let p be 5 - 1 - (17 + 473/(-22) - -7). What is q in -6*q + 0 - p*q**2 = 0?
-4, 0
Let r(s) be the first derivative of -s**5 - 159 + 5/4*s**4 + 0*s + 15/2*s**2 + 25/3*s**3. Factor r(v).
-5*v*(v - 3)*(v + 1)**2
Factor 2/7*k**2 + 366/7*k + 0.
2*k*(k + 183)/7
Let l(b) = 3*b**4 + b**3 + b**2 - b. Let h(t) = 14*t**4 - 15*t**3 + 12*t**2 + 17*t. Let p(a) = 5*h(a) - 35*l(a). Factor p(o).
-5*o*(o - 1)*(o + 3)*(7*o + 8)
Determine s so that -19/3*s - 68/3 - 1/6*s**2 = 0.
-34, -4
Let d(m) be the first derivative of -m**4/20 + 137*m**3/15 - 524*m**2/5 + 2064*m/5 + 1013. Factor d(l).
-(l - 129)*(l - 4)**2/5
Let r(l) = 75*l + 2970. Let x be r(-39). Let c(p) be the first derivative of -7 - 5/3*p**3 - x*p**2 - 405*p. Determine o, given that c(o) = 0.
-9
Suppose -27*c + 7*c + 720 = 0. Find h, given that -16*h + 0*h**2 - 2*h**2 + 20*h - c*h = 0.
-16, 0
Let b(h) be the first derivative of h**6/69 - 226*h**5/115 + 1508*h**4/23 + 20176*h**3/69 + 464*h**2/23 - 26912*h/23 + 282. Suppose b(f) = 0. Calculate f.
-2, 1, 58
Let n(z) be the third derivative of z**6/60 - 121*z**5/30 - 31*z**4/3 + 244*z**3/3 + 3400*z**2. Determine c so that n(c) = 0.
-2, 1, 122
What is b in 0 + 13/2*b**4 + 1/6*b**5 - 19/3*b - 13/2*b**2 + 37/6*b**3 = 0?
-38, -1, 0, 1
Let t(w) be the third derivative of 0*w - 35*w**4 - 25/12*w**5 - 1/24*w**6 - 4 - 120*w**3 - 22*w**2. Find a, given that t(a) = 0.
-12, -1
Suppose -7*k = -2*k + 4*a - 12, 5*k + 2*a - 16 = 0. Suppose -5*z = 3*o - 12, 0 = 2*z - 4*z + k*o - 16. Factor 2/15*l**3 + z + 4/15*l**2 + 2/15*l.
2*l*(l + 1)**2/15
Let i(j) be the first derivative of -54*j**2 - 29 - 2/3*j**3 - 1458*j. Factor i(n).
-2*(n + 27)**2
Suppose 8*j - 4*j - 123 = -5*n, 0 = 5*n - 5*j - 150. Let d be (n/42)/(-3)*(-8 - -2). Factor 3/7*r**3 + 0 + 0*r + 12/7*r**4 + d*r**5 + 0*r**2.
3*r**3*(r + 1)*(3*r + 1)/7
Let v(q) be the first derivative of 5*q**4 + 4*q**5 - 464 + 616 - 3*q**5. Let v(n) = 0. Calculate n.
-4, 0
Let d(m) be the first derivative of -m**4/42 + 74*m**3/63 - 141*m**2/7 + 1026*m/7 - 377. Factor d(s).
-2*(s - 19)*(s - 9)**2/21
Suppose -a + 0*a - 3*d - 6 = 0, 3*a - 2*d - 15 = 0. Factor 0*q**3 + 0*q**3 - 21*q**2 - 3*q**a + 48 - 24*q.
-3*(q - 1)*(q + 4)**2
Let g(u) = u**2 + 10*u - 117. Let w be g(7). Solve 4*l**2 - 6*l**4 + w*l**2 + l**4 - 21*l**2 + 20*l**3 = 0.
0, 1, 3
Let y = 3301 - 3301. Let v(q) be the third derivative of 1/270*q**5 + 13*q**2 + y*q - 1/54*q**4 + 0*q**3 + 0. Factor v(x).
2*x*(x - 2)/9
Factor 1/2*y**5 - 17/2*y**2 + 0*y + 0 - 15/2*y**4 - 33/2*y**3.
y**2*(y - 17)*(y + 1)**2/2
Let o(k) = -k**4 - k**3 - k**2. Let t(d) = 9*d**4 + 5*d**3 + 5*d**2 + 2*d. Let y(j) = 14*o(j) + 2*t(j). Let y(a) = 0. What is a?
-1, 0, 1
Let i = 29519/177186 + 2/29531. Let d(o) be the first derivative of -4*o**2 + 5/4*o**4 + 4*o + 19 - i*o**6 - 1/5*o**5 + 1/3*o**3. Let d(g) = 0. Calculate g.
-2, 1
Let v(o) be the third derivative of -o**5/60 + 11*o**4/12 - 7*o**3/2 - 6*o**2 + 49*o. Determine m, given that v(m) = 0.
1, 21
Suppose 5*f + 2*d = 19, -2*f + 16 = -0*f - 2*d. Find r, given that 126*r**3 + 14*r**3 + 5*r**f + 80*r**4 + 348*r**3 - 68*r**3 + 720*r**2 = 0.
-6, -4, 0
Let c(b) be the first derivative of 0*b - 77 + 1/15*b**5 + 0*b**3 - 1/4*b**4 + 0*b**2. What is r in c(r) = 0?
0, 3
Find a, given that 93*a - 16*a + 0*a**2 + 4608 + a + 2*a**2 + 114*a = 0.
-48
Suppose 2*v = -q + 6*v - 3, 0 = 3*q - 3*v + 18. Let u be ((-51)/(-6) + q)/((-6)/(-8)). Factor -6*t**4 + 10*t**4 - 9*t**2 + 3*t**5 - 3*t**3 + 3*t**u + 2*t**4.
3*t**2*(t - 1)*(t + 1)*(t + 2)
Let w(m) be the second derivative of m**6/60 + 7*m**5/40 - m**4/8 - 21*m**3/4 - 27*m**2/2 - 3201*m. What is k in w(k) = 0?
-6, -3, -1, 3
Let p(j) be the first derivative of -8*j**3/3 - 11*j**2/2 + 35*j + 70. Let k(h) = -6*h**2 - 12*h + 34. Let a(q) = 5*k(q) - 4*p(q). Factor a(b).
2*(b - 5)*(b - 3)
Let a = 35 + -33. Suppose -3*y + a = b - 3*b, 0 = 4*b + 3*y - 14. Factor 24*x + 2*x - 220*x**3 - 10*x - 16*x**b + 400*x**4.
4*x*(4*x + 1)*(5*x - 2)**2
Let v(y) be the third derivative of y**5/570 - 5*y**4/57 + 996*y**2. Solve v(n) = 0 for n.
0, 20
Let r(y) be the first derivative of -363*y**3/7 - 132*y**2/7 - 16*y/7 + 1230. Factor r(j).
-(33*j + 4)**2/7
Let h(q) = 5*q**2 + 55*q - 295. Let t(m) = 1645 + 6*m**2 - 4*m**2 + 27*m - 1792. Let r(b) = 6*h(b) - 14*t(b). Factor r(w).
2*(w - 12)**2
Determine c, given that -c**2 - 287 + 98 + 276*c - 91 + 5*c**2 + 0*c**2 = 0.
-70, 1
Let t(s) be the first derivative of -s**3/3 + 7*s**2/2 - s - 14. Let b(h) = h**2 - 6*h + 1. Let w(p) = 5*b(p) + 4*t(p). Let w(g) = 0. Calculate g.
1
Solve -15*x + 53*x**2 - 243*x - 80*x - 2*x**3 - x**2 = 0.
0, 13
Let x(z) be the first derivative of -z**4/14 + 30*z**3/7 + 94*z**2/7 + 9068. Factor x(c).
-2*c*(c - 47)*(c + 2)/7
Let q be -10*((-15)/(-25) - 36/45). Factor 2/3*s + 0 + 1/3*s**3 + s**q.
s*(s + 1)*(s + 2)/3
Suppose -3707 = 15*v - 43*v - 3623. Let q(k) be the first derivative of -2/5*k**2 + 1/5*k**v - 4/5*k + 1/5*k**4 + 1/25*k**5 - 26. Determine d so that q(d) = 0.
-2, -1, 1
Let p(s) be the second derivative of s**5/100 + 8*s**4/3 + 640*s**3/3 - s - 29. Solve p(h) = 0.
-80, 0
Let x(d) be the first derivative of -2/3*d**3 - 10658*d + 146*d**2 + 139. Factor x(a).
-2*(a - 73)**2
Let x(h) be the third derivative of -h**6/8 + 5*h**4/12 - 4*h**2 + h. Let s(r) = r**4 + r**3 - 1. Let a(m) = 5*s(m) + x(m). Determine q, given t