. Let c = -69/44 + i. Solve 0 + c*u - 4/11*u**2 + 2/11*u**3 = 0.
0, 1
Let z = -58295/24 + 2429. Let r(k) be the third derivative of -1/4*k**5 + 0*k + 0 - 5/6*k**3 - 6*k**2 + z*k**6 + 5/8*k**4. Determine n, given that r(n) = 0.
1
Suppose -2*k + 8*k - 6 = 0. Suppose 5*b = -3*m - 14, -m + k + 5 = -b. Factor -3/4*d**m + 1 + 0*d + 1/4*d**3.
(d - 2)**2*(d + 1)/4
Suppose -3*o + 623 = -4*s, -2*o + 0*o = -4*s - 410. Let v = o - 211. Let 0 - 5/3*u**v + 0*u + 20/3*u**3 = 0. What is u?
0, 1/4
Suppose 2*k = p + 7, -k - 7 = -0*k + 3*p. Let w = -159 - -159. Find i, given that w + 6/5*i**k + 3/5*i**3 + 3/5*i = 0.
-1, 0
Let k(b) be the second derivative of 1/18*b**4 - 12*b - 1/3*b**2 + 0 + 0*b**3. What is s in k(s) = 0?
-1, 1
Let v(l) be the third derivative of -l**6/50 + l**5/20 + 167*l**4/40 - 21*l**3/5 - l**2 - 41*l. Let v(a) = 0. Calculate a.
-6, 1/4, 7
Let d(n) be the third derivative of 5*n**8/336 - n**7/35 - 49*n**6/120 + n**5/2 + 29*n**4/6 - 4*n**3 - 2*n**2 - 133. Suppose d(v) = 0. Calculate v.
-2, 1/5, 2, 3
Suppose 0 = 6*z + z. Let d(c) be the third derivative of 0*c + z - 1/30*c**5 + 1/3*c**3 + 1/12*c**4 - 1/60*c**6 - 6*c**2. Find h such that d(h) = 0.
-1, 1
Let j(u) = u**3 + 2*u**2 - 41*u + 38. Let k(a) = 15*a**3 + 33*a**2 - 657*a + 609. Let x(g) = -33*j(g) + 2*k(g). Factor x(o).
-3*(o - 3)*(o - 1)*(o + 4)
Let y = 52 + -50. Solve -y*h + 803*h**2 + 1 - 802*h**2 + 0 = 0.
1
Let c be (-2716)/(-1067)*(19/(-6) - -3 - -2). Find f such that 20/3 + c*f + 2/3*f**2 = 0.
-5, -2
Let t(m) be the second derivative of m**6/40 - 3*m**5/16 - 33*m**4/16 + 77*m**3/8 - 15*m**2 + 346*m. Factor t(q).
3*(q - 8)*(q - 1)**2*(q + 5)/4
Let f(h) be the second derivative of 9*h - 5/2*h**2 - 16/3*h**3 + 0 - 1/30*h**5 + 2/3*h**4. Let y(g) be the first derivative of f(g). Factor y(d).
-2*(d - 4)**2
Let c(g) = g**2 + 13*g + 16. Let o(s) = -2*s**2 - 14*s - 17. Let l(q) = -5*c(q) - 4*o(q). Factor l(m).
3*(m - 4)*(m + 1)
Determine j, given that -12/7*j**3 + 15/7*j**4 - 33/7*j**2 - 6/7*j + 0 = 0.
-1, -1/5, 0, 2
Let l(u) be the second derivative of -u**6/30 + 11*u**5/20 - 5*u**4/12 - 47*u**3/6 - 15*u**2 - 139*u + 1. Solve l(b) = 0 for b.
-1, 3, 10
Suppose 14*b + 23 = 65. Factor -4*c - 4*c**4 + b*c**2 - 4*c**4 + 3*c**2 + 6*c**4.
-2*c*(c - 1)**2*(c + 2)
Let z(j) be the first derivative of 5*j**4/48 - 25*j**3/24 - 15*j**2/4 + 24*j - 30. Let i(h) be the first derivative of z(h). Solve i(m) = 0 for m.
-1, 6
Factor 4/5*t + 0 - 2/5*t**4 + 0*t**3 + 6/5*t**2.
-2*t*(t - 2)*(t + 1)**2/5
Suppose 5/6*j**2 + 6 - 49/6*j = 0. What is j?
4/5, 9
Solve 3*u**5 + 7*u**5 + 5*u**5 + 16*u + 23*u**4 - 104*u**3 + 13*u**4 + u**5 + 36*u**2 = 0.
-4, -1/4, 0, 1
Suppose -5*b + 1 + 9 = 0. Factor -2*l**b - l**2 + 12*l**2 + 9*l + 3*l**3 + 3*l**2.
3*l*(l + 1)*(l + 3)
Let l(d) be the second derivative of d**6/150 - 3*d**5/100 - d**4/60 + d**3/10 + 85*d. Solve l(y) = 0.
-1, 0, 1, 3
Let v(z) = -2*z**2 - 20*z - 46. Let b be v(-6). Suppose -14*o + b*o + 24 = 0. Suppose 0 + 0*r + 1/4*r**o = 0. Calculate r.
0
Let b(p) be the third derivative of p**7/560 - p**5/80 - 13*p**3/6 - 3*p**2. Let h(i) be the first derivative of b(i). Factor h(x).
3*x*(x - 1)*(x + 1)/2
Let m(k) be the first derivative of k**5/90 - k**4/12 + 2*k**3/9 + 5*k**2 + 10. Let f(s) be the second derivative of m(s). Find x, given that f(x) = 0.
1, 2
Let w be (9/(-6))/(1*3/12). Let o be (w/(-10) - (-8)/20) + 3. Let -27/4*a**2 - 3*a**o - 33/4*a**3 - 3/4*a + 3/4 = 0. Calculate a.
-1, 1/4
Let c(y) be the second derivative of y**4/42 + y**3/3 + 10*y**2/7 + 139*y. Factor c(j).
2*(j + 2)*(j + 5)/7
Suppose -30*b + 11 = -49. Solve 1/4*k**b - 1/4*k**3 + 0 + 1/2*k = 0.
-1, 0, 2
Let q = -833/6 + 418/3. Let o(f) be the first derivative of -q*f**4 + 2/3*f**3 + 0*f - 5 + 2*f**2. Let o(u) = 0. What is u?
-1, 0, 2
Let m(v) be the second derivative of v**5/40 + 7*v**4/3 - 115*v**3/12 + 29*v**2/2 + 243*v. Let m(p) = 0. What is p?
-58, 1
Let d(h) = 6*h**3 + 65*h**2 + 733*h - 789. Let m(n) = 5*n**3 + 63*n**2 + 732*n - 788. Let w(j) = 4*d(j) - 5*m(j). Solve w(v) = 0 for v.
-28, 1
Let m be 2 - (-3 + (8/4 - 0)). Find c, given that -10*c**4 - 14*c**2 + 12*c**4 + 2*c + 2*c + 4*c + 4*c**m = 0.
-4, 0, 1
Let c = -8856 + 35445/4. Determine o so that 39/4*o - c*o**2 + 3/2 = 0.
-1/7, 2
Let z(w) = 3*w**4 - 2*w**3 - 3*w**2 - 2*w. Let x(u) = u**4 - u**2 - u. Let r(i) = 4*x(i) - z(i). Factor r(t).
t*(t - 1)*(t + 1)*(t + 2)
Suppose -10 = -0*y - 2*y. Suppose -y = -x + 34. Solve -18 + x - 21 + 2*z**2 - 2*z = 0.
0, 1
Factor 2/3*h**2 - 2/3*h**3 + 0 + 0*h.
-2*h**2*(h - 1)/3
Suppose 0 = -7*t + 15 - 1. Factor -6*y - 21*y**5 - 26*y**2 + 5*y**2 - 18*y**t - 81*y**3 - 67*y**4 - 2*y**4.
-3*y*(y + 1)**3*(7*y + 2)
Let w(s) = -s**2 - 4*s - 15. Let x(g) = 2*g**2 + 10*g + 30. Let l(t) = -13*w(t) - 6*x(t). Factor l(b).
(b - 5)*(b - 3)
Let c = 383/21 - 123/7. Find l, given that -1/6*l**2 - c - 2/3*l = 0.
-2
Let h(f) be the third derivative of -f**5/210 + 19*f**4/84 + 2*f**3 + 326*f**2. Factor h(a).
-2*(a - 21)*(a + 2)/7
Suppose 10*j - 7*j + 14 = 4*c, -3*j = -c + 8. Let v(t) be the first derivative of -c - 1/2*t + 5/4*t**2 + t**3. Factor v(q).
(q + 1)*(6*q - 1)/2
Let r(x) be the first derivative of 2*x**5 - 10/3*x**3 - 5/6*x**6 + 21 + 0*x**2 + 5/4*x**4 + 0*x. Suppose r(m) = 0. Calculate m.
-1, 0, 1, 2
Determine b, given that -80*b + 70*b**2 + 2*b**4 + 441 - 32*b**3 - 415 + 14*b**2 = 0.
1, 13
Let y(a) be the third derivative of 24*a**2 + 0 - 2/165*a**5 + 5/44*a**4 + 0*a + 4/33*a**3. Factor y(b).
-2*(b - 4)*(4*b + 1)/11
Suppose -q = -2 - 2. Factor 11*i**4 - 21*i**q + 20*i - 20*i**2 + 0*i**2 + 15*i**4 - 5*i**3.
5*i*(i - 2)*(i - 1)*(i + 2)
Let w(f) be the first derivative of 24*f**2 + 9/4*f**4 + 12*f + 9 + 13*f**3. What is t in w(t) = 0?
-2, -1/3
What is w in 0*w**3 - 21*w**2 - 240*w + 6*w**3 + 144*w + 3*w**4 + 108*w = 0?
-4, 0, 1
Let b(o) be the second derivative of o**6/240 + o**5/16 + o**4/4 - 5*o**3/3 - 10*o. Let v(g) be the second derivative of b(g). Let v(s) = 0. What is s?
-4, -1
Let a(t) be the first derivative of -t**7/4200 - 32*t**3/3 - 40. Let o(x) be the third derivative of a(x). What is g in o(g) = 0?
0
Suppose 5*a = 15, 0 = -3*n + 3*a + 17 - 2. Let s = n - 6. Factor -173 - s*y**3 + 173 - 3*y**4.
-y**3*(3*y + 2)
Let a(h) = h**2 + 3*h - 1. Let u(b) = 2*b + b + b. Let v = 170 - 166. Let r(s) = v*a(s) - 3*u(s). Factor r(g).
4*(g - 1)*(g + 1)
Factor 0*a + 6/13*a**3 - 2/13*a**4 + 0*a**2 + 0.
-2*a**3*(a - 3)/13
Let v = -7 + 7. Suppose v = -5*n + 8 + 7. Determine i so that -240*i**5 + 8*i - 8*i**n - 8 + 8 - 30*i**2 - 284*i**4 + 74*i**2 = 0.
-1, -1/3, -1/4, 0, 2/5
Let w(d) = -6*d**2 - 731*d - 15. Let n(b) = 4*b**2 + 732*b + 12. Let p(t) = -5*n(t) - 4*w(t). Factor p(i).
4*i*(i - 184)
Determine b, given that 9/5*b**3 + 0*b + 0*b**2 + 0 - 6/5*b**4 + 1/5*b**5 = 0.
0, 3
Suppose -v = -4, 0 = 3*s - 5*v - 51 - 13. Suppose -6*a + s = a. Factor 5/3*c**a + 3*c**2 + 0 - 2/3*c - 4*c**3.
c*(c - 1)**2*(5*c - 2)/3
Suppose 30*r + 84 = 204. Let v(k) be the second derivative of 0*k**2 + 1/20*k**5 + 10*k + 1/30*k**6 + 0*k**3 - 1/42*k**7 + 0 - 1/12*k**r. Factor v(h).
-h**2*(h - 1)**2*(h + 1)
Factor -89*b + 26*b - 5*b**5 + 1 + 2*b**5 - 27*b**4 - 102*b**2 - 78*b**3 - 16.
-3*(b + 1)**4*(b + 5)
Let z(i) be the third derivative of i**5/60 - 29*i**4/24 + 14*i**3/3 - 6*i**2 - 4*i. Find t, given that z(t) = 0.
1, 28
Let x(o) be the third derivative of -o**5/140 - 19*o**4/56 + o**2 + 117*o. Factor x(q).
-3*q*(q + 19)/7
Let l(t) be the second derivative of -t**4/60 - 3*t**3/10 + 76*t. Determine h so that l(h) = 0.
-9, 0
Factor -9*n**2 + 8*n**2 - 120*n - 9*n**2 + 15*n**2 - 125.
5*(n - 25)*(n + 1)
Let i(s) = -8*s - 6. Let p be i(2). Let q(d) = d**2 + d. Let g(l) = 10*l**2 + 12*l. Let b(t) = p*q(t) + 2*g(t). Determine y so that b(y) = 0.
0, 1
Determine m so that 9/2*m**2 + 3/2*m**3 + 0 + 0*m = 0.
-3, 0
Let g(p) = -4*p**3 + 4*p**2 - 2*p + 381 + 6*p - 385. Let h(m) = 3*m**3 - 3*m**2 - 3*m + 3. Let d(r) = 6*g(r) + 7*h(r). Find b, given that d(b) = 0.
-1, 1
What is o in -36963/2*o - 1367631/2 - 1/2*o**3 - 333/2*o**2 = 0?
-111
Let z = 17 + -14. Let f(o) be the first derivative of 2*o**z + 1 - 3*o**3 - 1 + 3. Suppose f(u) = 0. What is u?
0
Let q(j) be the first derivative of j**8/3360 - j**7/560 + j**6/720 + j**5/80 - j**4/24 - 10*j**3 + 14. Let m(h) be