*(u - 2)**3/11
Suppose -4*d + 5*r + 62 = -8*d, -144 = 3*r - 102. Suppose 28/5 - 18/5*q + 2/5*q**d = 0. Calculate q.
2, 7
Let g(n) be the first derivative of -n**6/30 - 6*n**5/5 - 65*n**4/4 - 100*n**3 - 250*n**2 + 303. Determine j, given that g(j) = 0.
-10, -5, 0
Let l be (56/(-16)*-12)/(3 - 1). Let f be l*(-128)/216*-3. Factor 28/3*c**3 - 64*c**2 + 49/3*c**4 - f*c - 16/3.
(c - 2)*(c + 2)*(7*c + 2)**2/3
Let a = -114862/7 + 16414. Let 4/7 - 40/7*i**2 - a*i = 0. Calculate i.
-1, 1/10
Let j(t) be the first derivative of 0*t - 1/25*t**5 + 0*t**2 + 7/15*t**3 - 3/10*t**4 + 41. Factor j(w).
-w**2*(w - 1)*(w + 7)/5
Let t(c) be the first derivative of c**4/5 + 40*c**3/3 + 186*c**2/5 - 576*c/5 - 4745. Factor t(h).
4*(h - 1)*(h + 3)*(h + 48)/5
Let k = 5705/8562 + 1/2854. Let w(v) be the first derivative of -20/27*v**3 - 1/3*v**2 - k*v**4 - 4/15*v**5 + 0*v + 16 - 1/27*v**6. Factor w(z).
-2*z*(z + 1)**3*(z + 3)/9
Let c(p) = p**3 - 17*p**2 - 20*p + 38. Let a be c(18). Let -24*h**4 + 33*h**2 - 5*h**5 - 11*h**4 + 5*h**3 + 40*h**2 - 38*h**a = 0. What is h?
-7, -1, 0, 1
Let f(a) be the second derivative of a**5/10 - 13*a**4/6 + 22*a**3/3 + 7*a + 50. Let f(h) = 0. What is h?
0, 2, 11
Find p, given that 1/2*p**4 + 5832 + 24*p**3 + 396*p**2 + 2592*p = 0.
-18, -6
Solve 0 + 62/3*t - 1/3*t**3 - 29/3*t**2 = 0 for t.
-31, 0, 2
Let r(o) be the first derivative of -216 + 0*o - 5/12*o**6 + 1/2*o**5 - 15/2*o**3 + 0*o**2 + 45/8*o**4. Solve r(d) = 0 for d.
-3, 0, 1, 3
Let t(a) be the first derivative of 1/4*a**3 + 0*a**2 - 3/4*a - 54. Suppose t(u) = 0. What is u?
-1, 1
Let g(b) = 5*b**2 - 390*b + 8790. Let f(i) be the first derivative of -i**2/2 + i - 154. Let u(z) = -30*f(z) - g(z). Factor u(m).
-5*(m - 42)**2
Let -109*w**2 + 26*w + 84 + 58*w**2 + 15*w**4 + 3*w**5 + 70*w - 51*w**3 + 0*w**5 = 0. What is w?
-7, -1, 2
Let a(n) be the first derivative of -2*n**5/5 - 173*n**4/2 - 5158*n**3 - 22015*n**2 - 28900*n + 1750. Factor a(x).
-2*(x + 1)*(x + 2)*(x + 85)**2
Let k(j) be the second derivative of -1/10*j**6 + 0 + 13/4*j**4 + 9/4*j**5 + 0*j**2 + j**3 - 5/14*j**7 + 40*j. Let k(h) = 0. What is h?
-1, -1/5, 0, 2
Let a(f) be the second derivative of -2*f + f**2 - 1/10*f**6 + 1/84*f**7 + 1/12*f**4 + 1/5*f**5 - 20 - 3/4*f**3. Factor a(z).
(z - 4)*(z - 1)**3*(z + 1)/2
What is b in 66/5*b**2 + 3/5*b**3 + 216 + 468/5*b = 0?
-10, -6
Let g(d) = -6*d + 22. Let x be g(3). What is s in 13 + 41*s - x*s**2 - 9*s - 4*s**3 + 31 + 4 = 0?
-2, 3
Let n(w) be the third derivative of -98*w**2 + 1/40*w**6 + 0 + 0*w + 3/2*w**3 - 5/8*w**4 + 1/20*w**5. Determine d, given that n(d) = 0.
-3, 1
Let r(d) be the third derivative of -13*d**6/300 - 172*d**5/75 - 2353*d**4/60 - 338*d**3/5 - 698*d**2. Determine c so that r(c) = 0.
-13, -6/13
Let n be 146/(-5)*(-8670)/(-714). Let k = 358 + n. Factor 4/7*t**3 - 32/7 - k*t**2 - 60/7*t.
4*(t - 8)*(t + 1)**2/7
Let b(c) = c**2 - 28*c - 80. Let u be b(31). Suppose -18*l**3 - 41*l - u*l + 36*l - 16*l**2 - 3*l**4 - 17*l**2 = 0. What is l?
-3, -2, -1, 0
Let z(c) be the second derivative of c**7/14 - c**6/5 - 3*c**5/20 + c**4/2 - 71*c. Factor z(k).
3*k**2*(k - 2)*(k - 1)*(k + 1)
Suppose -56*j + 719 + 793 = 0. Suppose 0 = 28*m + j - 83. Factor -2/13*b**m + 0 - 2/13*b.
-2*b*(b + 1)/13
Let o = 139 + -135. Factor -26*n**2 - 2166*n + 8*n**3 + 2*n**3 + 2180*n + 2*n**o.
2*n*(n - 1)**2*(n + 7)
Suppose -36 + 291 = 51*y. Suppose 4*w - 15 - 9 = -y*b, -3*w = -2*b + 5. Let -1/5*l**b + 0 + 0*l - 1/5*l**3 + 2/5*l**2 = 0. What is l?
-2, 0, 1
Suppose 16*y + 27 = 123. Determine k so that -214*k - y + 123*k - 34*k**2 + 131*k = 0.
3/17, 1
Let -7/2*w**2 + 0 - 1/8*w**3 + 15/2*w = 0. Calculate w.
-30, 0, 2
Suppose -4 = a, -4*p + 3*a - 518 = -5*p. Let c = -2119/4 + p. Let 4 + c*j**2 - 2*j = 0. What is j?
4
Let t = 1577/2 - 787. Let q = -499/22 + 299/11. Find f such that -6*f + 6*f**4 - 6*f**2 + t*f**5 + q*f**3 + 0 = 0.
-2, -1, 0, 1
Let m = 13638 + -13631. Let f(u) be the third derivative of 10*u**4 - 200/3*u**3 + 0 - 2/105*u**m + 0*u - 1/5*u**6 + 11/15*u**5 - 35*u**2. Factor f(j).
-4*(j - 2)**2*(j + 5)**2
Suppose 2*b - 2 = -2*w, -99*w = -97*w + 2. Let y(t) = t**3 - t**2 - 3*t + 4. Let s be y(b). Factor 3/5*d - 1/5*d**3 - 2/5 + 0*d**s.
-(d - 1)**2*(d + 2)/5
Let -1/7*j**3 - 59319000/7 - 456300/7*j - 1170/7*j**2 = 0. What is j?
-390
Let b(c) be the second derivative of c**6/540 + c**5/54 + c**4/54 - 8*c**3/27 - 27*c**2/2 + 84*c. Let z(o) be the first derivative of b(o). Factor z(d).
2*(d - 1)*(d + 2)*(d + 4)/9
Let g(y) be the third derivative of 0*y**6 - 1/40*y**5 - y**2 + 0*y**3 + 1/420*y**7 - 6 + 0*y - 1/24*y**4. Factor g(c).
c*(c - 2)*(c + 1)**2/2
Let a(j) be the second derivative of j**4/16 + 251*j**3/4 + 1503*j**2/8 + 568*j. Determine n, given that a(n) = 0.
-501, -1
Let r(z) = -4*z + 48. Let p be r(2). Factor -25 + 5*i**2 - p*i + 22 + 63.
5*(i - 6)*(i - 2)
Suppose 5*v - 5*k - 5 - 30 = 0, 5 = -v - 5*k. Suppose -v*p - 5 = 0, -4*q = q + 4*p - 11. Factor 23*s**2 - 11*s - 31*s + 55*s**2 + 8 - 62*s**q + 18*s**4.
2*(s - 1)**3*(9*s - 4)
Let v(j) be the first derivative of 1/6*j**4 + 0*j**3 + 0*j**2 + 0*j**5 + 0*j + 25 - 1/9*j**6. Suppose v(t) = 0. Calculate t.
-1, 0, 1
Let p(i) be the third derivative of -65*i**3 - 33*i**2 + 1/12*i**5 + 0*i + 0 + 185/24*i**4. Let p(f) = 0. Calculate f.
-39, 2
Let n(g) be the third derivative of 41*g + 0 + g**2 - 25/12*g**4 + 5/6*g**3 + 25/12*g**5. Factor n(s).
5*(5*s - 1)**2
Let u(b) = 3*b**3 - 822*b**2 + 164810*b - 326432. Let w(j) = -4*j**3 + 828*j**2 - 164799*j + 326432. Let f(n) = -3*u(n) - 2*w(n). Solve f(s) = 0.
2, 404
Factor -196*k - 255*k - 234 + 16*k**2 - 14*k**2 + 523*k.
2*(k - 3)*(k + 39)
Let s = -1214 + 1216. Let r be (27/(-2))/1*-2. Find g, given that -3*g**3 + 25*g**s - g**2 + 16*g**4 - 6*g**3 - r*g**3 - 4*g = 0.
0, 1/4, 1
Suppose 1575/8*b + 0 - 3/8*b**2 = 0. What is b?
0, 525
Let h be (-8)/(-6) + 10/(-30). Let g be (h/(-6))/(1/(-6)) + 1. Factor -12*j + 69/5*j**g - 21/5*j**3 + 12/5.
-3*(j - 2)*(j - 1)*(7*j - 2)/5
Suppose 0 = -3*w + 5*w + 3*j - 37, w - 21 = -4*j. Suppose -2*b + 0*b - 3*s = 11, -w = -b + 3*s. Let -x**3 + 1197*x**2 - 1197*x**b + x**4 = 0. What is x?
0, 1
Suppose -15*v - 32*v - 28*v = -53*v. Let a(j) be the second derivative of -32*j + 8/3*j**3 + v*j**2 - 1/3*j**4 + 0. Solve a(w) = 0.
0, 4
Let b(f) = 5*f**2 - 12552*f + 7875135. Let w(v) = 5*v**2 - 12553*v + 7875140. Let s(g) = 3*b(g) - 2*w(g). Factor s(q).
5*(q - 1255)**2
Suppose 2*q - 83 + 85 = 0. Let m(r) = 8*r**5 - 35*r**4 + 40*r**3 - 15*r**2 + 2*r + 2. Let o(c) = c**5 - c - 1. Let x(j) = q*m(j) - 2*o(j). Solve x(y) = 0.
0, 1, 3/2
Let d(q) be the second derivative of q**6/195 + 9*q**5/130 + 7*q**4/78 - 15*q**3/13 + 28*q**2/13 - 40*q + 37. Solve d(l) = 0.
-7, -4, 1
Let o(r) be the second derivative of -25*r**4/48 + 337*r**3/6 + 27*r**2/2 + 10336*r. Solve o(c) = 0.
-2/25, 54
Suppose 0 = -14*x + 98 - 322. Let u be (-91)/(-28) + 4/x. Solve 2*z**5 + 0 + 8/5*z**2 + 8/5*z + 4/5*z**4 - 6*z**u = 0 for z.
-2, -2/5, 0, 1
Let w be (11/(99/135))/(1/2). Let d be (w/(-36))/(10*(-3)/48). Factor d + 8/3*s**2 + 4*s.
4*(s + 1)*(2*s + 1)/3
Let t(u) be the second derivative of 0*u**3 - 1/28*u**7 + 0*u**4 + 14*u - 1/20*u**6 + 0*u**2 - 1 + 3/20*u**5. What is x in t(x) = 0?
-2, 0, 1
Suppose 4*h - 9 = 7. Solve 5*g + 4 + 11*g + 10*g**2 + 16*g**3 + h*g**4 + 14*g**2 = 0.
-1
Suppose -2*i = -10, q - 3*i - 19 = -34. Let w(j) be the second derivative of -18*j - 1/195*j**6 + 0*j**3 - 2/39*j**4 + 2/65*j**5 + 0*j**2 + q. Factor w(o).
-2*o**2*(o - 2)**2/13
Let g be 39053/7173 + 4/(-9). Find v such that 2/5*v - 4/5*v**3 + 12/5 - 24/5*v**2 + 12/5*v**4 + 2/5*v**g = 0.
-6, -1, 1
Suppose -12 = v - 4*x, 19*v + 4*x - 20 = 18*v. Let s(z) be the second derivative of -5/2*z**2 + 9*z + 0*z**3 + 0 + 5/12*z**v. Factor s(h).
5*(h - 1)*(h + 1)
Let h(t) be the third derivative of -9/8*t**6 - 11/70*t**7 - 1/112*t**8 - 27/4*t**4 + 0*t**3 - 81/20*t**5 + 0 + 0*t - 113*t**2. Determine w so that h(w) = 0.
-3, -2, 0
Let s(z) = -6*z**2 - 50*z - 356. Let h(i) = -i**2 + 2*i + 3. Let j(a) = -5*h(a) + s(a). Let j(v) = 0. What is v?
-53, -7
Let h = 286 + -282. Factor -2*f**3 + 2*f + 6*f - 8*f**4 + 9*f**h - 4*f**2.
f*(f - 2)**2*(f + 2)
Let k = -582 + 622. Factor -4*x**2 - 30 - 52 - 11 - k*x - 3.
-4*(x + 4)*(x + 6)
Suppose 3*o + 15 = 9*d - 14*d, 15 = 