j**7/945 + j**6/540 + 3*j**3 + j - 12. Let w(f) be the third derivative of l(f). Solve w(z) = 0.
0, 1, 3
Factor -83*m**2 - m**4 + 6*m**3 + 27*m**2 - 21*m**3 + 38*m**2 + 34*m**2.
-m**2*(m - 1)*(m + 16)
Suppose 147*r**2 + 150*r**2 - 1728*r + 80509 + 106115 - 293*r**2 = 0. What is r?
216
Suppose 2*d - 6 = -8*c + 6*c, 4*d - 3*c = 12. Let 30*a**2 - 34*a**2 + 62*a - 30 + a**d - 30*a**2 + a**3 = 0. What is a?
1, 15
Let q be (-2)/((-4)/10) + -3. Suppose -5*v**5 - 20*v - 60*v**q - 954*v**3 + 437*v**3 - 30*v**4 + 452*v**3 = 0. What is v?
-2, -1, 0
Let p = 498 - 564. Let i be -2*(-1 - 24/p). Factor -24/11*j - i*j**2 + 8/11.
-2*(j + 2)*(7*j - 2)/11
Let g(q) be the third derivative of -q**8/2016 + 13*q**7/420 + 4*q**6/45 + 21*q**5/10 + 2*q**2 + 3*q. Let t(z) be the third derivative of g(z). Factor t(k).
-2*(k - 16)*(5*k + 2)
Let l(p) be the third derivative of p**7/35 + p**6/40 - p**5/10 - p**4/8 + p**2 - 209*p. Factor l(o).
3*o*(o - 1)*(o + 1)*(2*o + 1)
Let f = 55096/137815 + 6/27563. Factor 16/5*r**3 - f*r**4 + 0*r + 54/5 - 36/5*r**2.
-2*(r - 3)**3*(r + 1)/5
Let l(t) be the first derivative of -t**4/14 - 184*t**3/7 - 19044*t**2/7 - 1017. Factor l(r).
-2*r*(r + 138)**2/7
Let n(j) = -j**4 + j**3 - 2*j**2 + 1. Let x(y) = 3*y**3 - y**2 - 1. Let p be ((-138)/14)/3 - 20/(-70). Let c(h) = p*x(h) - 3*n(h). Factor c(m).
3*m**2*(m - 3)*(m - 1)
Let a(b) = 3*b**2 - 264*b + 3112. Let n be a(14). Let 1/3*i**n - i**3 + 2/3*i + 1/3*i**5 - 1/3*i**2 + 0 = 0. Calculate i.
-2, -1, 0, 1
Suppose 2*t = 5*u + 31, 5*t + 3*u = 7*u + 86. Let x be 26/(-39)*t/(-4). Factor s**x + s**5 + 16*s**4 - 13*s**4 - 3*s**2 + s - 3*s.
s*(s - 1)*(s + 1)**2*(s + 2)
Let k = -9997 + 9997. Let a(g) be the third derivative of -1/210*g**5 + 20*g**2 - 1/42*g**4 + k*g**3 + 0*g + 0. Determine b so that a(b) = 0.
-2, 0
Let n be (-2)/(-1) + 70 + -77. Let t be 0/(n + 0/7). Solve 4/7*r + t + 8/7*r**3 + 10/7*r**2 + 2/7*r**4 = 0 for r.
-2, -1, 0
Let r(q) be the third derivative of 0 + 19/40*q**6 - 303*q**2 - 40/3*q**4 + 0*q - 16*q**3 + 4/21*q**7 - 373/90*q**5 - 25/1008*q**8. Suppose r(i) = 0. What is i?
-2, -3/5, 4
Let n be ((-474)/(-4))/((-188349)/(-71752)). Factor 324/7*j**2 + n*j - 8/7.
4*(j + 1)*(81*j - 2)/7
Let b(k) be the second derivative of -33/8*k**2 - 1/80*k**5 - 31/48*k**4 + 0 + 65/24*k**3 - 179*k. Determine t, given that b(t) = 0.
-33, 1
Let r(b) be the second derivative of -121*b**7/252 + 209*b**6/60 + 1583*b**5/120 - 101*b**4/24 + 7*b**3/18 - 6*b + 141. Solve r(k) = 0.
-2, 0, 1/11, 7
Let h(k) be the third derivative of 0*k - 1/270*k**5 - 14/27*k**3 + 105 + 2*k**2 + 1/12*k**4. Factor h(l).
-2*(l - 7)*(l - 2)/9
Factor -103/7*b + 1/7*b**2 + 396/7.
(b - 99)*(b - 4)/7
Let q(p) = p**5 - p**4 + p**2 - p. Let m(f) = -557*f**3 + 14*f + 465*f**3 - 22*f**2 - 89*f**4 - 18*f**5 + 15*f**4. Let i(b) = m(b) + 2*q(b). Solve i(a) = 0.
-3, -1, 0, 1/4
Suppose 0 = -3*t - x + 985, 3*t + 3*x = -0*x + 981. Let n = -326 + t. Determine j so that 1/6*j**4 - 1/3*j + 5/6*j**2 - 2/3*j**5 + 0 + 2*j**n = 0.
-1, 0, 1/4, 2
Let o(g) be the second derivative of -g**5/90 + 89*g**4/54 - 175*g**3/27 + 29*g**2/3 - 406*g - 3. Factor o(d).
-2*(d - 87)*(d - 1)**2/9
Let i(g) = g**2 - 10*g + 29. Let m be i(8). Solve -2*d - d**2 - 29 - m*d + 45 = 0.
-16, 1
Suppose 2602 + 3408 = 1490*f + 1515*f. Factor 0 + 2/7*x**5 + 18/7*x**2 + 30/7*x**3 + f*x**4 + 0*x.
2*x**2*(x + 1)*(x + 3)**2/7
Solve 50/7*o - 2/7*o**4 - 50/7 + 52/7*o**2 - 52/7*o**3 + 2/7*o**5 = 0 for o.
-5, -1, 1, 5
Let u be ((-6)/4 + 0)*8/(-6). Suppose -31*z - 42*z + 72*z + z**u = 0. Calculate z.
0, 1
Let z = -219040/3 + 73014. Factor 0 + 1/3*j**2 + z*j.
j*(j + 2)/3
Let y be 45/(-9) + 12 + (-2 - 0). Factor -36*d**3 + d + 70*d - 2*d**y - 17*d + 16*d**4.
-2*d*(d - 3)**3*(d + 1)
Let x(d) be the first derivative of -d**6/18 - 2*d**5/3 - 7*d**4/12 + 2*d**3 - 8727. What is c in x(c) = 0?
-9, -2, 0, 1
Let n be (-5)/3*36/(-540). Let v(j) be the first derivative of -1/2*j**2 - 4/3*j + n*j**3 - 13. Find y such that v(y) = 0.
-1, 4
Suppose 2*o - 4*t - 2 = -2*t, 0 = -5*o + 3*t + 11. Suppose 18 = n + 2*q, 0 = 4*n + o*q - 82 + 10. Factor 3*u**2 + 9*u**2 - n*u**2 + 3*u**5 - 9*u**3.
3*u**2*(u - 2)*(u + 1)**2
Solve -50*g**2 + 28*g**3 - 288*g + 49*g**2 - 27*g**2 + g**4 - g**5 + 148*g**2 - 7*g**4 = 0 for g.
-6, 0, 2, 4
Let y(q) be the second derivative of 8*q**5/15 + 11*q**4/6 + 2*q**3 - 13*q**2 - 24*q. Let i(u) be the first derivative of y(u). Factor i(j).
4*(j + 1)*(8*j + 3)
Suppose 12 = -5*l + m, -4*m + 16 = -4*l - 0*m. Let k be (102/136)/((-3)/l). Let 5/4*c - k - c**2 + 1/4*c**3 = 0. What is c?
1, 2
Let j = 122 - 123. Let q be (-5 - 228/(-40))*(3 - j). Determine w, given that -16/5 - 28/5*w - 2/5*w**3 - q*w**2 = 0.
-4, -2, -1
Let v(y) = -y**2 + 226*y - 2769. Let r be v(13). Let a(p) be the second derivative of 0*p**3 + 1/3*p**4 + 0*p**2 + r - 1/20*p**5 + 3*p. Factor a(z).
-z**2*(z - 4)
Let f(g) be the first derivative of 5*g**4/12 + 34*g**3/9 + 38*g**2/3 + 56*g/3 + 1921. Factor f(o).
(o + 2)**2*(5*o + 14)/3
Let f(o) be the third derivative of o**7/1120 + o**6/120 - o**5/160 - o**4/8 - 59*o**3/6 - 37*o**2. Let n(w) be the first derivative of f(w). Factor n(q).
3*(q - 1)*(q + 1)*(q + 4)/4
Let j(k) be the second derivative of -k**5/15 + 17*k**4/6 - 32*k**3/3 - 32*k**2 + k - 66. Let l(q) be the first derivative of j(q). Factor l(o).
-4*(o - 16)*(o - 1)
Let z(a) = 6*a**2 - 50*a. Let p(w) = -7*w**2 + 51*w. Let n = -105 + 107. Let j(t) = n*p(t) + 3*z(t). Suppose j(s) = 0. What is s?
0, 12
Factor 22*p**3 + 1345*p**4 - p**5 - 668*p**4 - 698*p**4.
-p**3*(p - 1)*(p + 22)
Let p = 66052/45 + -13160/9. Let 0 - p*m**4 - 4/5*m**5 - 8*m**3 + 0*m**2 + 0*m = 0. What is m?
-5, -2, 0
Let l(y) be the first derivative of -y**3/18 - 51*y**2/4 + 77*y/3 + 2428. Determine b, given that l(b) = 0.
-154, 1
Let 300*w + 276*w**3 - 528 + 34*w**4 + 228*w**2 - 147*w + 1173*w - 37*w**4 - 1299*w**2 = 0. Calculate w.
1, 2, 88
Let m(b) be the third derivative of -b**8/504 + 13*b**7/315 + b**6/90 - 47*b**5/15 - 57*b**4/4 - 27*b**3 - 89*b**2 - 5. Solve m(n) = 0 for n.
-3, -1, 9
Let -8*d**2 - 80/11*d - 28/11*d**3 + 0 - 2/11*d**4 = 0. Calculate d.
-10, -2, 0
Let a(t) be the third derivative of t**8/168 + 2*t**7/105 - 2*t**6/3 - 5*t**5/3 + 125*t**4/4 - 15*t**2 + 7*t + 3. Find c, given that a(c) = 0.
-5, 0, 3, 5
Suppose 5*v + 3*a - 13 = 0, 8*v - a = 7*v + 1. Factor q**v + 12*q**2 - 10*q - 5*q**2 + q**3 + q**3.
2*q*(q - 1)*(q + 5)
Suppose 10*g = 9*g - 24. Let q(x) = -20*x**5 + 32*x**4 + 16*x**2 - 4*x + 24. Let p(m) = -m**5 + m**4 + m**2 + 1. Let a(u) = g*p(u) + q(u). Factor a(l).
4*l*(l - 1)*(l + 1)**3
Let m(b) = -10*b**2 + 135*b - 555. Let y(d) = d**2 - 17*d + 69. Let o(t) = -3*m(t) - 25*y(t). Determine u, given that o(u) = 0.
-6, 2
Let q = -228936 + 1144696/5. Solve 6/5*a**3 - 6/5*a - q*a**2 + 0 = 0.
-1/3, 0, 3
Let g(o) = -o**4 - o**3 - o. Let i(n) = -6*n**4 - 15*n**3 + 3*n**2 + 23*n - 20. Let x = -248 + 249. Let k(p) = x*i(p) - 5*g(p). Factor k(m).
-(m - 1)**2*(m + 2)*(m + 10)
Let j be 2/(-4)*(-34 + (-28)/(-7)). Let z be -5*(-308)/825 + 2/j. Determine g so that 0*g**2 + 0*g - 1/2*g**4 + 0 - z*g**3 = 0.
-4, 0
Let g = -48 + 45. Let i be -8 - g - (-11 - 0). Let 70*d - 75*d - 7*d**2 + 6*d**2 - i = 0. What is d?
-3, -2
Let h(i) = 36*i**2 - 314*i + 92. Let l(q) = 31*q**2 - 314*q + 94. Let j(v) = 5*h(v) - 6*l(v). Factor j(g).
-2*(g - 52)*(3*g - 1)
Let z(s) be the third derivative of -577*s**5/60 + 191*s**4/8 + 2*s**3/3 + s**2 - 2836*s. Factor z(k).
-(k - 1)*(577*k + 4)
Let r(j) be the first derivative of 20*j + 42*j**2 - 85*j**2 + 175*j**3 + 33 - 67*j**2. Determine g, given that r(g) = 0.
2/15, 2/7
Factor -1024/5 + 1152/5*y - 112/5*y**2 - 18/5*y**3 + 2/5*y**4.
2*(y - 8)**2*(y - 1)*(y + 8)/5
Let r = 89972 + -89970. Let 0*l + 1/6*l**3 + 0 - 5/6*l**r = 0. Calculate l.
0, 5
Suppose -h = 7*x - 9, -594*h - 3 = -4*x - 595*h. Let -11/5*l**x - 17/5*l - 2/5*l**3 - 6/5 = 0. Calculate l.
-3, -2, -1/2
Let i = -92 + 97. Suppose 9 = 2*t + 2*x - 3*x, -2*t - i*x = -3. Factor 0 + 2/7*g - 3/7*g**3 + 1/7*g**t - 1/7*g**2 + 1/7*g**5.
g*(g - 1)**2*(g + 1)*(g + 2)/7
Let g(c) be the first derivative of -c**4 - 40*c**3/3 - 22*c**2 + 280*c + 1294. Suppose g(m) = 0. Calculate m.
-7, -5, 2
Let n = 16569 + -97579/6. Let o = n - 305. Factor 25/6*u + 5/6*u**4 - o*u**3 - 5/2*u**