= -257 + 261. Find u, given that -90*u**3 - 11*u**4 - 190*u**3 + 178*u**2 - 75*u - 9*u**j + 212*u**2 - 95*u**2 = 0.
-15, 0, 1/2
Suppose -5*z - 3*z - 768 = 0. Let k = z + 99. Let 12*b**5 - 4*b**2 + 8*b - 2 - 2 + 4 + 4*b**4 - 20*b**k = 0. What is b?
-1, 0, 2/3, 1
Let v(n) be the third derivative of 0 + 0*n - 4/5*n**5 + 0*n**3 - 1/40*n**6 - 8*n**4 - 153*n**2. What is d in v(d) = 0?
-8, 0
Let i(n) be the second derivative of n**4/66 + 170*n**3/33 - 171*n**2/11 + 12*n + 33. Factor i(r).
2*(r - 1)*(r + 171)/11
Let b(c) be the third derivative of 0*c + 578/3*c**3 + 1/15*c**5 - 3*c**2 + 17/3*c**4 + 3. Factor b(f).
4*(f + 17)**2
Suppose -4*i - 571 + 1043 = 0. Factor -14*x**2 + 968*x**3 - 7 + 0*x**2 - i*x**2 - 9 - 144*x.
4*(2*x - 1)*(11*x + 2)**2
Let j(u) be the third derivative of u**8/20160 - u**7/252 + u**5/30 - u**4/4 - 24*u**2 + u. Let d(y) be the third derivative of j(y). Factor d(q).
q*(q - 20)
Let p(m) be the second derivative of 36*m + 2/25*m**5 - 22/5*m**2 + 4/3*m**3 + 23/15*m**4 + 0. Find c, given that p(c) = 0.
-11, -1, 1/2
Let z(n) = 275*n + 1929. Let q be z(-7). Let p(c) be the first derivative of -27 - q*c**3 + 0*c - 2*c**4 + 12/5*c**5 + 4*c**2. Factor p(f).
4*f*(f - 1)*(f + 1)*(3*f - 2)
Determine q so that -9*q**2 + 7*q**2 + 754 - 4*q**2 - 6*q**2 - 375*q + 11*q**2 = 0.
-377, 2
Let h be (135 - 131)*2/10. Let f(s) be the first derivative of 1 - 4*s**3 + 2*s**2 - s**4 + h*s**5 + 8*s. Factor f(o).
4*(o - 2)*(o - 1)*(o + 1)**2
Let j = -193009 + 193011. Suppose 0 + 4/7*u**j - 3/7*u**3 - 1/7*u = 0. What is u?
0, 1/3, 1
Let z(m) be the first derivative of -2*m**5/75 - 23*m**4/10 + 94*m**3/15 - 71*m**2/15 - 4518. Let z(l) = 0. Calculate l.
-71, 0, 1
Let v(c) be the third derivative of c**5/15 - 2*c**4/3 + 8*c**3/3 - c**2 + 873*c + 2. Suppose v(o) = 0. Calculate o.
2
Let j be (-57)/(-9) - (5/15 - -1). Let q(r) be the third derivative of 0 - 2/3*r**3 + 1/8*r**4 + 0*r + 14*r**2 + 1/60*r**j. Factor q(t).
(t - 1)*(t + 4)
Let l(w) = -8*w**3 - 8*w**2 - 4*w - 4. Let r be l(-3). Let a = r + -748/5. Factor -6/5*n + 3/5*n**4 + 9/5 - a*n**2 + 6/5*n**3.
3*(n - 1)**2*(n + 1)*(n + 3)/5
Suppose 0*g - 5*a = -5*g - 15, 0 = 2*g + 2*a - 14. Let u(k) be the first derivative of 53*k - k**g - 3*k**2 - 5*k - 11 - 8*k**2 + k**3. What is c in u(c) = 0?
4
Suppose -4*s = -13*v - 129, -335 = 4*s + 4*v - 311. Determine j, given that -178/9*j**s + 14/9*j**4 + 116/9*j**2 + 0 + 16/3*j = 0.
-2/7, 0, 1, 12
Let u(p) be the second derivative of -3*p**5/20 + 11*p**4/4 - 5*p**3 - 2130*p. Solve u(w) = 0.
0, 1, 10
Let i(u) be the first derivative of 3/4*u + 5/16*u**2 + 39 - 1/32*u**4 - 1/12*u**3. Solve i(r) = 0.
-3, -1, 2
Let r(k) be the third derivative of k**6/210 - 4*k**5/105 - 71*k**4/42 - 44*k**3/7 + 8807*k**2. Solve r(f) = 0.
-6, -1, 11
Let h(a) be the second derivative of -13/7*a**2 + 1/42*a**4 - 4/7*a**3 + 48*a + 0. Suppose h(k) = 0. What is k?
-1, 13
Let u(i) be the first derivative of -1/30*i**5 - 10*i**2 - 12 + i**4 + 0*i - 12*i**3. Let k(h) be the second derivative of u(h). Find n such that k(n) = 0.
6
Suppose 3*v = 4*z + 39, 5*z - 1 - 29 = -5*v. Suppose v*k - 32 - 22 = 0. Determine c, given that -48/7*c**3 + 0*c - 8/7*c**2 - k*c**4 + 14*c**5 + 0 = 0.
-2/7, 0, 1
Let w be ((-648)/6156)/(6/(-57)). Factor -w + 13/3*k - 13/3*k**2 + k**3.
(k - 3)*(k - 1)*(3*k - 1)/3
Factor 162*c**3 - 7 + 7 + 120*c**2 + 163*c**3 - 329*c**3.
-4*c**2*(c - 30)
Let k be 7/(-196)*70*(-27)/270. Suppose -6 - k*p**2 - 5/2*p = 0. Calculate p.
-6, -4
Let r(u) = -2*u**3 - 139*u**2 + 208*u - 355. Let o be r(-71). Factor 0*z**2 + 1/9*z**5 + o*z - 2/3*z**3 + 0 - 1/9*z**4.
z**3*(z - 3)*(z + 2)/9
Let f(s) = 12*s**2 + 8. Suppose -11*h - 173 + 74 = 0. Let l(z) = z**3 - 23*z**2 - 18. Let p(t) = h*f(t) - 4*l(t). Determine d so that p(d) = 0.
-4, 0
Suppose 4 = -4*u, 0 = -y + 5*u + 86 + 39. Let c = y + -109. Factor -12*s + 1 + 3*s**2 + c - 2*s + 2*s.
3*(s - 2)**2
Suppose 8*a = 75 + 53. Suppose -a - 4 = -5*p. Factor y**5 + 4*y - y**p - 2*y**3 + y**4 - 3*y.
y*(y - 1)**2*(y + 1)**2
Let m(o) = 2*o**2 - 4*o. Let a(s) = -2*s**2 + 4*s. Suppose t = 2*p - 10, 2*t - 7 = -p - 4*p. Let f(z) = t*m(z) - 5*a(z). Factor f(r).
2*r*(r - 2)
Let h(y) be the first derivative of 345/14*y**2 - 3/4*y**4 - 9/7*y**3 - 116 - 300/7*y + 3/35*y**5. Factor h(d).
3*(d - 5)**2*(d - 1)*(d + 4)/7
Factor 784/5*n - 1/5*n**4 + 24/5*n**3 - 1029/5 - 42*n**2.
-(n - 7)**3*(n - 3)/5
Let t be 4/(3 - 7)*0. Let x be t - 0/(1 - -4). Find k such that -k**3 + x - 1/2*k**4 + k + 1/2*k**2 = 0.
-2, -1, 0, 1
Let p = 2949/1840 - 36/23. Let w(y) be the second derivative of 0*y**2 + 9*y + 0 - p*y**5 + 0*y**3 - 1/8*y**4. Suppose w(l) = 0. Calculate l.
-2, 0
Let g(s) be the third derivative of -s**9/15120 + s**8/3360 + s**7/168 + 17*s**4/4 + 232*s**2. Let h(o) be the second derivative of g(o). What is j in h(j) = 0?
-3, 0, 5
Suppose 5*m + 20 = 3*p, 4*p - 12*m = -13*m + 19. Let f(c) be the first derivative of -10 + 1/15*c**4 + 2/75*c**p + 0*c - 2/45*c**3 - 2/15*c**2. Factor f(t).
2*t*(t - 1)*(t + 1)*(t + 2)/15
Let v(u) = 3*u + 1. Let n be v(-1). Let c be 0 - 6/n - -1. Factor 5*a**3 - 4*a**c + a + a**3 + a**5 + 3*a**2 - 7*a**2 + 0*a**5.
a*(a - 1)**4
Suppose 7*v - 26*v - 13243 = 0. Let b be (v/(-41))/(-3 + (-63)/(-12)). Solve 44/9*d**2 + 20/9*d**5 + 28/3*d**3 + b*d**4 + 8/9*d + 0 = 0.
-1, -2/5, 0
Let y(t) be the first derivative of -t**6/15 + 18*t**5/25 - 23*t**4/10 + 22*t**3/15 + 24*t**2/5 - 8*t + 742. Find z, given that y(z) = 0.
-1, 1, 2, 5
Let 121*f**5 + 473*f**4 + 1277/4*f**3 + 0 - 32*f**2 + 3/4*f = 0. Calculate f.
-3, -1, 0, 1/22
Let t(l) be the second derivative of -l**5/50 - 5*l**4/6 - 22*l**3/15 + 48*l**2/5 - 4361*l. Factor t(o).
-2*(o - 1)*(o + 2)*(o + 24)/5
Factor -2/11*l**2 + 190/11*l - 188/11.
-2*(l - 94)*(l - 1)/11
Let q be 13*((-30)/(-55))/((-468)/(-198)). Suppose 0*s + 0*s**2 - 3/5*s**4 + 1/5*s**5 + 0*s**q + 0 = 0. Calculate s.
0, 3
Let d be 1/((4 - -2) + (-10)/((-440)/(-228))). Let i(r) be the first derivative of 0*r - 13 - 1/4*r**4 - r**2 - d*r**3. Find y such that i(y) = 0.
-3, -2/3, 0
Let h(t) be the second derivative of -13 - 3*t + 0*t**2 - 1/8*t**3 - 13/32*t**4. Factor h(o).
-3*o*(13*o + 2)/8
Let t(n) be the second derivative of n**4/6 + 206*n**3 + 95481*n**2 - 5050*n. Let t(i) = 0. What is i?
-309
Let k(u) = -27*u + 569. Let f be k(21). Let x(a) be the first derivative of -1/4*a**3 + 3/8*a**2 - f + 3/2*a. Factor x(z).
-3*(z - 2)*(z + 1)/4
Find u, given that 1/3*u**2 - 2/3*u - 1/3*u**4 + u**3 - 1/3*u**5 + 0 = 0.
-2, -1, 0, 1
Suppose 1888/9*p + 416 + 1/9*p**3 + 242/9*p**2 = 0. Calculate p.
-234, -4
Let q(k) = k**2 - 20*k + 10. Let g be q(20). Let 128*v**2 - 75*v**3 + 79*v**3 - g*v**5 - 20 - 16 - 44*v**4 - 42*v = 0. What is v?
-3, -2/5, 1
Let n = 757/11 - 2995/44. Let h(l) be the first derivative of 0*l**3 + 3/8*l**4 - 3/4*l + 9 + 3/20*l**5 - n*l**2. Factor h(p).
3*(p - 1)*(p + 1)**3/4
Factor 96 + 2*y**2 - 866/3*y.
2*(y - 144)*(3*y - 1)/3
Let k(p) be the second derivative of 0 + 10/9*p**3 - 30*p + 1/18*p**4 - 11/3*p**2. Solve k(j) = 0 for j.
-11, 1
Suppose -108*b + 170*b = 248. Let s(p) be the second derivative of 0*p**b + 0 - 1/150*p**6 - 7*p + 3/100*p**5 + 0*p**2 - 2/15*p**3. Factor s(v).
-v*(v - 2)**2*(v + 1)/5
Let i(u) be the second derivative of -17*u**5/70 - 1021*u**4/21 - 20480*u**3/7 - 7200*u**2/7 + 2*u + 1855. Find v such that i(v) = 0.
-60, -2/17
Let u(d) be the second derivative of -7/120*d**6 + 0 - 9/8*d**3 - 110*d - 27/16*d**4 - 9/16*d**5 + 0*d**2. Solve u(f) = 0.
-3, -3/7, 0
Find w such that -124866 - 99016 + 625*w**2 + 38365*w - 71906 - w**3 - 50601*w - 84476*w = 0.
-3, 314
Suppose -2*o - 8 - 2 = 0. Let t(g) = -g**2 - 6*g + 4. Let b be t(o). Factor 5*n**3 + b*n**3 - 13*n**3 - n**2.
n**2*(n - 1)
Let o(k) be the third derivative of k**8/840 - k**7/105 + k**6/300 + 7*k**5/50 - 3*k**4/10 - 342*k**2. Suppose o(p) = 0. What is p?
-2, 0, 1, 3
Let n = -17 + 25. Suppose n*i - 22 = 2. Factor b**2 + 12*b**2 + 20*b**4 - 4*b**5 - 28*b**i - b**2.
-4*b**2*(b - 3)*(b - 1)**2
Suppose -w + 15 = -4*y, -w + 4*w - 18 = 3*y. Let n be w - (2 + -4 + -3). What is j in 4 - 6*j + 2*j - 24*j**2 + n*j**2 + 7*j**2 + 9*j**3 = 0?
-2/3, 2/3, 1
Let d(a) be the second derivative of -a**4/30 + 4196*a**3/15 - 4401604*a**2/5 - 3*a + 1318. Find z, given that d(z) = 0.
2098
Let 