k + 27)
Let f be (3 - -6) + 4/4. Let o(r) = r**2 - r + 2. Let l be o(2). Let -132*j**2 + 14*j + f*j + 357*j**l + 59*j**5 + 54*j**3 + 88*j**5 = 0. Calculate j.
-2, -1, 0, 2/7
Let g(x) be the first derivative of 3*x**4/4 - x**3 - 3*x**2 - 137. Factor g(i).
3*i*(i - 2)*(i + 1)
Let t = 243 - 243. Let a be ((t - 3) + 3)/(-2). Factor a*w + 0 - 1/8*w**3 + 1/8*w**2.
-w**2*(w - 1)/8
Let q(z) be the third derivative of -z**5/150 + z**4/12 + 10*z**3/3 - z**2 - 13. Factor q(m).
-2*(m - 10)*(m + 5)/5
Let z(w) be the second derivative of -4*w**6/15 - 16*w**5/5 + 139*w**4/24 - 89*w**3/24 + 9*w**2/8 - 59*w. Find i, given that z(i) = 0.
-9, 1/4, 1/2
Let t(q) = -14*q**3 - 44*q**2 - 72*q - 40. Let a(m) = 5*m**3 + 15*m**2 + 24*m + 13. Let y = -90 + 82. Let x(d) = y*a(d) - 3*t(d). Let x(u) = 0. What is u?
-2
Let v(d) be the first derivative of 2*d**3/9 + d**2/9 - 4*d/9 - 6. Let v(f) = 0. What is f?
-1, 2/3
Let n(i) be the third derivative of -3*i**8/128 - 61*i**7/560 - 3*i**6/64 + 13*i**5/32 + 9*i**4/16 - i**3/4 + 2*i**2 + 102*i. Solve n(b) = 0.
-2, -1, 2/21, 1
Let t(i) be the second derivative of -15*i + 0*i**2 + 0 + 1/6*i**3 - 1/36*i**4. Determine v, given that t(v) = 0.
0, 3
Let j be (199*3/(-273))/1. Let s = j - -34/13. Factor s - 3/7*r**2 - 3/7*r + 3/7*r**3.
3*(r - 1)**2*(r + 1)/7
Let w = -321437/7 - -45920. Find a, given that 9/7 + 12/7*a + w*a**2 = 0.
-3, -1
Let j be ((-10)/(-4) - 4)/((-3)/(-149)). Let n = j + 75. Factor v - 1/2 - n*v**2.
-(v - 1)**2/2
Suppose -4*p = -3*p - 66. Let 60*y**3 - 3*y**4 - 52*y**2 + p*y**2 + 30*y - 32*y**4 + 111*y**2 = 0. What is y?
-1, -2/7, 0, 3
Find z, given that -68/9*z - 2/9*z**2 + 0 = 0.
-34, 0
Determine s so that 6 + 0*s**3 - 9/2*s**2 + 1/2*s**4 - 2*s = 0.
-2, 1, 3
Let z be ((-6)/(-18))/(7/(-41)). Let r = 16/7 + z. Solve r*n + 1/2 - 1/6*n**2 = 0 for n.
-1, 3
Suppose 42 - 22 = 4*t. Find y, given that -10*y - 4*y**3 + 9*y + t*y = 0.
-1, 0, 1
Solve 36 + 33/5*z**4 + 54/5*z**3 - 27*z**2 - 132/5*z = 0.
-2, 1, 15/11
Let y = -2254 - -2257. Let c(h) be the second derivative of h - 1/6*h**y - 1/12*h**4 + h**2 + 0. Factor c(u).
-(u - 1)*(u + 2)
Let f be -1*371/123 + 3. Let d = 131/492 + f. Factor 1/2 - 3/4*p + d*p**2.
(p - 2)*(p - 1)/4
Suppose 23 = a - 5*y, -5*a + 7*y = 2*y - 35. Let q(n) be the first derivative of 0*n + 1/3*n**2 + 4/9*n**a - 6. Factor q(h).
2*h*(2*h + 1)/3
Let o = -63 + 84. Let l = o - 19. Solve 0 + 0*u + 3/4*u**3 - 3/4*u**l = 0 for u.
0, 1
Let x(i) = -i + 2. Let g be x(0). Suppose 5 - 1 = g*n. Factor -2*d - 2 + 4 + 20*d**n - 3 - 3.
2*(2*d - 1)*(5*d + 2)
Let q(g) be the second derivative of -g**7/14 + g**6/10 + 14*g + 6. Factor q(k).
-3*k**4*(k - 1)
Let z(f) = 2*f**3 - 7*f**2 + 3*f - 2. Let m be z(2). Let o(p) = -8*p - 62. Let x be o(m). Suppose c + 1/3 + 1/3*c**4 + c**5 - 2/3*c**x - 2*c**3 = 0. What is c?
-1, -1/3, 1
Determine k, given that 67/8*k**2 - 13/4*k + 0 - 57/8*k**3 + 17/8*k**4 - 1/8*k**5 = 0.
0, 1, 2, 13
Let n(g) be the third derivative of g**8/40320 + g**7/5040 - g**6/480 + g**5/5 + 5*g**2. Let m(t) be the third derivative of n(t). Factor m(j).
(j - 1)*(j + 3)/2
Let v(f) = -4*f - 5. Let y be v(2). Let r = -11 - y. Factor -3*n**2 - 2*n**2 + n**2 + r*n.
-2*n*(2*n - 1)
Let f(u) = u**2 + 2*u + 1. Let d(y) = y + 1. Let i(j) = -10*d(j) + 2*f(j). Solve i(o) = 0 for o.
-1, 4
Let 9*x**3 + 4*x**4 - x**3 - 284*x**5 + 280*x**5 = 0. What is x?
-1, 0, 2
Let i = -1225 - -1228. Let h(x) be the third derivative of 0*x - 9*x**2 - 1/240*x**6 + 0 + 0*x**5 + 1/48*x**4 + 0*x**i. Determine v, given that h(v) = 0.
-1, 0, 1
Let k(n) be the first derivative of -2*n**5/5 + 3*n**4/2 - 4*n**3/3 - 61. Factor k(b).
-2*b**2*(b - 2)*(b - 1)
Suppose 9 = -3*j, 0 = -3*h + 5*j + 4 + 5. Let v be 0/(h/(12/(-18))). Factor 0 + v*i - 3/5*i**4 - 3/5*i**3 + 0*i**2.
-3*i**3*(i + 1)/5
Let f = -6279 + 43957/7. Suppose 0 + 0*p + 8/7*p**2 - f*p**3 = 0. What is p?
0, 2
Let m(a) be the first derivative of -5 + 1/9*a**2 - 4/9*a + 2/27*a**3. Determine j so that m(j) = 0.
-2, 1
Suppose -3*f = -5*f - 134. Let u = f + 69. Factor 0*v**3 - 2/3*v + 2/3*v**5 + 0 - 4/3*v**u + 4/3*v**4.
2*v*(v - 1)*(v + 1)**3/3
Let r(g) be the second derivative of -g**6/1620 - g**5/270 - g**4/108 - 31*g**3/6 - 8*g. Let u(j) be the second derivative of r(j). Find t such that u(t) = 0.
-1
Let i(f) be the first derivative of -11 - 1/2*f**4 + 6/5*f**5 + 0*f**2 + 8*f + 1/3*f**6 - 14/3*f**3. Let i(t) = 0. What is t?
-2, -1, 1
Suppose 38 + 37 = 15*x. Let p(l) be the third derivative of 5*l**2 + 0 - 1/280*l**6 + 1/28*l**4 + 1/140*l**x + 0*l + 0*l**3. Determine u, given that p(u) = 0.
-1, 0, 2
Let j = -302 - -306. Let c(w) be the first derivative of 0*w**2 + 0*w - 4 + 1/18*w**j + 2/27*w**3. Factor c(h).
2*h**2*(h + 1)/9
Factor 32 - 6*k**2 - 1/2*k**4 - 16*k + 4*k**3.
-(k - 4)**2*(k - 2)*(k + 2)/2
Suppose 2*o + 2*c - 40 = 0, -3*o + 28 = 2*c - 27. Factor 34*t - t**2 - 14*t**2 - 29*t + o*t**3 - 5*t**4.
-5*t*(t - 1)**3
Determine a, given that -126/5*a**2 - 76/5*a + 32/5 = 0.
-8/9, 2/7
Let o = -112 - -103. Let n be -2 - (-6 - -4)/(o/(-21)). Find a, given that -2/3*a**2 - n - 8/3*a = 0.
-2
Let l = 1212 + -3553/3. Let i = 251/9 - l. Factor 4/9*g**2 - i*g - 2/9*g**3 + 0.
-2*g*(g - 1)**2/9
Let f(d) be the third derivative of d**7/35 - d**6/15 - d**5/20 - 9*d**2. Let n(a) = 7*a**4 - 9*a**3 - 4*a**2. Let q(w) = 6*f(w) - 5*n(w). Factor q(v).
v**2*(v - 2)*(v - 1)
Factor 5/2 - 2*k - 1/2*k**2.
-(k - 1)*(k + 5)/2
Let s be (0 + 1)*20/(-25)*-5. Let v(w) be the second derivative of 2/7*w**2 + 1/84*w**s - 2/21*w**3 + 0 + 2*w. Solve v(i) = 0.
2
Suppose 0 = -10*n + 31 + 29. Let p(f) be the third derivative of 3/5*f**3 + 0*f + 1/5*f**4 - 3*f**2 + 0 - 1/75*f**n - 1/75*f**5 + 1/525*f**7. Factor p(a).
2*(a - 3)**2*(a + 1)**2/5
Solve -6*h**4 - 2470*h**2 - 6 + 9*h - 4*h**3 + 2482*h**2 - 5*h**3 = 0.
-2, -1, 1/2, 1
Let r(g) be the third derivative of -g**5/40 + g**4/16 + g**3/2 + 122*g**2. Factor r(y).
-3*(y - 2)*(y + 1)/2
Suppose -10 - 134 = -8*o. Factor 14*u + 35*u**2 + o*u + 23*u**3 - 19*u**3 - 15*u**2 + 16.
4*(u + 1)*(u + 2)**2
Let n(w) be the second derivative of -w**5/4 - 25*w**4/12 + 65*w**3/6 - 35*w**2/2 - 122*w. Find b such that n(b) = 0.
-7, 1
Let z = 92 - 87. Factor 15*d + 10*d + 30 + z*d**2 - d + d.
5*(d + 2)*(d + 3)
Let d = 720 + -716. Let b(t) be the third derivative of -2/5*t**5 - 1/4*t**3 + 0 + 1/2*t**d + 0*t + 6*t**2. Factor b(r).
-3*(4*r - 1)**2/2
Factor -30*k**2 + 77*k**2 - 36*k - 57*k**2 - 29*k**2 - 3*k**3.
-3*k*(k + 1)*(k + 12)
Suppose -4*p - 20 = -6*n - 6*n, 3*n + p = 7. Let m = 2 + -2. Determine v, given that -1/3*v**n + m - 2/3*v = 0.
-2, 0
Find l such that 32*l + 2/3*l**3 - 8*l**2 - 128/3 = 0.
4
Let g(i) be the second derivative of i**6/60 - i**5/5 + 13*i**4/24 - i**3/2 + 3*i - 5. Suppose g(p) = 0. What is p?
0, 1, 6
Factor 4/7*a**3 - 52/7*a**2 + 40/7*a + 96/7.
4*(a - 12)*(a - 2)*(a + 1)/7
Let y be 2/6 - (-1 - (-221)/(-3)). Suppose y = 2*x + 67. Factor 2/3*l**3 + 10/9*l**2 - 2/9*l**x + 4/9*l + 0 - 2/9*l**5.
-2*l*(l - 2)*(l + 1)**3/9
Let v = 38 - 38. Suppose 0 = 5*d + 6*a + 6, -5*a = -2*d - 6*a - 1. Factor v*h**4 + 0*h**2 + 0 + 0*h + d*h**3 - 2/23*h**5.
-2*h**5/23
Suppose r + 3*r - 20 = 0. Let f(t) = -t**3 - t. Let y(n) = -2*n**3 - n**4 + 5*n + 4*n**3 + 2*n**3. Let g(s) = r*f(s) + y(s). Factor g(i).
-i**3*(i + 1)
Let o be 1 + 1 + (-8 - -8) + -140. Let s = 141 + o. Factor 0 + 3/8*k + 3/8*k**s + 3/4*k**2.
3*k*(k + 1)**2/8
Let j be ((-12)/(-5))/((-8)/(-20)). Let i(y) be the third derivative of 0 + j*y**2 + 1/30*y**5 + 0*y - 4/3*y**3 + 0*y**4. Factor i(x).
2*(x - 2)*(x + 2)
Let 2/3*p**4 + 0 + 0*p + 8/3*p**3 - 10/3*p**2 = 0. What is p?
-5, 0, 1
Let d = 52288 + -52286. Solve 9/4*y + 1/2*y**2 - d*y**3 - 3/2*y**4 - 1/4*y**5 + 1 = 0.
-4, -1, 1
Factor -4*w**3 + 21*w**2 + 3*w**2 + 27*w + 0 - 4 + 11.
-(w - 7)*(2*w + 1)**2
Factor -834*h**2 + 72 + 9*h + 835*h**2 + 18*h.
(h + 3)*(h + 24)
Let o(v) = v**3 - v**2 - v - 1. Let c(p) = -5*p**3 + 8*p**2 + 11*p - 6. Let x(f) = -c(f) - 4*o(f). Let x(u) = 0. What is u?
-2, 1, 5
Let u(h) be the third derivative of h**7/17640 + h**6/5040 - 3*h**4/4 - 8*h**2. Let r(d) be the second derivative of u(d). Factor r(g).
g*(g + 1)/7
Let j(p) = 13*p**2 + 83*p. Let y(b) = b**2 + b. Let d(s) = j(s) - 3*y(s). Let z(g) = g**2 + 9*g. Let l(a) = -4*d(a) + 35*z(a). Determine v so that