k) = 0. Calculate k.
-23, 2
Let v = 152439 + -152436. What is h in 12/5*h**2 - 1/5*h**v + 13/5*h + 0 = 0?
-1, 0, 13
Let n(v) be the third derivative of -1/30*v**6 + 14/9*v**4 - 1/315*v**7 + 16/3*v**3 + 0 - 2*v - 40*v**2 + 1/30*v**5. Find m such that n(m) = 0.
-4, -1, 3
Let r be (-94)/(-517) - (-3374)/77. Let s(y) be the first derivative of 0*y - r - 2/3*y**3 - 6/7*y**2 - 1/14*y**4. Factor s(h).
-2*h*(h + 1)*(h + 6)/7
Let y(v) = -5*v**2 - 31*v + 175. Let b(p) = -2*p**2 - 16*p + 87. Let l(c) = -7*b(c) + 3*y(c). Let j be l(7). Factor 2/7*s**2 + 0*s + j - 2/7*s**3.
-2*s**2*(s - 1)/7
Let n(y) be the third derivative of 0 - 2/3*y**4 + 1/12*y**6 - 4/3*y**3 + 7/30*y**5 - 20*y**2 + 0*y. Suppose n(j) = 0. What is j?
-2, -2/5, 1
Let u(i) be the third derivative of i**6/100 - 19*i**5/10 + 442*i**4/5 + 24336*i**3/5 - 103*i**2 - 25. Factor u(l).
6*(l - 52)**2*(l + 9)/5
Let o(t) = 5*t**3 + 16*t**2 + 73*t - 58. Let p(d) = d**3 + 4*d**2 + 17*d - 14. Let c(a) = -4*o(a) + 18*p(a). Factor c(v).
-2*(v - 5)*(v - 1)*(v + 2)
Let k(g) be the first derivative of 74 - 1/18*g**4 + 4/9*g**2 - 4/27*g**3 + 16/9*g. Factor k(b).
-2*(b - 2)*(b + 2)**2/9
Let v be -21*2/(-6) - 10 - 302/(-100). Let f(k) be the second derivative of 1/10*k**2 + v*k**5 + 17*k + 0 - 1/15*k**3 - 1/60*k**4. Factor f(x).
(x - 1)*(x + 1)*(2*x - 1)/5
Let w be 377 + -384 - -9*1. Solve -1/2 - 1/2*y**4 + y**w + 0*y**3 + 0*y = 0.
-1, 1
Suppose -6*d - 18 = -66. Let g(z) be the first derivative of -10/3*z**3 + d + 15/2*z**2 + 5/12*z**4 - 20/3*z. Determine k so that g(k) = 0.
1, 4
Let o(y) be the second derivative of -y**7/6300 - y**6/450 - 51*y**4/4 - 142*y. Let i(p) be the third derivative of o(p). Factor i(a).
-2*a*(a + 4)/5
Let h be (87/(-116))/((-1)/4). Factor -5*t**2 - t**3 - 4*t - 3*t**3 - 5*t**2 + 2*t**h + 4*t**2.
-2*t*(t + 1)*(t + 2)
Let y = 1993 + -2817. Let f = -5760/7 - y. Factor f*z**4 - 4/7*z**5 - 8/7*z**2 + 0 + 0*z**3 + 4/7*z.
-4*z*(z - 1)**3*(z + 1)/7
Let m(v) be the third derivative of v**6/180 - 13*v**5/90 - 5*v**4/6 + 3*v**2 - 206. What is u in m(u) = 0?
-2, 0, 15
Let j be (-5 - -8 - -4) + (-4 - -184). Let s be 28/55 + 17/j. Suppose -6/5*g**3 + 0*g**2 + 6/5*g - 3/5 + s*g**4 = 0. Calculate g.
-1, 1
Let z = 1958 + -1988. Let l be z/(-8)*((-77)/(-35) + -2). Factor 5/4*c**4 - 1/4*c**5 + 0 + l*c**2 + 0*c - 7/4*c**3.
-c**2*(c - 3)*(c - 1)**2/4
Let h(w) = 7*w**2 + 362*w - 357. Let k(v) = 60*v**2 + 2895*v - 2853. Let r(a) = 51*h(a) - 6*k(a). Suppose r(u) = 0. Calculate u.
1, 363
Let t be 6/11 + (-70272)/121451. Let k = 380/543 + t. Factor 2/9*y**4 - 2/3*y + 2/9*y**2 - 4/9 + k*y**3.
2*(y - 1)*(y + 1)**2*(y + 2)/9
Suppose -d - 4 = -3*y - 24, 5*d = -5*y + 60. Suppose -d*j = -30*j + 32. Solve 3/4*g**j - 6*g + 12 = 0 for g.
4
Let h be (70650/(-73476))/(2/(-8)). Factor -2/13*i**2 - h + 20/13*i.
-2*(i - 5)**2/13
Let z(d) be the second derivative of -d**5/30 + 137*d**4/9 - 19040*d**3/9 + 36992*d**2/3 + d + 25. Suppose z(f) = 0. What is f?
2, 136
Let k(o) be the second derivative of -9*o**4/7 - 47*o**3/21 + o**2 - 481*o. Factor k(d).
-2*(d + 1)*(54*d - 7)/7
Suppose 2*u = -50*y + 55*y + 1, -4*u + 11 = -y. Factor -1/2*v**5 + 10*v**2 + u*v**3 - v**4 + 19/2*v + 3.
-(v - 3)*(v + 1)**3*(v + 2)/2
Let t(h) be the second derivative of h**5/20 + 17*h**4/4 + 60*h**3 + 344*h**2 + 274*h + 2. Factor t(i).
(i + 4)**2*(i + 43)
Suppose -k + 16 = 6*k + 2. Let o(q) be the second derivative of -1/35*q**5 + 16*q + 0*q**k - 1/14*q**4 + 1/105*q**6 + 0 + 0*q**3. What is g in o(g) = 0?
-1, 0, 3
Let x be (-7 - -8)*(6*1)/2. Suppose -h**5 - 125*h**3 - 126*h**x + 250*h**3 + 2*h**4 + 0*h**5 = 0. What is h?
0, 1
Let s = 151 + -141. Determine y, given that 5*y**2 + 11*y**5 + s*y**4 - 15*y**2 - 6*y - 9*y**5 + 10*y**3 - 6*y = 0.
-3, -2, -1, 0, 1
Suppose 12 = 14*l - 16. Factor 22*f + l*f**3 - 64*f + 40*f.
2*f*(f - 1)*(f + 1)
Let h(s) be the second derivative of -s**5/20 - 17*s**4/48 + s**3/4 + 22*s**2 - 11*s + 1. Let n(l) be the first derivative of h(l). Find y such that n(y) = 0.
-3, 1/6
Factor 3*o**2 - 29790*o - 7*o**2 - 9817322 + 2932677 - o**2 - 37487560.
-5*(o + 2979)**2
Let i(s) be the second derivative of s**8/8400 - s**7/700 + s**3/6 + s**2/2 - 2*s + 4. Let l(j) be the second derivative of i(j). Factor l(p).
p**3*(p - 6)/5
Factor -2/5*t**2 + 16*t + 0.
-2*t*(t - 40)/5
Let u(k) be the first derivative of 5*k**2 - 2*k**3 - 4*k + 2/5*k**5 + 28 - 1/2*k**4. Find h, given that u(h) = 0.
-2, 1
Suppose 13*n + 10*n + 14*n = 30*n. Let m(d) be the first derivative of 8 + 1/3*d**3 + n*d - 1/4*d**4 + d**2. Factor m(j).
-j*(j - 2)*(j + 1)
Let s(n) be the third derivative of n**8/1344 + 31*n**7/840 - 23*n**6/160 - 33*n**5/80 - 2008*n**2. Let s(h) = 0. Calculate h.
-33, -1, 0, 3
Let v(k) be the second derivative of 55 - 27/40*k**6 + 81/80*k**5 + 17/8*k**3 + 45/16*k**4 - k + 3/4*k**2. Let v(r) = 0. Calculate r.
-1/3, 2
Let o(u) = 120*u**3 - 20160*u**2 - 61415*u - 41515. Let a(j) = 5*j**3 - 840*j**2 - 2559*j - 1730. Let v(d) = 95*a(d) - 4*o(d). Factor v(k).
-5*(k - 171)*(k + 1)*(k + 2)
Let l be ((-15)/24 + 0)/(33066/(-1836) + 18). Let 35/2 + 35/4*a**2 - l*a = 0. What is a?
2/7, 7
Let o(b) = -10*b**3 + 8*b**2 + 22*b + 7. Let a(c) = -110*c**3 + 88*c**2 + 242*c + 78. Let m(u) = 6*a(u) - 68*o(u). What is p in m(p) = 0?
-1, -1/5, 2
Let p(z) = -67*z + 201. Let c be p(3). Let o(b) be the first derivative of -1/3*b**6 + 0*b + 6 + 0*b**3 + c*b**2 + 1/2*b**4 + 0*b**5. Solve o(w) = 0.
-1, 0, 1
Suppose 3*c + 0*c - 4*y - 286 = 0, -c + 3*y = -92. Let n = c + -95. Factor -42*u**4 - 203*u**4 + 124*u**n - 264*u**3 - 20*u**2.
-5*u**2*(7*u + 2)**2
Let h(t) = -t**3 + 5*t**2 + 48*t + 23. Suppose 4*u - 10*p - 40 = -9*p, -2*p = 0. Let x be h(u). Factor 0*w + 0*w**4 + 1/4*w**x - 1/4*w**5 + 0 + 0*w**2.
-w**3*(w - 1)*(w + 1)/4
Let y be (43 - 23) + -17 - 1. Factor -2 - 2/9*x**3 + 2*x**y + 2/9*x.
-2*(x - 9)*(x - 1)*(x + 1)/9
Suppose -3*i + 7*i + 2*b - 162 = 0, 3*i - 120 = -3*b. Let r = i + -37. Factor -4*o + 4 + o**4 - 2*o**r - 3*o**2 + 2*o**3 + 2*o**3.
-(o - 2)**2*(o - 1)*(o + 1)
Let j(w) be the third derivative of -w**8/336 - 19*w**7/105 + 41*w**6/40 - 119*w**2 + 6. Suppose j(z) = 0. What is z?
-41, 0, 3
Let i(o) be the first derivative of -2*o**6/9 + 64*o**5/15 + 77*o**4/3 + 256*o**3/9 - 152*o**2/3 - 320*o/3 - 2371. Suppose i(r) = 0. Calculate r.
-2, -1, 1, 20
Factor 1602 + 6*a**3 + 849*a + 246*a - 2*a**3 + 140*a**2 + 558 + a**3.
5*(a + 3)*(a + 9)*(a + 16)
Let x(p) be the third derivative of 0 + 1/5*p**5 - 2*p + 0*p**7 + 39*p**2 + 0*p**3 - 1/168*p**8 + 0*p**4 + 7/60*p**6. Suppose x(n) = 0. What is n?
-2, -1, 0, 3
Let y(p) be the first derivative of 7/16*p**3 - 3/8*p**4 + 6 + 17/160*p**5 - 1/8*p**2 - 12*p. Let m(b) be the first derivative of y(b). Solve m(o) = 0 for o.
2/17, 1
Suppose 0 = 93*f - 176*f + 249. Let c(y) be the second derivative of 3/230*y**5 - 15*y + 0*y**2 - 1/345*y**6 - 1/69*y**4 + 0*y**f + 0. Let c(j) = 0. What is j?
0, 1, 2
Let y(d) = d**2 + 1102*d - 15624. Let u be y(14). Suppose 9/4*h**3 + u + 1/2*h - 7/4*h**2 - 5/4*h**4 + 1/4*h**5 = 0. Calculate h.
0, 1, 2
Suppose -2489*i + 2532*i - 81 - 48 = 0. Determine x, given that -16/3*x**i + 0 + 0*x**2 + 4*x**4 - 2/3*x**5 + 0*x = 0.
0, 2, 4
Let z(i) be the third derivative of -17/10*i**5 - 3*i - 22*i**2 + 9/40*i**6 + 0 + 19/8*i**4 + 3*i**3. Factor z(f).
3*(f - 3)*(f - 1)*(9*f + 2)
Let w = 254 - 229. Solve -45 - x**3 - 6*x**2 - 51 - 56 + 134 + w*x = 0.
-9, 1, 2
Let d(f) = 3*f**2 + 90*f - 2112. Let n(w) = 29*w**2 + 809*w - 19006. Let a(h) = -38*d(h) + 4*n(h). Solve a(y) = 0 for y.
46
Suppose -236 - 239 = -14*h - 475. Factor n**2 + h + 1/2*n**3 - 3/2*n.
n*(n - 1)*(n + 3)/2
Let h(a) = -4*a**4 - a**3 + 62*a**2 + 192*a + 186. Let n(u) = -u**4 - u**3 + u**2 + 2. Let x(b) = -h(b) + 3*n(b). Let x(l) = 0. Calculate l.
-3, -2, 10
Let b(m) = m**2 + 3*m - 12. Let v be b(5). Solve 10*s**5 + v*s**4 + 19*s**4 - 11*s**4 - 6*s**5 = 0.
-9, 0
Let q(m) be the first derivative of 16/5*m**5 + 17 + 26*m + 6*m**3 - 2*m**2 - 8*m**4. Let o(u) be the first derivative of q(u). Factor o(l).
4*(l - 1)*(4*l - 1)**2
Let z = 1793 - 1793. Let b(j) be the third derivative of 0*j**4 + 0 + 0*j**3 + 1/3*j**6 + 1/14*j**7 + 1/3*j**5 + z*j + 3*j**2. Solve b(k) = 0 for k.
-2, -2/3, 0
Let c(o) = o**2 + 12*o + 8. Let x = -63 - -49. Let v be c(x). Determine g,