 2499. Determine q so that -17/3*q**r + 0 - 2/3*q = 0.
-2/17, 0
Suppose 473 - 413 = 10*h. Let x(t) be the third derivative of -1/6*t**4 + 0 - 1/150*t**h + 17*t**2 + 4/15*t**3 + 4/75*t**5 + 0*t. Find a, given that x(a) = 0.
1, 2
Determine r so that 71/2*r**2 + 1/4*r**5 + 0 - 211/4*r**3 + 17*r**4 + 0*r = 0.
-71, 0, 1, 2
Let j = -89802 - -89804. Factor 2/9*d**3 + 0*d - 4/9*d**j + 0.
2*d**2*(d - 2)/9
Let v be 3/(-11*(-6)/132). Let w(b) = -8*b**2 + 6*b. Let f(s) = 0*s**2 - 6*s**2 - s**2 + 5*s. Let g(i) = v*w(i) - 7*f(i). Factor g(x).
x*(x + 1)
Let v(m) be the first derivative of -3/2*m**2 + 0*m + 1/300*m**5 - 1/120*m**4 - 1/15*m**3 - 15. Let k(y) be the second derivative of v(y). Factor k(f).
(f - 2)*(f + 1)/5
Solve 46*q + 95*q + 95*q - 399*q - 196 + 61*q - 2*q**2 = 0 for q.
-49, -2
Let u be ((1 + -3)/4)/(18/(-252)). Suppose -23*g**2 + u*g**2 + g**3 - 4*g + 13*g**2 = 0. What is g?
-1, 0, 4
Suppose -4*w - 6 = -2*p, 5*w + 15 = w + 5*p. Suppose -2*n - 2*q + 10 = w, 2*q + q - 9 = 0. Factor -2/11*y + 0 + 2/11*y**n.
2*y*(y - 1)/11
Let w(i) be the first derivative of -7/5*i**2 + 177 - 8/5*i + 1/10*i**4 - 4/15*i**3. Solve w(n) = 0.
-1, 4
Let v = 50209/119 + -7095/17. Determine j so that -v - 2/7*j**2 + 16/7*j = 0.
4
Let c(d) be the third derivative of 1/105*d**7 + 16/3*d**3 + 1/60*d**6 + 0 + 0*d + 279*d**2 - 2/5*d**5 + 1/3*d**4. Suppose c(g) = 0. Calculate g.
-4, -1, 2
Let b = 127 - 123. Let x(l) be the third derivative of 17*l**2 + 1/102*l**5 + 2/17*l**3 + 0*l - 1/12*l**b + 0. Determine v, given that x(v) = 0.
2/5, 3
Let w(d) = -3*d**3 - 101*d**2 - 491*d - 418. Let p be w(-28). Factor 4/7*k**p + 1024/7 - 128/7*k.
4*(k - 16)**2/7
Find x, given that -2883 + 396*x - 210*x - 2*x**2 - x**2 = 0.
31
Let t(c) be the second derivative of -c**6/40 + 3*c**4/2 + 8*c**3 - 127*c**2/2 + 2*c - 21. Let s(o) be the first derivative of t(o). What is m in s(m) = 0?
-2, 4
Let w(k) be the first derivative of 0*k - 1/4*k**2 + 59 + 1/18*k**3. Factor w(d).
d*(d - 3)/6
Suppose -c + q + 22884 = 2*c, -q = -4*c + 30513. Find m, given that -c*m**2 - 18*m - 2*m**3 - 13*m**3 + 7590*m**2 = 0.
-2, -3/5, 0
Let o(n) = -7*n**2 - 13*n + 4. Let a be o(-2). Suppose -4*g - 25 = -9*g + a*j, -15 = 3*j. Factor 1/3*t**4 + 2/3 + 5/3*t**g + 7/3*t + 3*t**2.
(t + 1)**3*(t + 2)/3
Factor -33*g**3 + 31185*g**2 + 823*g**3 - 3160*g - 16845*g**4 - 124820 + 8421*g**4 + 8429*g**4.
5*(g - 2)*(g + 2)*(g + 79)**2
Suppose -36969*a = -36846*a. Factor 0 + 0*t + 1/2*t**5 + a*t**4 + 0*t**2 - 2*t**3.
t**3*(t - 2)*(t + 2)/2
Let b(v) be the first derivative of -v**4 - 1880*v**3/3 - 109504*v**2 + 445568*v + 1028. Determine u so that b(u) = 0.
-236, 2
Let o(p) = -9*p + 60. Let y be o(3). Let x be -37 + y - (-2 + (-64)/30). Factor 2/15*i**2 + 0 + x*i**5 - 2/15*i**3 - 2/15*i**4 + 0*i.
2*i**2*(i - 1)**2*(i + 1)/15
Let m(r) be the first derivative of -9*r**3/2 + 651*r**2/2 - 144*r - 1850. Find i such that m(i) = 0.
2/9, 48
Let h(y) be the first derivative of 4*y**3 - 68 + 9*y**2 + 8*y + 1/2*y**4. Factor h(s).
2*(s + 1)**2*(s + 4)
Let n(z) be the second derivative of -z**6/180 - 7*z**5/30 + 8*z**4/3 - 2*z**3/3 - 15*z**2 + 122*z. Let o(g) be the second derivative of n(g). Solve o(f) = 0.
-16, 2
Let u(c) = -3*c + 53. Let s = -57 - -74. Let w be u(s). Let -2*g - 25*g + 18 + 3*g**w + 6*g = 0. Calculate g.
1, 6
Let g be 9 + -6 - ((-1)/1 + -1). Suppose 5*f = g*j - 100, -j + 2*f = -3*j + 60. Find p such that -36 - 39*p**2 + 76*p + j*p**2 - 30*p**2 + 4*p**3 = 0.
1, 9
Let b(h) = 10*h**2 - 6*h - 3. Let d(l) = l**3 + 24*l**2 - 52*l - 2. Let m be d(-26). Let x(f) = f**2 + f - 1. Let s(q) = m*b(q) + 14*x(q). Solve s(k) = 0 for k.
1/3, 4
Let u(z) be the first derivative of 10 - 9/2*z**2 + 8*z + 26/3*z**3 + 9/4*z**4. Let r(i) = -3*i**3 - 9*i**2 + 3*i - 3. Let o(b) = 17*r(b) + 6*u(b). Factor o(m).
3*(m - 1)*(m + 1)**2
Let z(x) = -17*x**3 - 325*x**2 + 557*x + 181. Let a(i) = 101*i**3 + 1941*i**2 - 3343*i - 1087. Let b(r) = -6*a(r) - 34*z(r). Factor b(s).
-4*(s - 2)*(s + 23)*(7*s + 2)
Suppose 0 = 17*b - 122 - 252. Suppose 7*t + 1 = b. Determine r so that -1/2*r - 3 + 1/2*r**3 + t*r**2 = 0.
-6, -1, 1
Let r = 823064 + -120990871/147. Let j = -40/49 - r. What is u in j*u**3 + u**4 - 4*u**2 + 4/3*u - 2/3*u**5 + 0 = 0?
-2, 0, 1/2, 1, 2
Suppose -23*l + 35000 = 2*l. Let z = l - 1398. Factor -1/2 - 1/4*x**z + 3/4*x.
-(x - 2)*(x - 1)/4
Solve -24/5*l**3 + 0 + 122/5*l**2 - 2/5*l**4 - 96/5*l = 0 for l.
-16, 0, 1, 3
Let c = -58367 + 175109/3. Solve -c*v**4 - 8/3 + 2/3*v**5 + 16/3*v**2 - 4/3*v**3 + 2/3*v = 0 for v.
-1, 1, 4
Let r(q) = -q**3 - 55*q**2 - 56*q - 102. Let v be r(-54). Let c be -1 - (-159)/153 - v/(-9). Find w, given that -c*w - 2/17*w**2 + 14/17 = 0.
-7, 1
Let h = 47641/63516 - 1/15879. Let l(d) be the first derivative of 2 + 1/12*d**3 - 1/4*d**2 - h*d. Factor l(g).
(g - 3)*(g + 1)/4
Let g(a) = -10*a**2 - 54*a - 28. Let r(v) = -3*v**2 - 7. Let h(t) = -g(t) + 4*r(t). Factor h(n).
-2*n*(n - 27)
Factor -12*q**2 - 92/5*q - 4/5*q**3 + 156/5.
-4*(q - 1)*(q + 3)*(q + 13)/5
Suppose -s = 5*j - 22 - 42, 3*j + 4*s - 35 = 0. Let y be 217/42 + (j/(-6) - -2). Find n, given that -2/5*n**y + 0 + 0*n**3 + 4/5*n**2 - 4/5*n**4 + 2/5*n = 0.
-1, 0, 1
Let o(j) be the second derivative of 5*j**4/12 + 685*j**3/3 - 1380*j**2 - 1765*j. Factor o(x).
5*(x - 2)*(x + 276)
Determine r, given that 320/3*r**2 + 0*r + 2/3*r**4 - 88/3*r**3 + 0 = 0.
0, 4, 40
Let d be (31/(-11) - 1/(-1) - 98/(-49))*11. Factor i**4 - 1/3*i**5 + 0 + 0*i**3 - 4/3*i**d + 0*i.
-i**2*(i - 2)**2*(i + 1)/3
Let b(j) be the second derivative of j**7/6720 + 3*j**6/320 - 23*j**4/4 + 4*j + 1. Let r(q) be the third derivative of b(q). Find u, given that r(u) = 0.
-18, 0
Let s be 1 + 45819/14076 + -4. Let u = s + -2/391. Factor -u*c**3 + 1/8*c**4 + 1/4*c - 1/8 + 0*c**2.
(c - 1)**3*(c + 1)/8
Let g be (12/(-22))/(24/(-132)). Find v such that 35*v**2 + 2*v**4 + v**4 + 42*v**g - 168*v + 100*v**2 + 342 - 930 = 0.
-7, -2, 2
Let k(u) = 2*u**2 - 30*u - 417. Let m(z) = -2*z**2 + 24*z + 412. Let h(a) = 4*k(a) + 5*m(a). Factor h(p).
-2*(p - 14)*(p + 14)
Suppose 56*g + 56 = 55*g. Let j be 2/1 - -3 - (-28)/g. Factor -j*i - 1/2*i**3 + 0 + 3*i**2.
-i*(i - 3)**2/2
Let z be (-1)/2 - -121*(-7)/(-1680). Let v(b) be the third derivative of 0*b**3 + 23*b**2 + 0 + z*b**5 + 0*b - 1/48*b**4. Factor v(n).
n*(n - 2)/4
Suppose 7*w - 26 = 2. Let d be 12/(w*(-5)/(-10)). Let k**2 - 2*k**2 - d*k - k**2 = 0. Calculate k.
-3, 0
Determine l so that -1217307 + 1911*l - 3/4*l**2 = 0.
1274
Let d = -864899/11 - -78628. Factor d*n**3 + 12/11*n**2 - 2/11 + 1/11*n.
(n + 1)*(3*n - 1)*(3*n + 2)/11
Let o(i) be the second derivative of i**4/42 - 65*i**3/21 + 18*i**2 + 50*i - 12. Factor o(r).
2*(r - 63)*(r - 2)/7
Let z(k) be the first derivative of 3*k**5/4 - 55*k**4/24 + 5*k**3/3 + 85*k**2/2 - 54. Let w(g) be the second derivative of z(g). Suppose w(u) = 0. Calculate u.
2/9, 1
Let v(x) be the first derivative of 28561/2*x**6 + 3888*x + 158 + 243867/5*x**5 + 66924*x**4 + 47736*x**3 + 18792*x**2. Factor v(k).
3*(k + 1)*(13*k + 6)**4
Let v(z) be the third derivative of -z**7/525 + 13*z**6/150 + 29*z**5/150 - 9*z**4/10 + z**2 - 2782*z. Determine s so that v(s) = 0.
-2, 0, 1, 27
Let z(q) be the first derivative of -q**3/3 - 17*q**2/2 - 60*q - 11528. Let z(u) = 0. What is u?
-12, -5
Let b(w) be the first derivative of -5*w**4/48 + 13*w**3/12 - 5*w**2/8 + 79*w + 62. Let t(s) be the first derivative of b(s). Let t(u) = 0. What is u?
1/5, 5
Let z = 240844 + -240834. Factor 80*n**3 + 15/2 - 50*n**2 - z*n.
5*(2*n - 1)**2*(8*n + 3)/2
Let b(v) be the second derivative of -v**7/42 + v**6/30 + 7*v**5/20 - 13*v**4/12 + v**3 - 2*v - 121. Factor b(k).
-k*(k - 2)*(k - 1)**2*(k + 3)
Let h(b) be the first derivative of 1/10*b**4 - 74 - 1/5*b**2 + 18/5*b - 6/5*b**3. Solve h(j) = 0 for j.
-1, 1, 9
Let k be 11/(-2)*6424/220. Let i = 161 + k. Determine n, given that -i*n - 1/5*n**3 + 0 + 3/5*n**2 = 0.
0, 1, 2
Let i = 126 + -123. Suppose 4*s - 10 = i*m, -3*m + 5*s = -8*m + 30. Factor 0 + 0*w - 5/3*w**5 + 0*w**m + 10/3*w**4 - 5/3*w**3.
-5*w**3*(w - 1)**2/3
Let t(q) = q**3 + q + 5. Let p(m) = 5*m**3 + 912*m**2 - 2761*m + 10. Let g(o) = p(o) - 2*t(o). Suppose g(d) = 0. Calculate d.
-307, 0, 3
Let g(f) be the first derivative of -5*f**6/4 - 163*f**5/10 - 143*f**4/8 + 907*f**3/6 - 329