. Calculate h.
-5, -2, 2
Determine x, given that 21/2*x**2 - 3/2*x**3 + 147/2*x - 1029/2 = 0.
-7, 7
Let t(c) be the first derivative of c**7/420 + 2*c**6/15 - 148*c**3/3 - 106. Let m(i) be the third derivative of t(i). Factor m(n).
2*n**2*(n + 24)
Let v(g) = 4*g - 3*g - 3 + 0 + 1. Let a be v(5). Factor -343*l + 343*l + 10*l**2 + 5*l**a.
5*l**2*(l + 2)
Let h(k) be the third derivative of -61*k**5/180 - k**4/2 + 8*k**2 - 74. Let h(m) = 0. Calculate m.
-36/61, 0
Factor 2/15*w**2 + 84 + 194/15*w.
2*(w + 7)*(w + 90)/15
Let k be (-14)/(-980)*10 - (-700)/588. Determine f, given that -40/3*f - k - 53/3*f**2 - 17/3*f**3 = 0.
-2, -1, -2/17
Let q(x) be the first derivative of -x**5/20 - x**4/16 + 2*x**3/3 + 3*x**2/2 + 1577. Let q(c) = 0. Calculate c.
-2, 0, 3
Let c(m) be the third derivative of m**8/112 - m**7/35 - 27*m**6/20 - 22*m**5/5 + 53*m**4/8 + 45*m**3 + 2*m**2 - 7*m - 14. Suppose c(q) = 0. Calculate q.
-5, -2, -1, 1, 9
Suppose -2 = 4*p - 5*x, 0 = 479*p - 477*p - 3*x + 2. Let -3/4*f + 3/2*f**p + 0 = 0. What is f?
0, 1/2
Let z(x) be the third derivative of x**5/20 - 3*x**4/2 + 11*x**3/2 + 122*x**2. Factor z(q).
3*(q - 11)*(q - 1)
Suppose 244*z - 250*z = 24. Let h be 2 + 0 + (8 - 4) + z. Factor -8/11*l - 24/11*l**h - 10/11*l**3 + 0.
-2*l*(l + 2)*(5*l + 2)/11
Let s(w) be the third derivative of -w**6/900 - 14*w**5/75 + 29*w**4/15 - 352*w**3/45 - 954*w**2. Suppose s(x) = 0. What is x?
-88, 2
Let p(m) be the third derivative of m**8/112 - m**7/10 - 69*m**6/40 - 117*m**5/20 + 2931*m**2. Factor p(c).
3*c**2*(c - 13)*(c + 3)**2
Let s(c) be the third derivative of -c**5/330 - 31*c**4/66 - 61*c**3/33 + 3029*c**2. Factor s(y).
-2*(y + 1)*(y + 61)/11
Let b(d) = 3*d**2 - 7*d - 63. Let s be b(6). Let a(u) be the third derivative of 7/180*u**5 + 0 + 0*u - 12*u**2 - 1/9*u**s - 5/72*u**4. Solve a(p) = 0 for p.
-2/7, 1
Determine x, given that -171/2*x + 324 - 1/6*x**3 + 7*x**2 = 0.
9, 24
Let n be 1280/4800*(-3)/(-2). Factor 0 + 4/5*j + 0*j**3 + n*j**4 - 6/5*j**2.
2*j*(j - 1)**2*(j + 2)/5
Let g be 14/4 + 1/(-2) - (-3977 - -3971). Let -6*d**2 - 3/4*d**5 + 3/2*d**4 + 0 + 21/4*d**3 - g*d = 0. What is d?
-2, -1, 0, 2, 3
Let s(j) = -j**3 - 7*j**2 - 7*j - 32. Let c be s(-7). Determine n so that -c*n - 8 + 17*n + 5*n**2 + 33 - 30*n = 0.
1, 5
Let v(n) be the third derivative of 0 - 1/3*n**3 + n + 1/90*n**5 - 1/18*n**4 - 31*n**2. Determine j, given that v(j) = 0.
-1, 3
Suppose 2*x = 3*a - 2113 + 2097, -5*x - 35 = -5*a. Determine f, given that 0*f**3 + 0 - 2/3*f**4 + 0*f + 8/3*f**a = 0.
-2, 0, 2
Let c = 417600/7 - 59656. Determine h, given that 19/7*h**2 + 2/7*h**3 + c + 25/7*h = 0.
-8, -1, -1/2
Let r be (-25)/3*((-35)/10)/7*(-12 - -15). Factor -r*y**3 - 7*y**4 - 6*y**2 + 0*y - 1/2*y**5 + 0.
-y**2*(y + 1)**2*(y + 12)/2
Let q(i) = 2*i**3 - 7*i**2 + 6*i + 8. Let h be q(4). Let c be (h/(-45))/(-3 + 13/5). Suppose 0 - c*s**2 - 10/3*s**3 - 8/15*s = 0. What is s?
-2/5, 0
Let o(s) be the third derivative of s**6/280 + 3*s**5/7 + 59*s**4/56 - 3*s**2 - 11*s. What is k in o(k) = 0?
-59, -1, 0
Let 43*t - 14 + 24*t**2 + t**4 - 2*t**4 - 30*t + 10*t**2 - 19*t**2 - 13*t**3 = 0. Calculate t.
-14, -1, 1
Factor 3858642*w + 2778*w**2 + 1786551246 + 2/3*w**3.
2*(w + 1389)**3/3
Let r = 16138 + -16138. Let y(p) be the second derivative of 0*p**2 + 1/10*p**5 + r + 21*p - p**3 + 1/3*p**4. Let y(j) = 0. What is j?
-3, 0, 1
Suppose -1 = -3*c - 5*g, -3*g = 2*c + 11 - 12. Let -6/5 + 1/5*n**c + n = 0. What is n?
-6, 1
Determine z, given that 44/5*z**3 - 64*z + 512/5 + 4/5*z**4 - 64/5*z**2 - 1/5*z**5 = 0.
-4, 2, 8
Let w(y) be the first derivative of 9/2*y**2 - 3/20*y**5 - 10 - 6*y + 5/4*y**4 - 7/2*y**3. Let h(m) be the first derivative of w(m). Factor h(c).
-3*(c - 3)*(c - 1)**2
Let n(w) be the second derivative of -w**5/10 - 61*w**4/12 - 71*w**3/3 - 28*w**2 - 2894*w - 2. Factor n(m).
-(m + 2)*(m + 28)*(2*m + 1)
Let h(c) be the second derivative of c**6/1800 + c**5/150 - c**4/24 - c**3/6 + c**2 + 2*c. Let v(p) be the second derivative of h(p). Solve v(u) = 0 for u.
-5, 1
Let m(q) be the second derivative of q**9/7560 + q**8/1120 - q**7/1260 - q**6/120 + q**4/3 + q**2 + 12*q. Let h(k) be the third derivative of m(k). Factor h(d).
2*d*(d - 1)*(d + 1)*(d + 3)
Let u(i) = -3*i**3 - 15*i**2 - 31*i - 153. Let a be u(-5). Determine g so that 4/7*g + 2/7*g**a + 2/7 = 0.
-1
Let d be (-15)/105 + 80160/21. Let -d - 93*m**2 + 3817 - 3*m**3 - 6*m**2 = 0. What is m?
-33, 0
Suppose -790/3*d - 5/3*d**2 + 1080 = 0. What is d?
-162, 4
Let t(h) = -h**3 - 4*h**2 + 4*h - 3. Let l be t(-5). Determine d so that 3*d + 6*d - l*d**3 + d + 4*d**2 - 12*d**2 = 0.
-5, 0, 1
Let a(i) be the third derivative of -i**6/30 + 117*i**5/5 - 13689*i**4/2 + 1067742*i**3 + 1148*i**2. Find d such that a(d) = 0.
117
Factor -2/3*y**2 + 4/3*y + 2.
-2*(y - 3)*(y + 1)/3
Let w(g) = -2*g**3 + 7*g**2 + 3*g + 7. Let r be w(4). Let -150 + 24*c + 60 + 42 - r*c**2 = 0. Calculate c.
4
Let q be (-172)/903*9*7*1/(-7). Let 3*b - 3*b**3 - 6/7 - q*b**4 + 18/7*b**2 = 0. Calculate b.
-2, -1, 1/4, 1
Let c = -14 - -26. Suppose -t + 50 = -4*d, 5*d - d = 3*t - 118. Factor t - h**2 - 35 - c*h - 35.
-(h + 6)**2
Let r(s) = 13*s**2 + s - 2. Let m be r(1). Suppose -m*k = -16*k. Let 0*j**2 + 1/6*j**3 - 1/6*j + k = 0. Calculate j.
-1, 0, 1
Determine q so that 133*q**2 - 76821*q**3 - 45*q**4 + 76854*q**3 + 8*q**2 + 84 + 3*q**5 - 216*q = 0.
-2, 1, 14
Let k(a) = 5*a**3 - 3*a**2 - 27*a - 32. Let d = -80 - -96. Let p(t) = 26*t**3 - 16*t**2 - 136*t - 160. Let x(u) = d*k(u) - 3*p(u). Factor x(s).
2*(s - 4)*(s + 2)**2
Let r(m) = 39*m**3 - 1433*m**2 + 26488*m + 365048. Let q(n) = -14*n**3 + 478*n**2 - 8828*n - 121683. Let l(c) = 8*q(c) + 3*r(c). Solve l(a) = 0.
-9, 52
Find u, given that 378/5*u - 1822/5*u**2 + 262/5*u**4 + 1174/5*u**3 + 8/5*u**5 + 0 = 0.
-27, -7, 0, 1/4, 1
Let j(u) be the first derivative of -5*u**3/12 - 335*u**2/8 - 590*u + 4021. Factor j(l).
-5*(l + 8)*(l + 59)/4
Let w(k) be the second derivative of 121*k**5/80 - 3773*k**4/24 + 683*k**3/6 - 31*k**2 + 2872*k + 2. Solve w(u) = 0 for u.
2/11, 62
Factor 1/10*a**3 + 0 + 12/5*a - a**2.
a*(a - 6)*(a - 4)/10
Let c(l) = l**5 - l**4 - l - 1. Let f(d) = -11*d**5 + 7*d**4 + 45*d**3 - 77*d**2 + 46*d + 10. Let a(q) = 30*c(q) + 3*f(q). Find r such that a(r) = 0.
-9, 0, 1, 4
Factor -2023*f - 1/2*f**2 - 4092529/2.
-(f + 2023)**2/2
Let w(k) be the first derivative of -3*k**5/35 + 15*k**4/28 - k**3/7 - 9*k**2/2 + 54*k/7 - 579. Suppose w(i) = 0. What is i?
-2, 1, 3
Suppose 21/5*g**2 - 18/5*g + 1/5*g**4 + 0 - 8/5*g**3 = 0. Calculate g.
0, 2, 3
Let a(m) be the third derivative of 4/105*m**7 + 202*m**2 + 1/12*m**4 - 2/15*m**5 + 0*m**3 + 0 + 1/30*m**6 + 0*m - 1/56*m**8. Determine z so that a(z) = 0.
-1, 0, 1/3, 1
Find u, given that -7521*u + 1621*u**2 + 324818 + 94520*u - 5937*u + 245368*u - 7*u**2 + 2*u**3 = 0.
-403, -1
Let q(l) be the first derivative of 10/9*l**3 - 2/3*l**5 - l**2 + 5/6*l**4 + 0*l - 2/9*l**6 - 42. Determine d so that q(d) = 0.
-3, -1, 0, 1/2, 1
Suppose 5*s - 3*z + 0*z = -12, 8*s - 2*z + 8 = 0. Let b(m) be the second derivative of -1/48*m**4 - 1/160*m**5 + 2*m + s*m**3 + 0*m**2 + 0. Factor b(l).
-l**2*(l + 2)/8
Let b be (56/42)/(4/6). Suppose 4*p = b*m - 4, 0*p - p - 5*m = -10. Find z such that 1 + 1/4*z**4 - 5/4*z**2 + p*z + 0*z**3 = 0.
-2, -1, 1, 2
Let q be (-10)/(-15)*12744/(-9). Let j = -4719/5 - q. Factor -14/5*n + 49/5 + j*n**2.
(n - 7)**2/5
Let m(x) be the second derivative of 15 + 10/9*x**4 + 0*x**2 - 4*x - 100/9*x**3 - 1/30*x**5. Factor m(t).
-2*t*(t - 10)**2/3
Let u(z) be the third derivative of 0 + 0*z**3 + 1/300*z**6 + 0*z - 112*z**2 + 1/10*z**4 + 7/150*z**5. Suppose u(g) = 0. What is g?
-6, -1, 0
Let a = 109781/8 - 329263/24. Determine y so that a + 28/9*y - 2/9*y**2 = 0.
-1, 15
Let g(p) be the second derivative of p**4/4 - 92*p**3 + 12696*p**2 + 4*p + 28. Suppose g(y) = 0. Calculate y.
92
Suppose -2*n + 4*n = 4. Factor -175*w**n - 3 + 173*w**2 + 5.
-2*(w - 1)*(w + 1)
Suppose 26 = a + 4*j, 804*a + j - 16 = 799*a. Suppose -3/2 + 3/2*l**a + 1/4*l**3 - 1/4*l = 0. Calculate l.
-6, -1, 1
Let r(w) = -w**2 + 12*w + 220. Let c be r(22). Let s(b) be the first derivative of 4/3*b**3 + 0*b**2 - 19 - 1/2*b**4 - 2/5*b**5 + c*b. Factor s(l).
-2*l**2*(l - 1)*(l + 2)
Let q(u) = 8*u**2 - 1400*u + 122544. Let g(l) = 23*l**2