2, 59
Let i(k) be the third derivative of -k**5/20 + 59*k**4/8 - 57*k**3 - 359*k**2 - 16*k. Suppose i(a) = 0. What is a?
2, 57
Let c be ((-4)/(-6))/((-20)/(-150)). Factor c*n + 556*n**2 - 30 - 555*n**2 + 24*n.
(n - 1)*(n + 30)
Suppose 69*t - 8970 = 54*t. Let m = t - 596. Factor -2/5 - 6/5*j**2 + m*j - 18/5*j**3.
-2*(j + 1)*(3*j - 1)**2/5
Let m(f) be the first derivative of -f**6/12 - 29*f**5/5 + f**4/8 + 29*f**3/3 - 1286. What is j in m(j) = 0?
-58, -1, 0, 1
Let t = 99 - 98. Let g be 25 + (t/(-3))/(1/9). Solve -28*j - g*j + 5*j**2 + 42 + 83 = 0 for j.
5
Suppose -7 = 2*p - 3*w - 32, 10 = 2*p + 2*w. Suppose p*b - 18 = -2. Suppose -33 + 49 + 6*c**3 + 23*c + 17*c + 28*c**b = 0. Calculate c.
-2, -2/3
Let v(h) be the third derivative of -h**8/147 + 2*h**7/105 + 27*h**6/35 + 296*h**5/105 + 32*h**4/21 - 7*h**2 - 5*h - 2. Find u such that v(u) = 0.
-4, -2, -1/4, 0, 8
Let c(j) be the second derivative of 2*j**6/15 - 16*j**5/5 - 260*j**4/3 - 2102*j. Factor c(s).
4*s**2*(s - 26)*(s + 10)
Suppose -3*z - 21 = -5*i, 0 = 105*i - 101*i - 5*z - 35. Let s(j) be the third derivative of 5/3*j**3 + 0*j + 29*j**2 + i + 1/30*j**5 + 1/2*j**4. Factor s(g).
2*(g + 1)*(g + 5)
Suppose -4*m = 3*m - 742. Suppose m*w = 108*w - 6. Suppose g**4 + g**4 + 34*g - 16*g + 6*g**2 - 10*g**w = 0. What is g?
-1, 0, 3
Let i(c) be the second derivative of -7/15*c**3 + 48*c + 8/5*c**2 + 0 - 1/30*c**4. Factor i(w).
-2*(w - 1)*(w + 8)/5
Let n be ((-46)/230)/((-10)/(-6) - (28 - 26)). Factor -n*x - 2/5*x**2 + 3/5*x**3 + 2/5.
(x - 1)*(x + 1)*(3*x - 2)/5
Let g(j) = 13*j - 4 - 13*j**2 - 37*j**2 + 10*j. Let s(o) = -o**2 - o + 1. Let m(p) = 2*g(p) + 4*s(p). Find a, given that m(a) = 0.
2/13, 1/4
Let g(z) be the first derivative of -z**3 + z**2 + 4*z + 55. Let f be 2 - (-2 - (-2 + 7)). Let k(l) = 7*l**2 - 4*l - 9. Let t(o) = f*g(o) + 4*k(o). Factor t(y).
y*(y + 2)
Let l = 2033 + -2027. Let q(z) be the third derivative of 0*z - l*z**2 - 1/150*z**5 + 1/15*z**4 + 0 - 1/5*z**3. Determine d so that q(d) = 0.
1, 3
Suppose 0 = 1718*n - 1714*n - 8. Suppose -5*r = 5*g - 5, 0*g = 2*g + r - 4. Factor 0 + 5/2*c**g - c + 3/2*c**n.
c*(c + 1)*(5*c - 2)/2
Let l(a) be the third derivative of -a**7/945 - 3*a**6/20 - 157*a**5/270 + 3*a**4/4 + 158*a**3/27 - 3*a**2 + 4*a - 82. Let l(f) = 0. Calculate f.
-79, -2, -1, 1
Suppose 5*b - 3*x + 866 = 0, -4*x = -9*b + 5*b - 696. Let l be 5 + b/40 - 1/2. Solve 0*t - 4/5 + l*t**2 = 0 for t.
-2, 2
Suppose 40*i = 58*i - 180. Let y(p) be the second derivative of 0 + 1/2*p**2 + 1/60*p**4 + 1/5*p**3 - i*p. Suppose y(a) = 0. What is a?
-5, -1
Factor -372/11*c**2 - 376/11*c - 126/11 + 2/11*c**4 - 120/11*c**3.
2*(c - 63)*(c + 1)**3/11
Factor 777924/5 + 1764/5*o + 1/5*o**2.
(o + 882)**2/5
Let a(c) be the third derivative of -c**5/150 + 436*c**4/15 - 760384*c**3/15 + 2861*c**2. Factor a(m).
-2*(m - 872)**2/5
Let s(i) be the third derivative of -i**7/70 + 11*i**6/40 + 9*i**5/10 - 9*i**4 + 2*i**2 + 54*i. Determine m so that s(m) = 0.
-3, 0, 2, 12
What is q in 464/5*q - 1/5*q**3 - 2112/5 - 17/5*q**2 = 0?
-33, 8
Let h(s) = 17*s**3 + 36*s**2 - 77*s - 114. Let d(x) = 240*x**3 + 505*x**2 - 1075*x - 1595. Let w(a) = -6*d(a) + 85*h(a). Solve w(m) = 0 for m.
-8, -1, 3
Solve 109/3*o**2 - 4/3 + 68/3*o + 37/3*o**3 = 0.
-2, -1, 2/37
Let u(i) = -39*i**3 - 4*i**2 - 6*i + 2. Let m be u(-2). Determine p so that 190*p**4 - 12 - 85*p - 45*p**5 + 13 + 9 - m*p**3 + 240*p**2 = 0.
2/9, 1
Let v(t) be the second derivative of -t**6/6 + 33*t**5/2 + 1735*t**4/12 + 470*t**3 + 710*t**2 + 2*t + 74. Solve v(y) = 0.
-2, -1, 71
Let c(t) be the second derivative of t**4/72 - 391*t**3/18 + 152881*t**2/12 + 13*t. Determine i, given that c(i) = 0.
391
Let p = 289224/13645 - -10/2729. Find q, given that -26/5*q**4 + 14/5*q - 8/5*q**5 + 114/5*q**3 - p*q**2 + 12/5 = 0.
-6, -1/4, 1
Let n(m) be the third derivative of 0*m + 1/6*m**5 + 0 + 1/24*m**6 - 5/24*m**4 - 5/3*m**3 - 62*m**2. Factor n(b).
5*(b - 1)*(b + 1)*(b + 2)
Let j(r) = 40*r**2 + 1326*r + 1884. Let b(i) = 2*i**2 + 20*i. Let n(d) = 38*b(d) - 2*j(d). Factor n(f).
-4*(f + 2)*(f + 471)
Let b(c) be the third derivative of c**8/3360 + 11*c**7/1050 - 157*c**6/1200 + 151*c**5/300 - 7*c**4/10 - 1662*c**2. Solve b(o) = 0.
-28, 0, 1, 2, 3
Let o(a) be the second derivative of a**6/780 - 8*a**5/195 + 5*a**4/39 + 400*a**3/39 - 61*a**2 - a + 14. Let b(l) be the first derivative of o(l). Factor b(m).
2*(m - 10)**2*(m + 4)/13
Let y = 11749/220 - 1769/44. Factor -21*g + 9/5*g**2 + y.
3*(g - 11)*(3*g - 2)/5
Let s be 36 + (20313/(-703) - 7). Factor -s*w**3 - 162/19 + 34/19*w**2 - 126/19*w.
-2*(w - 9)**2*(w + 1)/19
Let i = 22575 + -135445/6. Let b(v) be the second derivative of i*v**3 + 29*v + 5*v**2 - 5/4*v**4 + 0. Factor b(c).
-5*(c - 1)*(3*c + 2)
Let h = 5731 - 452740/79. Let k = h + 192/395. Find r such that 9/5*r**3 + k*r**2 - 3/5*r - 6/5*r**5 + 0 - 3/5*r**4 = 0.
-1, 0, 1/2, 1
Let a = -97 - -67. Let o be (a/(-50) - 6/10)/(-4). Factor o*q**3 + 1/4*q**2 + 0 - 1/4*q**4 + 0*q.
-q**2*(q - 1)*(q + 1)/4
Let v(x) be the first derivative of -x**6/2 - 51*x**5/5 + 9*x**4/4 + 913*x**3 + 2541*x**2 - 481. Find m such that v(m) = 0.
-11, -2, 0, 7
Let t be 270/117 + 2583/(-1170). Determine n, given that 2/5 + 3/5*n**3 + 6/5*n + t*n**4 + 13/10*n**2 = 0.
-2, -1
Let n(v) be the first derivative of 1/4*v**4 - 16*v + 0*v**2 + 17 - 1/10*v**6 + 3/5*v**5 - 2*v**3. Let m(f) be the first derivative of n(f). Factor m(w).
-3*w*(w - 4)*(w - 1)*(w + 1)
Let x be 0 + (3 - (-6)/(-2)). Let d be (-3 - -11)/1 - (6 - 0/4). Solve x + 16/11*l + 2/11*l**d = 0 for l.
-8, 0
Find h, given that -36/5 - 48/5*h**3 - 24*h**2 - 4/5*h**4 - 112/5*h = 0.
-9, -1
Let r = -915 - -679. Let k = 1184/5 + r. Let -2/5*x**2 - k*x + 0 = 0. What is x?
-2, 0
Let n(y) be the third derivative of 37 + 0*y**3 + 0*y**4 - 5/12*y**5 - 1/84*y**7 + 0*y - y**2 - 7/48*y**6. Suppose n(c) = 0. Calculate c.
-5, -2, 0
Let w(z) be the second derivative of z**5/130 - 111*z**4/26 - 112*z**3/13 + 668*z**2/13 - 5*z + 6. Solve w(c) = 0 for c.
-2, 1, 334
Let f(m) = m**3 - m**2 + 5. Let q(d) = -2*d**3 - 38*d**2 + 280*d + 10. Let s(t) = -2*f(t) + q(t). Determine v, given that s(v) = 0.
-14, 0, 5
Let m(a) = -5*a**3 + 60*a**2 + 3043*a - 3122. Let w(d) = -10*d**3 + 120*d**2 + 6085*d - 6255. Let i(s) = -5*m(s) + 2*w(s). Factor i(b).
5*(b - 31)*(b - 1)*(b + 20)
Solve 7394*v**3 - 331*v**2 - 7391*v**3 - 842*v**2 - 1176*v = 0.
-1, 0, 392
Let a(u) be the first derivative of -u**5 - 55*u**4/4 - 35*u**3/3 + 735*u**2/2 + 1153. Factor a(x).
-5*x*(x - 3)*(x + 7)**2
Let p be ((-121)/22 - -6)*(4 - 20/7). Determine w so that -2/7*w**5 + 0*w - p*w**2 + 0*w**4 + 0 + 6/7*w**3 = 0.
-2, 0, 1
Let k = 1457 - 1465. Let n be (1 + 6/k)*(-1136)/(-1846). Factor -2/13*y - 4/13 + n*y**2.
2*(y - 2)*(y + 1)/13
Let k = 1102934 + -1099454. Factor 1008 - k*q - 1172/7*q**2 - 2*q**3.
-2*(q + 42)**2*(7*q - 2)/7
Let y(b) = 2*b**2 - 2*b + 1. Let i(m) = -8*m**2 + 82*m - 607. Let d(a) = -i(a) - 5*y(a). Solve d(l) = 0 for l.
-43, 7
Let u(g) = 128*g**3 + 31609*g**2 + 25220*g + 5043. Let w(t) = 127*t**3 + 31606*t**2 + 25220*t + 5042. Let q(f) = 2*u(f) - 3*w(f). Factor q(c).
-5*(c + 252)*(5*c + 2)**2
Let -80*s**3 - 4468*s**5 - 10*s**4 - 6 - 70*s**2 + 6 - 15*s + 4483*s**5 = 0. What is s?
-1, -1/3, 0, 3
Let -4748/5*u - 2/5*u**2 - 2817938/5 = 0. Calculate u.
-1187
Let a(z) = -2*z**3 + 4*z**2 + 5*z + 1. Let o be a(-1). Let 27 - 17 + 5 + 39*u + 24*u**o = 0. What is u?
-1, -5/8
Let o be 2496/(54 + -106) - -48. Solve -7/4*k**2 - 9*k + o = 0 for k.
-36/7, 0
Let c = 10397/3030 - 199/1515. Factor c - 4/5*w - 1/10*w**2.
-(w - 3)*(w + 11)/10
Let d be 6*3/144 - (258/144 - 3). Solve 16/3 + 20/3*p**3 - 4/3*p**4 - 4/3*p**5 - 32/3*p + d*p**2 = 0.
-2, 1
Let v be (25 - -5)/6 - 8. Let b be (-15)/90 - (0 + v/2). What is u in -2*u + 2/3 - 2*u**4 + b*u**3 + 4/3*u**2 + 2/3*u**5 = 0?
-1, 1
Let a = -5333/4 - -16001/12. Let p(n) be the second derivative of 2/3*n**3 - 1/10*n**5 + 0 + 0*n**2 + 22*n + a*n**4. Determine c so that p(c) = 0.
-1, 0, 2
Let l(a) be the second derivative of -a**6/135 - 7*a**5/18 - 55*a + 4. Suppose l(g) = 0. What is g?
-35, 0
Let n(u) be the second derivative of -u**7/168 - 31*u**6/120 - 111*u**5/80 - 77*u**4/48 + 14*u**3/3 + 27*u**2/2 - 1623*u. Suppose n(j) = 0. Calculate j.
-27, -2, -1, 1
Factor 82*t**4 + 80*t**4