**3/6 + 5*m**2 + 9*m + 81. Factor n(w).
5*(w + 2)*(204*w + 1)**2
Solve -438*h + 12 + 434/3*h**2 = 0.
6/217, 3
Let g(r) be the third derivative of r**8/336 + 207*r**7/70 + 32033*r**6/40 - 96721*r**5/60 + 3*r**2 - 31*r + 1. Factor g(w).
w**2*(w - 1)*(w + 311)**2
Let i = -12327 - -12330. Let w(f) be the first derivative of 0*f**4 + 1/6*f**6 - 1/2*f**2 - 2/5*f**5 + 18 + 0*f + 2/3*f**i. Factor w(n).
n*(n - 1)**3*(n + 1)
Let n = -123 + 131. Let f(x) = x**2 + 12*x + 1. Let u be f(-12). What is a in -8*a**2 - 2*a + 1 - u + 2 + n*a = 0?
-1/4, 1
Let t(k) be the third derivative of 1/210*k**7 - 72*k**2 - 1/30*k**5 + 0*k**4 + 0*k**6 + 1/6*k**3 - 2*k + 0. What is x in t(x) = 0?
-1, 1
Factor 1444/3*p**3 + 19040*p - 78400/3 + 6612*p**2.
4*(p - 1)*(19*p + 140)**2/3
Let w(y) be the second derivative of -y**7/63 + 22*y**6/45 - 7*y**5/3 - 274*y**4/9 - 793*y**3/9 - 338*y**2/3 + 2*y - 335. Suppose w(b) = 0. Calculate b.
-2, -1, 13
Let c = -42 - -72. Suppose -50*w + c*w - 2*w**3 - 5*w**4 - 40 + w**3 + 6*w**3 + 30*w**2 = 0. What is w?
-2, -1, 2
Let t(y) be the second derivative of 35*y**4/12 - 25*y**3/2 + 5*y**2 - 4*y + 59. Factor t(r).
5*(r - 2)*(7*r - 1)
Let k(t) = -29*t**2 - 997*t + 998. Let m(u) = -20*u**2 - 665*u + 665. Let v(z) = 5*k(z) - 7*m(z). Factor v(i).
-5*(i - 1)*(i + 67)
Let t = 534922/5 - 106978. What is q in -18/5*q**2 - t + 148/5*q = 0?
2/9, 8
What is b in 6498/17 + 228/17*b + 2/17*b**2 = 0?
-57
Let g(v) = 12*v**4 + 2*v**3 - v**2 + 1. Let t(n) = -35*n**4 + 6*n**3 - 38*n - 27. Let o(u) = -3*g(u) - t(u). Determine f so that o(f) = 0.
-12, -1, 2
Let y(v) be the third derivative of v**5/60 - 307*v**4/24 + 51*v**3 + 679*v**2. Factor y(d).
(d - 306)*(d - 1)
Determine s so that -110 - 1/2*s**2 - 49/2*s = 0.
-44, -5
Let o(l) be the first derivative of -15*l**4 + 535*l**3/3 - 795*l**2/2 - 70*l - 583. Factor o(g).
-5*(g - 7)*(g - 2)*(12*g + 1)
Let u = -34 - -84. Suppose 6*f - 170 = -u. Factor -f*q - 3*q**2 + 16*q - q**2 + 12*q.
-4*q*(q - 2)
Determine u, given that 76/3*u - 4 + 13/3*u**2 = 0.
-6, 2/13
Factor -462/23*l + 2/23*l**2 + 0.
2*l*(l - 231)/23
Let z(y) be the second derivative of 0*y**3 + 1/225*y**6 + 1/45*y**4 - 7 + 0*y**2 + 1/50*y**5 + 9*y. Factor z(f).
2*f**2*(f + 1)*(f + 2)/15
Suppose -71*d = -88*d + 55216. Let w be (2/24 + 0)/(812/d). Solve -2 + w*r**2 + 5/3*r = 0.
-6, 1
Let -74/5*o**3 + 2/5*o**4 - 1104/5*o**2 + 0 - 3528/5*o = 0. Calculate o.
-6, 0, 49
Let p(i) be the second derivative of i**6/165 - 23*i**5/110 + 51*i**4/22 - 135*i**3/11 + 378*i**2/11 + i + 2899. Factor p(k).
2*(k - 14)*(k - 3)**3/11
Let x(h) be the second derivative of 0*h**5 - 4 + 0*h**2 - 1/30*h**4 + 1/225*h**6 + 2/45*h**3 - 9*h. Find k, given that x(k) = 0.
-2, 0, 1
Let k(w) be the first derivative of 40/7*w - 2/21*w**3 - 38 - 19/7*w**2. Find c such that k(c) = 0.
-20, 1
Let k(z) be the third derivative of z**8/672 + z**7/210 - z**6/80 - z**5/30 + z**4/12 + 4*z**2 - 719*z. Determine u so that k(u) = 0.
-2, 0, 1
Let q(c) = c**2 - 1. Let k(w) = -5*w**2 - 2*w - 4. Let g(i) = k(i) - 4*q(i). Let f(u) = 3*u**2. Let l(j) = -17*f(j) - 6*g(j). Let l(x) = 0. What is x?
-4, 0
Let w(g) be the third derivative of g**7/42 - g**6/12 - g**5 + 15*g**4/4 + 45*g**3/2 - 2159*g**2. Suppose w(a) = 0. Calculate a.
-3, -1, 3
Let g = 117 + -101. Suppose 0*t + 2*t**5 - 11*t**4 - 9*t**4 + g*t**4 + 4*t**2 - 2*t = 0. Calculate t.
-1, 0, 1
Let b(r) = 36*r**4 - 363*r**3 - 414*r**2 - 30*r. Let o(s) = -5*s**4 + 52*s**3 + 59*s**2 + 4*s. Let t(w) = 2*b(w) + 15*o(w). Factor t(c).
-3*c**2*(c - 19)*(c + 1)
Let z = 427 + -385. Solve -90*w - 65*w - 80*w - 63*w + z + 257*w - w**2 = 0.
-42, 1
Determine d, given that -18/5 + 98/15*d**5 + 68/5*d**2 - 406/15*d**4 - 42/5*d + 284/15*d**3 = 0.
-3/7, 1, 3
Let b(a) be the second derivative of 105/2*a**3 - 65/12*a**4 - 38*a + 25*a**2 + 3. Factor b(c).
-5*(c - 5)*(13*c + 2)
Let s(u) be the first derivative of -2*u**5/35 + 5*u**4/7 - 24*u**3/7 + 8*u**2 - 64*u/7 - 1570. Factor s(c).
-2*(c - 4)*(c - 2)**3/7
Solve -9/5*a**2 - 21 - 318/5*a = 0 for a.
-35, -1/3
Let l(u) be the first derivative of -u**6/16 - 3*u**5/5 - 9*u**4/32 + 23*u**3/2 + 21*u**2 - 72*u - 3362. Determine w so that l(w) = 0.
-4, 1, 3
Suppose 0*i = 10*i - 700. Solve 18*h**4 - 8*h**2 + i*h**2 - 10*h - 2*h**3 - 100*h**3 = 0.
0, 1/3, 5
Let u(z) = -6*z**2 - 3660*z - 1816418. Let p(d) = 7*d**2 + 3622*d + 1816418. Let n(c) = -4*p(c) - 5*u(c). Factor n(b).
2*(b + 953)**2
Suppose -2*u - h - 208 = 2*u, -5*u = -h + 269. Let p = u + 56. Factor p - 4*r + 4/3*r**2.
(2*r - 3)**2/3
Let c = 19363/10 + -9644/5. Let a be (-7 - -1)*1/(-2). Solve 5*p**2 - c*p**a + 0 + 0*p - 25/2*p**4 = 0.
-1, 0, 2/5
Factor -255*y - y**3 + 120*y + 135*y - 13*y**2.
-y**2*(y + 13)
Let v(n) be the second derivative of -n**5/15 + 2*n**4 - 40*n**3/3 + 63*n**2 - 30*n + 1. Let s(h) be the first derivative of v(h). Find l, given that s(l) = 0.
2, 10
Let d(s) = -s**3 + 89*s**2 + 466*s + 378. Let z be d(94). Let o(r) be the first derivative of -4/3*r**z - 5/6*r**3 - 2/3*r - 24. Factor o(i).
-(3*i + 2)*(5*i + 2)/6
Let o = 293 - 147. What is l in -o*l**5 - 7*l**4 + 4*l**3 + 8*l**2 + 142*l**5 - l**4 = 0?
-2, -1, 0, 1
Let w = -2150 + 2154. Let b(r) be the second derivative of 0*r**3 + 0 - 3/80*r**5 + 3/2*r**2 + 13*r - 3/16*r**w. Factor b(h).
-3*(h - 1)*(h + 2)**2/4
Suppose a - 889 + 899 = 5*k, k - 3*a = 2. Let 0*s - 2/13 + 2/13*s**k = 0. Calculate s.
-1, 1
Let j(b) be the first derivative of 6 - 13*b + 0*b**2 - 2/3*b**3 + 1/3*b**4. Let p(l) be the first derivative of j(l). Find n, given that p(n) = 0.
0, 1
Suppose 5*r = -4*l - 7, -2*r - 4*l - 1 = -3. Let y be 95/285 - 8/r. Factor -14/3*f - 4/3 + 10/3*f**2 + 8/3*f**y.
2*(f - 1)*(f + 2)*(4*f + 1)/3
Factor -328/9*t + 4/9*t**3 + 320/9 + 4/9*t**2.
4*(t - 8)*(t - 1)*(t + 10)/9
Find g, given that -g - 6*g**5 - 938*g**2 + 15*g + 894*g**2 + 44*g**4 - 8*g**3 = 0.
-1, 0, 1/3, 1, 7
Let t(c) = 2*c + 34. Let f be t(-15). Suppose 264 = 4*g + 4*u, -f*g + 108 = -2*g - 4*u. Solve 96*s - 5*s**2 - 26*s - g + 0*s**2 - 183 = 0.
7
Let j = -259209 + 259212. Determine p so that -6*p + 43/6*p**j + 0 + 12*p**2 + 5/6*p**4 = 0.
-6, -3, 0, 2/5
Let b(o) be the second derivative of -7*o**6/15 + 29*o**5/20 + 9*o**4/2 - 58*o**3/3 + 4*o**2 - 2009*o. Factor b(x).
-(x - 2)**2*(x + 2)*(14*x - 1)
Let d = -248567 - -248569. Factor -8/3 + d*y**2 - 8/3*y + 8/3*y**3 + 2/3*y**4.
2*(y - 1)*(y + 1)*(y + 2)**2/3
Let p be 2 + (1 - 3 - -3). Let a be p*(-4)/(-4 + 0) + -2. Factor -r + a - 2 - r**2 - r.
-(r + 1)**2
Let f be (-3)/10*12/(-18). Let l be ((-2)/(-38))/(155*(-1)/(-589)). Find p such that 1/5*p**3 + 1/5*p**2 - l - f*p = 0.
-1, 1
Let p(v) be the third derivative of 0*v + 16/3*v**4 + 6 + 2/15*v**6 - 28/15*v**5 + 15*v**2 + 2/105*v**7 + 0*v**3. Factor p(g).
4*g*(g - 2)**2*(g + 8)
Let z be 87/6*2 + (1 - 1). Let w(s) be the first derivative of 3*s**2 - s**3 + 2 - z + 14. Suppose w(p) = 0. What is p?
0, 2
Factor 2819960 - 11710986 - 2499599 - l**3 - 740*l**2 + 65*l**2 - 151875*l.
-(l + 225)**3
Let s = 10136 - 10136. Let t(n) be the second derivative of 20*n - 1/60*n**4 + 0*n**3 + s*n**2 + 0 - 1/150*n**6 - 1/50*n**5. Factor t(m).
-m**2*(m + 1)**2/5
Let s(n) be the first derivative of 0*n**2 - 31 + 0*n**4 - 1/3*n**3 + 1/5*n**5 + 0*n. Suppose s(y) = 0. What is y?
-1, 0, 1
Let c(q) be the second derivative of 21/2*q**2 + 9/4*q**4 + 15/2*q**3 + 38*q + 3/20*q**5 + 0. Let c(w) = 0. Calculate w.
-7, -1
Let j be (5/(-4))/((-15)/6)*4. Suppose -33 = -9*v - j*v. Factor 10*f**2 - 7*f**v + f**3 + 11*f**3.
5*f**2*(f + 2)
Factor 51974*x + 4*x**2 + 9820465 - 70838*x + 12420191.
4*(x - 2358)**2
Let y = 290 + -282. Suppose -y*x**2 + 3 - 6*x - x**4 + 6*x**3 - 5 + 0 + 11 = 0. What is x?
-1, 1, 3
Let w be (-51)/(-12) + -2*(-2)/(-16). Factor w*z - 59 - 14*z + 121 + 14*z**2 - 66.
2*(z - 1)*(7*z + 2)
Let q(d) be the third derivative of -1/2016*d**8 + 2/3*d**3 - 1/30*d**5 - 1/105*d**7 - 17/360*d**6 + 0*d - 3 + 50*d**2 + 35/144*d**4. Solve q(t) = 0.
-8, -3, -1, 1
Let m = 71037 + -1208409/17. Let t = m + 46. Factor 0*u - 2/17*u**3 + 2/17*u**4 + t*u**5 + 0 - 2/17*u**2.
2*u**2*(u - 1)*(u + 1)**2/17
Let y(s) be the second derivative of -1/90*s**5 + 107 + 37/54*s**4 - s - 71/27*s**3 + 35/9*s**2. Solve y(q) = 0.
1, 35
Let o(n) be the third derivative of 0 + 0*n - 1/3*n**5 - 88*n**2 - 1/24*n**