**2/4 + 43*q - 1038. Factor d(n).
(n + 2)*(n + 43)*(2*n + 1)/2
Let z(n) be the third derivative of n**7/840 + 29*n**6/240 + 11*n**5/48 - 19*n**4/16 + 59*n**2 + 3*n. Factor z(v).
v*(v - 1)*(v + 2)*(v + 57)/4
Let w = 395432 - 1186292/3. Factor 2/9*g**3 - 2/9*g + 4/3 - w*g**2.
2*(g - 6)*(g - 1)*(g + 1)/9
Suppose -17*w + 20*w - 5*g = -13, g + 25 = 6*g. Factor -1/9*b**w + 13/9*b**2 + 0 - 2/9*b**3 - 10/9*b.
-b*(b - 2)*(b - 1)*(b + 5)/9
Factor -269 - 173 + 21 + 61 + 25*r**2 - 98*r - 27*r**2.
-2*(r + 4)*(r + 45)
Suppose -926/19*p**2 + 0*p**3 + 2/19*p**4 - 924/19*p + 0 = 0. Calculate p.
-21, -1, 0, 22
Let i(j) be the second derivative of -j**7/210 - 8*j**6/45 - 17*j**5/6 - 25*j**4 - 88*j**3/3 + 120*j. Let d(k) be the second derivative of i(k). Factor d(m).
-4*(m + 5)**2*(m + 6)
Solve 0 + 1140/7*w**2 + 4/7*w**4 + 144/7*w**3 - 2888/7*w = 0 for w.
-19, 0, 2
Suppose 0 = w + 3*t - 50, -w = w + 4*t - 110. Suppose 131*z**3 - w*z**3 - 64*z**3 + 12*z + 14*z**2 = 0. What is z?
-6, -1, 0
Suppose -21*w - 2 = -22*w. Factor -4*m**4 + 11*m**2 - 22*m**w - 57*m**2 + 40*m**3 + 32*m.
-4*m*(m - 8)*(m - 1)**2
Let k(v) = -v**3 - v**2 - v - 3. Let z(x) = 6*x**3 - 130*x**2 - 262*x - 110. Let m(t) = 8*k(t) + z(t). Determine q, given that m(q) = 0.
-67, -1
Let j(t) = 9*t + 50. Let o be j(-6). Let s(w) = -w**3 - w**2 + w. Let q(m) = 0*m + 0*m - 21 + 16*m**2 + 9. Let h(z) = o*s(z) - q(z). Factor h(l).
4*(l - 3)*(l - 1)*(l + 1)
Let b(x) be the second derivative of 0*x**2 + 41*x + 0*x**4 + 9/20*x**5 + 0 + 0*x**3 + 1/10*x**6. Factor b(p).
3*p**3*(p + 3)
Let h(s) = -14*s - 131. Let x be h(-14). Factor 71 + x*b**2 - 25*b**3 - 11*b + 291*b + 29.
-5*(b - 5)*(b + 2)*(5*b + 2)
Let h(f) be the third derivative of -f**7/20 + 19*f**6/10 - 481*f**5/40 + 57*f**4/4 + 27*f**3 + 1866*f**2. What is u in h(u) = 0?
-2/7, 1, 3, 18
Let o(j) be the second derivative of 5*j**7/56 + 87*j**6/40 + 159*j**5/10 + 79*j**4/4 - 72*j**3 - 96*j**2 + 942*j. Find z such that o(z) = 0.
-8, -2, -2/5, 1
Let u(k) be the second derivative of 0*k**2 + 21*k + 3/20*k**5 - 1 - k**4 + 2/5*k**6 - 1/2*k**3. Let u(f) = 0. What is f?
-1, -1/4, 0, 1
Factor -12707*d**2 + 25367*d**2 - 12730*d**2 - 186*d + 32 - 6*d**3 + 38.
-2*(d + 5)*(d + 7)*(3*d - 1)
Suppose 68*m + 60 = 73*m. Let k be 2/(-48)*((2 - 23) + m). Factor 3/4*w**3 - k*w - 3/8*w**4 - 3/8*w**5 + 3/4*w**2 - 3/8.
-3*(w - 1)**2*(w + 1)**3/8
Let l(q) = 676*q**3 + 35363*q**2 + 10832*q + 799. Let f(g) = 676*g**3 + 35364*g**2 + 10832*g + 788. Let r(m) = 3*f(m) - 4*l(m). Let r(b) = 0. What is b?
-52, -2/13
Let a(y) be the first derivative of -y**3/15 - 4348*y**2/5 - 18905104*y/5 - 11557. Find m such that a(m) = 0.
-4348
Let j(p) = 10*p**4 - 64*p**3 - 575*p**2 - 957*p - 447. Let i(n) = -46*n**4 + 320*n**3 + 2874*n**2 + 4786*n + 2236. Let s(q) = 3*i(q) + 14*j(q). Factor s(t).
2*(t + 1)**2*(t + 15)**2
Let x be (-2 + 4/8)*16. Let t = x - -35. Factor -108*p**4 - t*p**3 + 104*p**4 - 36*p**2 - 9*p**3 - 4*p**3.
-4*p**2*(p + 3)**2
Let x(q) be the third derivative of -q**7/840 + 13*q**6/480 + 109*q**5/240 + 95*q**4/96 - 872*q**2. Factor x(a).
-a*(a - 19)*(a + 1)*(a + 5)/4
Let t(n) be the second derivative of n**5/30 + 5*n**4 + 704*n**3/3 + 3872*n**2/3 + 2*n - 2280. Factor t(q).
2*(q + 2)*(q + 44)**2/3
Let y(i) be the third derivative of -i**8/84 + 26*i**7/105 + 2*i**6/15 - 52*i**5/15 - 19*i**2 + 40*i. Determine o, given that y(o) = 0.
-2, 0, 2, 13
Let i(h) be the third derivative of -53/12*h**5 - 3/8*h**6 + 67*h**2 + 0*h + 5/336*h**8 + 40*h**3 + 0 + 5/3*h**4 + 5/42*h**7. Let i(k) = 0. Calculate k.
-4, -1, 1, 3
Let g be (-7)/(-21) + 1/(-3). Suppose g*b - 5*h - 1 = 3*b, 0 = 4*h + 8. Find q, given that b - 5*q**3 + 8*q**3 + 4*q**2 - 3*q - 7*q**2 = 0.
-1, 1
Suppose -2*c - 36 = c. Let v be (c/21)/(4/(-14)). Determine b so that 24*b**2 - 14 - 57*b**v - 26*b + 23*b**2 + 2*b**3 = 0.
-1, 7
Suppose 0 = 2*w - 4*x - 16, 0 = -5*w + 3*x - 6*x + 105. Suppose 448 = 138*s + 86*s. Factor -1 + 33/4*h - w*h**s + 4*h**3.
(h - 4)*(4*h - 1)**2/4
Let t(y) be the first derivative of 0*y + 5/2*y**4 + 0*y**2 + 10 + 2/5*y**5 + 0*y**3. Factor t(f).
2*f**3*(f + 5)
Let g be 3 - (-1)/1 - (-1197235)/(-978). Let l = 1221 + g. Let 5/6*b**3 + 5/6*b**2 - 5/6*b - l = 0. Calculate b.
-1, 1
Factor 1266 + 58*y**2 + y**3 - 70*y**2 - 1368 - 79*y.
(y - 17)*(y + 2)*(y + 3)
Let s(a) be the third derivative of -a**5/60 + 11*a**4/6 + 47*a**3/2 + 5857*a**2. Determine u, given that s(u) = 0.
-3, 47
Suppose 0 = 5*d - 25, y - 76 + 17 = -5*d. Suppose 2*k + 15*k - y = 0. Factor 105/4*v**k + 5 - 24*v + 25/4*v**3.
(v + 5)*(5*v - 2)**2/4
Let v = -204253/2 + 102129. Factor -1/2*j**3 + 13/2*j - 7/2 - v*j**2.
-(j - 1)**2*(j + 7)/2
Let w = -41 + 44. Suppose -2*s**w + 2*s**2 - 3*s + 16 + 22*s + s = 0. What is s?
-2, -1, 4
Let t(i) = -i**2 - 16*i + 21. Let v be t(-17). Factor 0*b**4 + 7*b**2 + 3*b**v + 81*b + 74*b**2 + 6*b**3 + 21*b**3 + 0*b**3.
3*b*(b + 3)**3
Let p(g) be the third derivative of 0 - 4/9*g**3 + 4*g - 12*g**2 + 1/360*g**6 - 1/30*g**5 + 1/6*g**4. What is c in p(c) = 0?
2
Suppose 6 = -2*m, 14*m - 5431 = -2*n + 11*m. Factor 1497*l + n*l + 5*l**3 + 466*l**2 + 1563*l - 126*l**2.
5*l*(l + 34)**2
Factor 2871917*z**4 - 88*z**2 - 1413*z - 2871920*z**4 - 1512 - 377*z**2 - 63*z**3.
-3*(z + 3)**2*(z + 7)*(z + 8)
Let y be (12/(-36))/((305/(-30))/61). What is w in -5/4*w - 3/2*w**y + 0 - 1/4*w**3 = 0?
-5, -1, 0
Let q(r) be the second derivative of 12/13*r**3 + 1/78*r**4 - 1 + 324/13*r**2 - 24*r. Suppose q(t) = 0. Calculate t.
-18
Let q(j) be the second derivative of j**7/70 - 2*j**6/25 + 3*j**5/25 + 1854*j. Factor q(c).
3*c**3*(c - 2)**2/5
Let x be (229 + -6)/(6/(-12)). Let z = x + 3124/7. Solve -z + 2/7*l**4 - 1/7*l**5 - 8/7*l**2 + 2/7*l**3 + l = 0 for l.
-2, 1
Let t(v) be the third derivative of -v**5/15 + 863*v**4/6 + v**2 - 3804*v. Factor t(k).
-4*k*(k - 863)
Let z(b) = -23*b**3 + 1297*b**2 - 3439*b - 4640. Let p(y) = -20*y**3 + 1135*y**2 - 3010*y - 4060. Let m(i) = -17*p(i) + 15*z(i). Let m(j) = 0. Calculate j.
-1, 4, 29
Let x(w) be the second derivative of 1/180*w**6 - 15*w - 4 + 1/18*w**4 + 0*w**3 + 1/24*w**5 + 0*w**2. Factor x(a).
a**2*(a + 1)*(a + 4)/6
Suppose -1160 = -k - l, 5*l = 3*k - 3009 - 463. Suppose -30*n**2 - 26*n + k*n**3 - 1154*n**3 - 9*n = 0. What is n?
-1, 0, 7
Let f = -4683 + 4686. Let o(y) be the third derivative of 0*y + 5*y**2 + 0 - 1/90*y**5 + 2/9*y**4 - 16/9*y**f. Determine p so that o(p) = 0.
4
Factor 75*h**2 - 143 + 165*h - 48 - 46*h - 129 + 121*h + 5*h**3.
5*(h - 1)*(h + 8)**2
Let n(h) be the first derivative of 0*h**2 - 123 - 1/11*h**4 - 2/55*h**5 - 2/33*h**3 + 0*h. Solve n(b) = 0.
-1, 0
Factor 194/7*z - 600/7 + 2/7*z**2.
2*(z - 3)*(z + 100)/7
Let f(c) be the first derivative of c**6/120 - c**5/80 - c**4/12 + c**3/6 + 98*c + 117. Let v(r) be the first derivative of f(r). Solve v(t) = 0 for t.
-2, 0, 1, 2
Solve 224/3*d - 304 + 1/3*d**2 = 0 for d.
-228, 4
Let r = -8884 + 8889. Let t(p) be the second derivative of -3/4*p**4 + 12*p - 9/40*p**r - 5/4*p**3 + 0 - 1/40*p**6 - 9/8*p**2. Factor t(i).
-3*(i + 1)**3*(i + 3)/4
Let t(q) = -3*q**4 + 11*q**3 + 53*q**2 - 11*q + 27. Let n(p) = p**4 - 6*p**3 - 26*p**2 - 2*p - 14. Let k(a) = -5*n(a) - 2*t(a). Factor k(j).
(j + 2)**4
Suppose -259/4*k**2 + 169/8*k**4 - 253/2*k + 429/8*k**3 + 57 - 5/4*k**5 = 0. Calculate k.
-2, 2/5, 3/2, 19
Suppose 103 = -4*t + 115. Find m such that 146*m**3 - 45*m**4 - 65*m**2 - 60*m - 20 + 40*m**4 - 176*m**t = 0.
-2, -1
Let s = 14 + -11. Solve -1031*p + 517*p + p**s - p**4 + p**2 + 513*p = 0.
-1, 0, 1
Let l(h) be the second derivative of h**6/20 + 6*h**5/5 + 59*h**4/8 + 11*h**3 + 13*h + 28. Suppose l(x) = 0. Calculate x.
-11, -4, -1, 0
Let g(c) be the third derivative of c**6/24 + 59*c**5/6 - 1195*c**4/24 + 100*c**3 + 139*c**2 - 18*c. Factor g(w).
5*(w - 1)**2*(w + 120)
Let o(y) be the second derivative of -y**6/10 + 23*y**5/10 - 13*y**4/12 - 5*y**3 - 1340*y - 1. Determine f so that o(f) = 0.
-2/3, 0, 1, 15
Let a(g) = -g**3 + 14*g**2 - 8*g. Let j be a(4). Suppose l - 5*l + j = 0. Factor -l*h**2 + h**5 + 28*h**2 - 12*h**3 - 5*h**5 - 12*h**4.
-4*h**2*(h + 1)**3
Let d(w) = 2*w**2 - 4*w - 2. Let y(m) = -48*m**2 + 62*m - 82. Let n(u) = 50*d(u) + 2*y(u). Factor n(a).
4*(a - 22)*(a + 3)
Let a be (-3)/2*13/(18564/(-272)). Factor -22/7*b - 36/7 - a*b**2.
-2*(b 