et n = 12584 - 12561. Let w(z) be the first derivative of 3/2*z - 1/6*z**3 - n + 1/2*z**2. What is m in w(m) = 0?
-1, 3
Let k(s) be the third derivative of -s**6/180 - 5*s**5/18 + 41*s**4/18 - 56*s**3/9 + 10*s**2 - 9*s. Factor k(c).
-2*(c - 2)*(c - 1)*(c + 28)/3
Suppose 231*i - 84*i = 294. Let h(k) be the first derivative of 72/7*k + 2/21*k**3 + 12/7*k**i + 13. Factor h(x).
2*(x + 6)**2/7
Let p(t) be the second derivative of 1/135*t**5 + 0*t**3 + 0*t**4 + 0 - 12*t - 1/540*t**6 - 33/2*t**2. Let d(n) be the first derivative of p(n). Factor d(w).
-2*w**2*(w - 2)/9
Let s be -6*((-27)/6 + 4). Determine i so that -5*i**3 - 102*i - i**4 + s*i**3 + 102*i - i**2 = 0.
-1, 0
Suppose 0 = 6*b + 10 - 178. Factor -4*u**3 - 2341*u**5 - 19*u**3 + 2340*u**5 - 12*u + b*u**2 + 8*u**4.
-u*(u - 3)*(u - 2)**2*(u - 1)
Let s(r) be the first derivative of 16/3*r + 14/9*r**3 + 265 + 7/6*r**4 - 6*r**2 - 1/9*r**6 - 2/5*r**5. Solve s(k) = 0 for k.
-4, -2, 1
Determine g, given that 8/3*g**2 + 0 + 1/3*g**3 + 7/3*g = 0.
-7, -1, 0
Let j = -2181/29 + 6572/87. Find m such that -14/3 + j*m**2 + 5/3*m = 0.
-7, 2
Let h be 4 + 0 + ((-728)/(-585))/28*30. Factor -4*d - 2/3 - h*d**3 + 10*d**2.
-2*(d - 1)**2*(8*d + 1)/3
Suppose -d = 3*c - 15, 34*d + 3*c - 15 = 38*d. Let p(z) be the second derivative of -5/36*z**4 + d + 5/18*z**3 + 0*z**2 + 13*z. Factor p(y).
-5*y*(y - 1)/3
Let z(p) = 916*p**2 + 3666*p + 11. Let w be z(-4). Factor 1/6*c**4 + 1/3*c**2 + 0 - 1/2*c**w + 0*c.
c**2*(c - 2)*(c - 1)/6
Let u(y) be the second derivative of y**5/130 + 59*y**4/78 + 506*y**3/39 + 784*y**2/13 - 3*y - 646. Determine m, given that u(m) = 0.
-49, -8, -2
Suppose -22 = -2*m + 34. Suppose 4*k + 32 = 2*v, -v + 0*v + m = -5*k. Factor -8 - 2*p**3 + 28*p**2 - 55*p**2 + 29*p**2 + v*p.
-2*(p - 2)*(p - 1)*(p + 2)
Let v be -1 + 20 + (-5 + 5 - 2). Find r, given that -61*r**2 + 140*r + v*r**2 + 4*r**3 + 85 - 185 = 0.
1, 5
Let q(z) be the first derivative of -39/2*z**2 - 1/15*z**5 + 4*z**3 + 0*z + 32 - 1/6*z**4. Let c(h) be the second derivative of q(h). Let c(t) = 0. What is t?
-3, 2
Let g = -433771 + 433774. Suppose -62*s**2 - 59582/3 + 2/3*s**g + 1922*s = 0. Calculate s.
31
Let b(w) = 4*w + 15*w**2 - 90 + 47*w**3 - 53*w**3 + 5*w. Let p(c) = 3*c**3 - 7*c**2 - 4*c + 44. Let y(n) = -5*b(n) - 9*p(n). Factor y(o).
3*(o - 3)**2*(o + 2)
Let l = 44 - 33. Suppose 22 = -0*i + l*i. Solve -72 + 8*q**3 - 4*q**i - 12*q + 20*q**2 - 4*q**3 = 0.
-3, 2
Let a(d) be the third derivative of d**7/105 + 9*d**6/10 + 112*d**5/5 + 608*d**4/3 - 1346*d**2 + d. Factor a(w).
2*w*(w + 8)**2*(w + 38)
Let l(r) = r + 63. Let k be l(7). Let 36*g + k + 2*g**2 + 70*g - g**2 + g**2 + 34 = 0. What is g?
-52, -1
Factor -139*g**2 + 20*g + 70*g**2 - 67 + 7 + 74*g**2.
5*(g - 2)*(g + 6)
Suppose 4*g + 9 = 1, 0 = 5*m + 4*g - 182. Let c = -30 + m. Factor -4*r - 40*r**4 + c*r**4 + 4*r**2 - 12*r**3 + 20*r**5 + 36*r**2 - 8 - 4*r**3.
4*(r - 1)**3*(r + 1)*(5*r + 2)
Let h(p) be the second derivative of -p**5/130 - 15*p**4/13 - 900*p**3/13 - 27000*p**2/13 + 63*p - 3. Factor h(c).
-2*(c + 30)**3/13
Let a(j) be the second derivative of -8077205*j**4/12 - 6355*j**3/3 - 5*j**2/2 - 59*j + 11. Solve a(y) = 0 for y.
-1/1271
Let z = 62026 + -434180/7. Suppose 0*j + 0 - 12/7*j**2 + 2/7*j**4 - z*j**3 = 0. Calculate j.
-2, 0, 3
Let p(y) be the third derivative of -y**6/1800 - y**5/60 - 7*y**4/40 - 2*y**3 + 201*y**2. Let q(u) be the first derivative of p(u). Let q(g) = 0. Calculate g.
-7, -3
Let i(z) = 3*z**4 - 18*z**3 - 53*z**2 - 32*z - 5. Let p(n) = -n**2 - 50 + n**4 - 3*n + 3*n + 49. Let h(u) = i(u) - 5*p(u). Factor h(j).
-2*j*(j + 1)*(j + 4)**2
Let j = -5220 - -36623/7. Let s = j - 145/14. Determine x so that x**2 - 1/2*x**5 - 1 - s*x + 0*x**4 + 2*x**3 = 0.
-1, 1, 2
Let b be 18/32*(-188)/(-5358). Let k = b - -225/152. Let 1/6 - 7/6*n + 7/3*n**2 - 5/2*n**4 + k*n**5 - 1/3*n**3 = 0. Calculate n.
-1, 1/3, 1
Let v(k) be the first derivative of -k**3/15 - 57*k**2/10 - 812*k/5 - 4853. Find t such that v(t) = 0.
-29, -28
Factor 2813*t**2 - 29205 - 1948*t**2 + 19425*t - 5*t**3 - 4080*t**2.
-5*(t - 3)**2*(t + 649)
Let h = 4 - 1. Suppose -p + h*t + 27 = -15, -3*t - 9 = 0. Factor -72 + 35 + 20*m**2 + 16*m + p.
4*(m + 1)*(5*m - 1)
Let m be -9 - 1 - ((-715)/132 + -5). Let w(j) be the second derivative of 8*j - 1/8*j**5 + m*j**4 - 5/12*j**3 + 0 + 0*j**2. Factor w(r).
-5*r*(r - 1)**2/2
Suppose 154*i - 156*i + 4*g = 116, 2*g + 54 = -i. Let z be (i/(-560))/((-2)/(-60)). Solve 0 + 1/5*j**z + 16/5*j**2 + 64/5*j = 0.
-8, 0
Let m(s) be the first derivative of s**6/180 - 7*s**4/72 + s**3/6 - 8*s + 105. Let g(n) be the first derivative of m(n). What is o in g(o) = 0?
-3, 0, 1, 2
Factor 93 + 48*g + 3/4*g**2.
3*(g + 2)*(g + 62)/4
Let u = 1151975 + -1151973. Solve -2/13*p**3 - 4/13*p**u + 0*p + 0 = 0 for p.
-2, 0
Let f(z) be the first derivative of 0*z**2 + 19 + 2/33*z**3 + 1/165*z**6 + 12*z + 2/55*z**5 + 5/66*z**4. Let o(a) be the first derivative of f(a). Factor o(w).
2*w*(w + 1)**2*(w + 2)/11
Let t(d) be the first derivative of d**4 + 100*d**3/3 - 496*d**2 + 2112*d - 903. Find a such that t(a) = 0.
-33, 4
Let t be (3/2)/(6/72). Suppose 0*w + t = 2*w. Determine r so that -12*r**2 + 3 + w*r + 24*r + 6 = 0.
-1/4, 3
Let t = -65387/2 + 327327/10. Factor -t + 24/5*p**2 - 42/5*p - 2/5*p**3.
-2*(p - 7)**2*(p + 2)/5
Suppose -344*y = -124*y. Let l(o) be the third derivative of 16*o**2 + y*o**3 + 0*o + 1/32*o**4 - 3/160*o**5 + 1/320*o**6 + 0. Factor l(j).
3*j*(j - 2)*(j - 1)/8
Let m be ((-472 + 465)*8/190)/((-14)/35). Find p, given that 0*p**2 + 0*p - 8/19*p**3 + 0 - 24/19*p**4 + m*p**5 = 0.
-2/7, 0, 2
Suppose -2*x = -4*i + 2*x - 52, 0 = 5*i - x + 77. Let m be ((-20)/35)/(i/(-28) + -2). Suppose -2/5*y**3 + 3/10*y**2 + 1/10*y**4 + m*y - 2/5 = 0. What is y?
-1, 1, 2
Let s(r) be the first derivative of -r**4/4 - 16*r**3/3 - 8*r**2 + 384*r - 4758. Let s(v) = 0. What is v?
-12, -8, 4
Let f(o) = -2*o**3 + 14*o**2 + 60*o + 5. Let y be f(10). Let g(l) be the first derivative of -y + 1/19*l**2 - 2/57*l**3 + 12/19*l. Solve g(j) = 0.
-2, 3
Suppose -5*v - 22 = -19*d + 16*d, 2*v - 4 = -2*d. Factor d*s - 17*s - 7*s + 2*s**2 - 22.
2*(s - 11)*(s + 1)
Let z(l) = 2*l**2 + 14*l. Let y be z(-10). Let i = 63 - y. Factor 9*x**3 + 10*x**3 + 23*x**3 + 10*x - 5*x**5 - 5*x**4 - 27*x**i + 25*x**2.
-5*x*(x - 2)*(x + 1)**3
Let h be 7 + 99/(-11)*1/(-3). Suppose h*r - 6*r - 68 = -2*t, 0 = t + r - 35. Factor -g**2 + 85*g + 0*g**2 - 73*g - t.
-(g - 6)**2
Solve 3/4*s**3 + 11/4*s**2 + 3/2*s - 1/4*s**5 - 3/4*s**4 + 0 = 0 for s.
-3, -1, 0, 2
Let t(m) be the first derivative of -1/2*m**2 + 12 - 1/12*m**4 - 1/3*m**3 - 19*m. Let j(k) be the first derivative of t(k). Determine p so that j(p) = 0.
-1
Factor 92 - 175*x - 5*x**3 + 6 + 55*x**2 + 50 - 23.
-5*(x - 5)**2*(x - 1)
Let o(d) = 4*d**3 + 62*d**2 + 185*d - 272. Let t(r) = 8*r**3 + 118*r**2 + 369*r - 544. Let i(y) = 7*o(y) - 3*t(y). Factor i(l).
4*(l - 1)*(l + 4)*(l + 17)
Suppose -r + 44 = 2*q, 2*q = 7*q + 2*r - 112. Suppose -4 - q = -14*t. What is p in -8/9*p + 0 + 2/9*p**t = 0?
0, 4
Let r be 6/(-48)*(-4 + 1). Suppose o - n - 50 = -46, 5*o - 3*n = 16. Factor 3/8*i - r*i**3 - 3/8*i**o + 3/8.
-3*(i - 1)*(i + 1)**2/8
Suppose 2*b = 3*v - 12, 10*v - 16*b + 12*b = 24. Factor 3/2*j**3 - 3*j**2 + v - 1/4*j**4 + 2*j.
-j*(j - 2)**3/4
Let c = -750 + 750. Let l(f) be the first derivative of -12 + 0*f**2 - 1/12*f**4 + 1/18*f**6 + c*f**3 + 0*f**5 + 0*f. Factor l(v).
v**3*(v - 1)*(v + 1)/3
Let x = 43 + -41. Let h be -18*(-3*x/(-6))/(-1). Factor h*l**2 - 8*l + 2*l - 9*l**2.
3*l*(3*l - 2)
Factor -62/11*w + 2/11*w**2 + 40.
2*(w - 20)*(w - 11)/11
Let p(u) = 3*u**3 + 43*u**2 + 92*u + 60. Let v(h) = -h**2 + h. Let k(l) = -28*l + 136. Let g be k(5). Let f(w) = g*v(w) - p(w). Factor f(y).
-3*(y + 1)*(y + 2)*(y + 10)
Solve 720*o**2 - 327*o**3 - 31*o - 3*o**5 - 26*o - 814 + 9*o + 54*o**4 - 338 = 0 for o.
-1, 3, 4, 8
Let z = -8810 - -4240. Let g = 22934/5 + z. Find q, given that 96/5*q**2 - 18/5*q**5 - 32/5 - 26/5*q**3 - g*q**4 + 24/5*q = 0.
-4, -1, 2/3
Let c(t) = 4*t**2 + 148*t - 145. Let p be c(-38). Let r(l) be the first derivative of -l**3 - 6*l - 9/2*l**2 - p. Let r(i) = 0. Calculate i.
-2, -1
Let j(d) be the second derivative of 0 + 1/15*d**5 - 9/2*d**2 + 1/3*d**4 + 12*d + 0*d**3. Let c(n) be the first derivati