8 - 83*m + 101. Let c(s) be the first derivative of t(s). Suppose c(r) = 0. Calculate r.
1, 7
Let c(x) be the third derivative of 85*x**2 + 7/1140*x**6 - 8/285*x**5 + 0*x + 10/19*x**3 + 0 - 101/228*x**4. Solve c(q) = 0 for q.
-3, 2/7, 5
Let d(j) be the first derivative of 2*j**5/5 - 65*j**4/2 + 84*j**3 + 149. Factor d(o).
2*o**2*(o - 63)*(o - 2)
Factor -247*l**3 - 98*l - 42*l - 32*l**2 - 144 + 248*l**3.
(l - 36)*(l + 2)**2
Let o(k) be the first derivative of k**6/90 - 2*k**5/15 + 2*k**4/3 + k**3 - 3*k - 55. Let c(x) be the third derivative of o(x). Find y, given that c(y) = 0.
2
Suppose -116*z = -33*z - 40*z - 86. Let x(c) be the third derivative of -3*c**z + 1/4*c**3 + 7/360*c**5 + 0*c - 2 + 1/720*c**6 + 5/48*c**4. Factor x(k).
(k + 1)*(k + 3)**2/6
Let y(l) be the first derivative of -l**4/4 + 10*l**3 - 28*l**2 + 2*l - 37. Let d be y(28). Factor 0*r + 5/4*r**d - 5/4.
5*(r - 1)*(r + 1)/4
Let l(s) = -8*s**2 + s. Let j(a) = -165*a**2 - 185*a - 900. Let o(r) = j(r) - 20*l(r). Factor o(f).
-5*(f + 5)*(f + 36)
Let l(z) be the first derivative of z**6/120 + z**5/8 - 10*z**3/3 - z**2/2 - 119. Let i(p) be the third derivative of l(p). Factor i(n).
3*n*(n + 5)
Let o(f) be the first derivative of -2/15*f**5 - 110/9*f**3 + 25*f**2 + 209 + 13/6*f**4 + 0*f. Solve o(s) = 0.
0, 3, 5
Let z(b) be the third derivative of b**6/200 + 97*b**5/50 + 240*b**4 + 9216*b**3/5 + 4*b**2 + 205*b. Factor z(o).
3*(o + 2)*(o + 96)**2/5
Suppose 0 = -n + 4*j + 836 - 830, -n = -5*j - 7. Solve 1521/8 + 1/8*q**n - 39/4*q = 0 for q.
39
Let c(x) be the first derivative of 0*x + 0*x**4 - 1/12*x**6 + 1/4*x**2 - 148 + 1/5*x**5 - 1/3*x**3. Suppose c(n) = 0. Calculate n.
-1, 0, 1
Let h be (-1 - 1) + 8 - (6 - 3). Suppose 28 - 43 = -5*g - h*d, d = 3*g - 9. Find c such that 2/9*c**g + 0 + 0*c - 2/9*c**2 = 0.
0, 1
Let d be 31 + (-1604)/28 + 30. Suppose 2/7*p**2 + 2/7*p**5 + d*p**3 - 16/7 + 2*p**4 - 4*p = 0. Calculate p.
-4, -2, -1, 1
Solve -1538*x - 1932*x**2 - 1283*x**2 + 252*x + 5846*x - 3205 + 1855*x + 5*x**3 = 0.
1, 641
Let 0 - 4/7*o**3 + 150/7*o + 5*o**2 - 1/7*o**4 = 0. Calculate o.
-5, 0, 6
Factor 40/7*l**2 + 0 + 0*l - 22/7*l**3 + 1/7*l**4.
l**2*(l - 20)*(l - 2)/7
Suppose -13*l = 903 - 825. Let p be 23/7 - (0 - l/(-42)). What is d in -10/7*d**2 - p*d**3 + 25/7*d**5 + 0 - 1/7*d + 10/7*d**4 = 0?
-1, -1/5, 0, 1
Let z(q) be the second derivative of -q**7/105 + 382*q**6/25 - 218886*q**5/25 + 27871484*q**4/15 - 5958*q. Factor z(n).
-2*n**2*(n - 382)**3/5
Let j = -669/148 - -353/74. Let s(d) be the second derivative of 0 + 42*d - j*d**4 + 0*d**2 - d**3. Factor s(z).
-3*z*(z + 2)
Let l(d) = 28*d**2 - 9056*d + 9068. Let a(q) = -22*q**2 + 9055*q - 9063. Let y(w) = -4*a(w) - 3*l(w). Suppose y(i) = 0. What is i?
1, 2262
Let s(x) be the second derivative of x**9/5040 + 3*x**8/1120 - x**7/120 - 11*x**4/2 + 55*x. Let b(r) be the third derivative of s(r). Find d such that b(d) = 0.
-7, 0, 1
Let t(r) be the third derivative of -r**7/70 - 5*r**6/4 + 51*r**5/20 + 3*r**2 + 170. What is l in t(l) = 0?
-51, 0, 1
Suppose 4*n + 37 = 5*u, 66*n - 17 = -u + 70*n. Let m be 21/(-7) - (-18)/4. Find o such that 0 - 3/4*o**u + 3/4*o**4 - 15/4*o**2 + m*o + 9/4*o**3 = 0.
-2, 0, 1
Let d(f) = -17*f + 206. Let h be d(-10). Let j = h - 1103/3. Determine n, given that -10/3 + 5*n + j*n**2 = 0.
-1, 2/5
Let b be 6 - 0 - 51/(-238)*-22. Suppose -5*d - 20*y + 24*y = 10, 2*d - 3*y = -11. Factor b*m**d - 22/7*m + 8/7.
(m - 2)*(9*m - 4)/7
Let j be ((-8)/10 - 4)*15/(-4). Let x be 24/j - (-11)/(-33). Factor 3/4*a + 1/4*a**2 - x.
(a - 1)*(a + 4)/4
Let m = 4299 - 4299. Let f(g) be the second derivative of 0 - 1/40*g**6 + 3/8*g**2 - 16*g + 3/40*g**5 - 1/4*g**3 + m*g**4. Suppose f(c) = 0. What is c?
-1, 1
Let s(d) = 399*d + 5586. Let t be s(-14). Let n be 7/6 - (-2)/4. Suppose -2/3*h + t + n*h**2 = 0. Calculate h.
0, 2/5
Let r = -1559/286 - -16633/2002. Factor 0 + 78/7*c**2 - 8/7*c**3 + r*c.
-2*c*(c - 10)*(4*c + 1)/7
Suppose 5*d = t + 5, 3*t - 15 + 6 = 3*d. Factor 32 - 34*c + 74*c + 2*c**d - 27*c - 33*c.
2*(c - 8)*(c - 2)
Let i(a) be the third derivative of -3/16*a**5 - 1/280*a**7 - 9/32*a**4 + 8*a**2 + 0*a**3 + 0 + 0*a - 7/160*a**6. Factor i(z).
-3*z*(z + 1)*(z + 3)**2/4
Factor 95*u**3 - 580/3*u - 20/3 - 275/3*u**2.
5*(u - 2)*(u + 1)*(57*u + 2)/3
Suppose -68*n = -16*n + 224*n - 828. Let o(g) be the second derivative of -1/6*g**3 - n*g**2 + 0 + 1/90*g**6 + 7/60*g**5 + 13/36*g**4 + 5*g. Factor o(s).
(s - 1)*(s + 2)*(s + 3)**2/3
Suppose 2*y - 7*g = -11*g + 12, 3*y + 2*g = 6. Let k(l) be the second derivative of l**3 + y - 3/10*l**5 + 1/6*l**4 + 1/15*l**6 - 2*l**2 - 2*l. Factor k(j).
2*(j - 2)*(j - 1)**2*(j + 1)
Let -3944/19 + 2/19*x**2 + 3942/19*x = 0. What is x?
-1972, 1
Factor 129*b**3 + 15*b**4 - 48*b**2 - 305*b**2 - 31*b**2 + 399424*b - 399292*b.
3*b*(b - 2)*(b + 11)*(5*b - 2)
Factor 579*w + 335241 + 1/4*w**2.
(w + 1158)**2/4
Factor 608/3 - 4/3*i**2 - 44/3*i.
-4*(i - 8)*(i + 19)/3
Let v(q) be the first derivative of -q**7/210 + 3*q**5/10 - 27*q**3/2 + 69*q**2/2 + 181. Let n(t) be the second derivative of v(t). Let n(w) = 0. Calculate w.
-3, 3
Let h(f) be the third derivative of 0*f + 1/90*f**6 - 1/10*f**5 + 1/3*f**4 + 2/3*f**3 + 0 + 4*f**2. Let c(y) be the first derivative of h(y). Factor c(n).
4*(n - 2)*(n - 1)
Suppose 8 = h + 3*m, -3*h + 19*m - 23*m + 14 = 0. Suppose o + u - 12 = 0, 22 = -o + 3*o + 3*u. Factor -3*t**4 - 46 - 48*t**h + 46 - 36*t - 7*t**3 - o*t**3.
-3*t*(t + 2)**2*(t + 3)
Let u = -6126 + 6126. Let f(q) be the first derivative of -18 + 1/2*q**4 + u*q**3 + 0*q - q**2. Let f(i) = 0. Calculate i.
-1, 0, 1
Let d = -188773/5 + 37757. Factor -d*u + 0 + 2/5*u**2.
2*u*(u - 6)/5
Factor 26*z - 26*z - 5100*z**3 - 13*z**4 - 12*z**2 + 57*z**4 + 5132*z**3.
4*z**2*(z + 1)*(11*z - 3)
Let x(m) be the first derivative of -2*m**5/5 - 9*m**4/2 + 34*m**3/3 + 225*m**2 + 400*m - 1695. Let x(n) = 0. Calculate n.
-8, -5, -1, 5
Suppose -2*u + 3*f = -5, -145*u - 14*f + 6 = -147*u. Suppose 483*s**2 + 441/2*s**3 + u + 86*s = 0. Calculate s.
-2, -2/21
Let a(w) be the third derivative of 0 + 2/9*w**3 - 5/108*w**4 + 0*w + 1/270*w**5 - 48*w**2. Suppose a(m) = 0. Calculate m.
2, 3
Suppose -4*u - 4 + 24 = 0. Let t(y) = -y**3 + 4*y**2 + 8*y - 15. Let p be t(u). Determine v, given that 0*v - 3*v**3 + p - 3/7*v**5 - 9/7*v**2 - 15/7*v**4 = 0.
-3, -1, 0
Let -64/9*a + 40/9*a**3 - 4/9*a**4 + 16/9*a**2 - 2/3*a**5 + 0 = 0. Calculate a.
-2, 0, 4/3, 2
Let 4120*w**2 - 40*w + 32 + 2*w**4 + 21*w**3 + 2*w**4 - 12*w**3 + 13*w**3 - 2*w**5 - 4136*w**2 = 0. Calculate w.
-2, 1, 4
Suppose 18 = -g + 4*i, 16 = -4*g + 3*i - 4. Let d be ((-348)/(-435))/(g/(-10)). Determine c so that 37/7*c**2 + 1/7*c**d - 60/7*c - 10/7*c**3 + 36/7 = 0.
2, 3
Suppose 12*l = -3*l + 15. Factor k**3 - 3 + 13*k - l - 5*k - 5*k**2.
(k - 2)**2*(k - 1)
Determine l so that 1455*l**2 + 5142*l - 2338*l - 1354*l + 5*l**3 = 0.
-290, -1, 0
Let x(z) be the second derivative of z**8/224 + 19*z**7/140 - z**6/4 + 29*z**2 + 26*z. Let b(o) be the first derivative of x(o). Find m such that b(m) = 0.
-20, 0, 1
Suppose 2*u + 5 = 3*j, -2*u = 4*j - 17 - 13. Let d be (-2)/u - 121/(-165)*6. Find x such that 2/5*x - 1/5*x**d - 2/5*x**3 + 0*x**2 + 1/5 = 0.
-1, 1
Let j(b) be the first derivative of -5*b**4/4 + 55*b**3 + 175*b**2 - 804. Factor j(f).
-5*f*(f - 35)*(f + 2)
Let r(o) be the first derivative of 3*o**7/154 - 19*o**6/1320 + o**5/330 + 8*o**2 + 85. Let z(v) be the second derivative of r(v). Solve z(f) = 0 for f.
0, 1/5, 2/9
Let l = -375927 + 375929. Let p = -109 - -765/7. Factor -l*i + 8/7 + p*i**3 + 4/7*i**2.
2*(i - 1)**2*(i + 4)/7
Let h(u) be the first derivative of 15 + u**2 + 2/5*u**3 + 1/30*u**4 - 10/3*u. Factor h(c).
2*(c - 1)*(c + 5)**2/15
Let b(l) = -159*l**3 - 10260*l**2 - 4392*l - 408. Let o(x) = 79*x**3 + 5130*x**2 + 2179*x + 204. Let q(d) = 4*b(d) + 9*o(d). Factor q(r).
3*(r + 68)*(5*r + 1)**2
Let y = -184/1517 - -1885/3034. Let f be (-9)/12 + (1 - 0). Factor y*b**2 + 0 + 3/4*b - f*b**3.
-b*(b - 3)*(b + 1)/4
Let o be 16/2 - 30/5. Solve j**5 + 14*j**3 + 85*j**2 - 28*j**2 + 9 - 15*j - 7*j**4 - 34*j**2 - 25*j**o = 0 for j.
-1, 1, 3
Suppose 34*b + 30*b - 211 + 19 = 0. Let t(k) be the first derivative of 0*k - 5*k**2 - 5/4*k**4 + 5*k**b + 14. Factor t(p).
-5*p*(p - 2)*(p - 1)
Let n(v) be the first derivati