 - 1)
Let n = 63/5 + -187/15. Let w(h) be the second derivative of 3*h + n*h**3 + 1/10*h**4 + 0*h**2 + 0 + 1/50*h**5. Suppose w(i) = 0. What is i?
-2, -1, 0
Determine o, given that 0 - 2/5*o**2 - 4/5*o + 2/5*o**3 = 0.
-1, 0, 2
Let w(q) be the first derivative of q**4/42 + 2*q**3/21 - 4*q**2/21 - 582. Let w(a) = 0. Calculate a.
-4, 0, 1
Let s(h) be the second derivative of 5*h**7/42 + h**6/15 - 27*h**5/2 - 99*h**4 - 549*h**3/2 - 243*h**2 - 487*h. Factor s(b).
(b - 9)*(b + 3)**3*(5*b + 2)
Let c(g) be the second derivative of -g**4/60 - 8*g**3/15 - 32*g**2/5 + g - 53. Find m, given that c(m) = 0.
-8
Let p(d) = -d**3 + 12*d**2 + 365*d - 24. Let m be p(26). Let 2/3 - 1/6*f**m - 1/2*f = 0. Calculate f.
-4, 1
Let p(w) be the third derivative of 0*w + 0 - 2/15*w**5 - 2/9*w**4 + 46*w**2 - 1/315*w**7 - 1/30*w**6 + 0*w**3. What is n in p(n) = 0?
-2, 0
Let h be 56/(-42)*6/(-1 + -1). Solve -1584*c**h + 36*c**2 + 12*c + 12*c**3 + 1602*c**4 + 3*c**5 + 27*c**3 = 0 for c.
-2, -1, 0
Let z(k) = -k**2 + k - 1. Let r(t) = 2*t**2 - 100 + 30 + 32*t - 88. Let n(g) = -r(g) - 4*z(g). Factor n(v).
2*(v - 9)**2
Let d(u) be the third derivative of 19*u**5/10 - 15*u**4/8 - u**3 + 111*u**2. What is f in d(f) = 0?
-2/19, 1/2
Suppose -3 = 4*r - 7. Let n(p) = 86*p**5 + 31*p**4 + 9*p**3 + 5*p**2 + 5*p. Let v(h) = h**5 - h**4 + h**3 + h**2 + h. Let g(d) = r*n(d) - 5*v(d). Factor g(a).
a**3*(9*a + 2)**2
Let t(u) be the second derivative of 3*u**5/80 - u**3/2 + 27*u - 3. Factor t(f).
3*f*(f - 2)*(f + 2)/4
Let z(a) = a**4 + a**3 - a. Let c(j) = -12*j**4 - 68*j**3 - 116*j**2 - 44*j. Let w(k) = -c(k) - 16*z(k). Find d such that w(d) = 0.
-1, 0, 15
Let u(x) be the second derivative of -x**7/1400 - x**6/100 - 3*x**5/50 - x**4/5 - 19*x**3/3 + 24*x. Let o(l) be the second derivative of u(l). Factor o(q).
-3*(q + 2)**3/5
Let b = -1622 + 1622. Suppose -1/5*v**3 + b*v + 4/5 - 3/5*v**2 = 0. What is v?
-2, 1
Suppose 15*j + 36 = 21*j. Suppose -j = -240*r + 238*r. Factor 6/5*z**r + 0 - 4/5*z**4 + 1/5*z**5 + 1/5*z - 4/5*z**2.
z*(z - 1)**4/5
Let l = 247/2 - 123. Let i(u) be the second derivative of 1/6*u**3 - 1/20*u**5 + l*u**2 - 1/12*u**4 + 0 - 4*u. Factor i(f).
-(f - 1)*(f + 1)**2
Let n = 76 + -152. Let o = n - -79. Factor 0*w + 0 - 1/3*w**2 - 4/3*w**4 + 5/3*w**o.
-w**2*(w - 1)*(4*w - 1)/3
Suppose 3*f = 4*n - 37 - 8, -n = -3*f - 9. What is z in n + 8 - 5*z**2 - 20 - 5*z**3 = 0?
-1, 0
Suppose 2*w - 26 = -5*l, -l + 6 = -4*w - 8. Suppose 9 = 3*j + m, l*m - m + 27 = 3*j. Find z, given that -3/2*z**j - 3*z**3 + 0*z**2 + 3*z + 3/2 = 0.
-1, 1
Factor -20*v - 584 + 133*v + 2*v**3 + 685*v + 82*v**2 - 298.
2*(v - 1)*(v + 21)**2
Let s(i) be the second derivative of i**7/105 - 27*i**5/25 - 36*i**4/5 - 81*i**3/5 + i + 31. Factor s(r).
2*r*(r - 9)*(r + 3)**3/5
Let k(w) be the third derivative of w**5/390 - w**4/26 + 3*w**3/13 + 37*w**2 + 3. What is o in k(o) = 0?
3
Let c(p) be the third derivative of p**7/3780 - p**6/360 + p**5/90 + 7*p**4/24 - 12*p**2. Let k(q) be the second derivative of c(q). Let k(m) = 0. What is m?
1, 2
Let q be 217/(-147) + 7 + (-72)/(-63). Factor -q*k**2 - 25/3*k - 5/3*k**3 - 10/3.
-5*(k + 1)**2*(k + 2)/3
Factor -3/7*a**2 - 24/7*a + 0.
-3*a*(a + 8)/7
Determine k, given that -20/3*k**2 - 8*k + 4/3*k**5 + 20/3*k**4 + 20/3*k**3 + 0 = 0.
-3, -2, -1, 0, 1
Let j(k) = -2*k**3 - k**2 - 2*k - 1. Let r be j(-1). Suppose q**2 - 7*q**2 - 30*q**r - 4*q**5 + 16*q**3 + 8*q**4 + 4*q**2 = 0. Calculate q.
-2, 0, 2
Let s(b) be the second derivative of 30*b - 1/20*b**5 + 2/3*b**3 - 1/12*b**4 + 2*b**2 + 0. Factor s(a).
-(a - 2)*(a + 1)*(a + 2)
Factor -5 + 3207*u**3 + u**2 + 6*u**2 + 6*u**2 + 11*u - 3210*u**3.
-(u - 5)*(u + 1)*(3*u - 1)
Let g = 8530/11 - 42584/55. Let -g*x**2 + 0 + 3/5*x**3 + 3/5*x = 0. What is x?
0, 1
Let l(c) = -2*c**3 - 3*c**2 + 9*c + 1. Let j(x) = -10*x**3 - 14*x**2 + 44*x + 6. Let b(h) = -3*j(h) + 14*l(h). Determine q so that b(q) = 0.
-1, 2
Suppose -117*q + 114 + 120 = 0. What is z in 2/11*z**q + 2/11*z + 0 = 0?
-1, 0
Let i = -30397 - -30400. Factor -8 - 98/3*u**i - 238/3*u**2 + 160/3*u.
-2*(u + 3)*(7*u - 2)**2/3
Let w(r) be the first derivative of 10*r**3/3 + 5*r**2 - 3. Let d(z) = 2*z**2 + 2*z. Let f(m) = 16*d(m) - 3*w(m). Determine i, given that f(i) = 0.
-1, 0
Let v(y) = -y + 1. Let r(j) = -4*j**4 + 44*j**2 - 77*j + 37. Let n(f) = -r(f) + 5*v(f). Determine d so that n(d) = 0.
-4, 1, 2
Factor 9/2*c - 3/2*c**2 + 0.
-3*c*(c - 3)/2
Factor -14*h - 147/2 - 1/2*h**2.
-(h + 7)*(h + 21)/2
Let n(u) be the first derivative of 55 - 1/27*u**3 - 9*u - u**2. Factor n(g).
-(g + 9)**2/9
Let n be 11/10*238/1309. Solve n*c**2 + 1/5*c + 0 = 0.
-1, 0
Let m(n) be the third derivative of -16*n**7/175 - 77*n**6/300 - 11*n**5/150 + 17*n**4/60 - n**3/15 - 172*n**2. Determine u, given that m(u) = 0.
-1, 1/16, 1/3
Let p(d) be the first derivative of -4*d**3/3 + 16*d**2 - 48*d + 132. Factor p(c).
-4*(c - 6)*(c - 2)
Suppose -4 = 2*q - 10. Suppose 5*l - 5 = 25. Factor 7*i - 3*i - l*i**3 - i + q*i**5.
3*i*(i - 1)**2*(i + 1)**2
Let w = 40933/30 + -1364. Let m(x) be the third derivative of w*x**5 + 0*x + 4/27*x**3 + 0 + 5*x**2 + 3/20*x**6 + 10/27*x**4. Determine n so that m(n) = 0.
-1, -2/9
Let r(x) = 12*x + 68. Let o be r(-6). Let k be (-11)/(88/(-36))*o/(-9). Find f such that 0*f**3 + 2/11*f**4 - 2/11*f**5 + 0*f + 0 + 0*f**k = 0.
0, 1
Suppose 132 - 7 = 25*c. Let g(y) = 8*y**3 + 6*y**2 + 3*y - 5. Let v(s) = 7*s**3 + 2*s**3 + 3*s - 6 + 2*s**2 + 4*s**2. Let u(r) = c*v(r) - 6*g(r). Factor u(j).
-3*j*(j + 1)**2
Suppose 3*t = -h - 3*h - 24, -3*h + 7 = -4*t. Let z = t - -14. Solve -2*n**4 + 4 - 3*n**2 + n**3 + z*n + 0*n**2 + 9*n**2 - 3*n**3 = 0 for n.
-1, 2
Let y(d) be the second derivative of -1/84*d**7 - 21*d - 3/20*d**5 + 0 + 0*d**2 + 1/6*d**4 + 1/15*d**6 - 1/12*d**3. Factor y(a).
-a*(a - 1)**4/2
Let w(y) be the first derivative of y**5/20 + y**4/4 + y**3/3 + 4*y + 11. Let h(k) be the first derivative of w(k). Factor h(v).
v*(v + 1)*(v + 2)
Let u = 31/60 - -1/12. Let x = -233 - -1168/5. Factor 0 - x*o + u*o**3 + 3/5*o**4 - 3/5*o**2.
3*o*(o - 1)*(o + 1)**2/5
Let z be 120/320 + (-3)/(-24). Factor -8 - 3*q**2 + z*q**3 + 1/4*q**4 - 10*q.
(q - 4)*(q + 2)**3/4
Find r, given that 44858*r**2 - 44913*r**2 + 5*r - 3*r = 0.
0, 2/55
Solve -4*r**2 - 1/3*r**5 + 2/3*r**3 + r**4 + 0 + 8/3*r = 0.
-2, 0, 1, 2
Let l(h) = -h**2 + h + 1. Let r(j) = 8*j**2 + 184*j - 5. Let u(n) = 5*l(n) + r(n). Factor u(m).
3*m*(m + 63)
Let m = -1355 + 16261/12. Factor 1/12*o - m*o**2 + 1/6.
-(o - 2)*(o + 1)/12
Let p(o) be the first derivative of 2 + 0*o**3 + 2/55*o**5 + 3/22*o**4 - 4/11*o**2 + 0*o. Factor p(v).
2*v*(v - 1)*(v + 2)**2/11
Let h(d) = d**2 - 7*d + 5. Let n be h(7). Factor -13*t**3 + n*t**3 + 9*t**3 + 0*t + 3*t**2 - t**4 - 5*t + 2.
-(t - 1)**3*(t + 2)
Find o such that -21 - 72 - 23 + 6*o**2 - 2*o**2 - 112*o + 0*o**2 = 0.
-1, 29
Let y(g) be the third derivative of -g**6/360 + g**5/36 + 25*g**2. Factor y(d).
-d**2*(d - 5)/3
Let i(z) be the third derivative of -z**10/317520 - z**9/158760 - z**4/4 - 19*z**2. Let x(a) be the second derivative of i(a). Suppose x(h) = 0. Calculate h.
-1, 0
Let t(i) be the first derivative of -5/3*i**3 + 15/2*i**2 + 50*i - 23. Determine s so that t(s) = 0.
-2, 5
Let h(y) be the third derivative of y**5/60 + 3*y**4/8 + 3*y**3 - 3*y**2 + 14*y. Determine q so that h(q) = 0.
-6, -3
Let t(v) be the first derivative of 529*v**4/4 + 46*v**3 + 6*v**2 - 6*v + 17. Let n(x) be the first derivative of t(x). Determine q, given that n(q) = 0.
-2/23
Let j(v) = -4*v**3 - 2*v**2 + 10*v - 2. Let t(m) = -m**4 + m**3 - m**2 + m - 1. Let i(d) = j(d) - 2*t(d). Suppose i(x) = 0. Calculate x.
-1, 0, 2
Let v(q) be the first derivative of q**4/16 + 47*q**3/12 - 56. Solve v(k) = 0.
-47, 0
Let q(m) be the second derivative of -m**6/20 + 7*m**4/8 - 3*m**3/2 - m + 133. Factor q(n).
-3*n*(n - 2)*(n - 1)*(n + 3)/2
Let j(u) = 90 + u + 3*u - 110 - u. Let m be j(8). Suppose -1/6*q**m + 0*q**3 + 0*q + 0*q**2 + 0 + 1/6*q**5 = 0. What is q?
0, 1
Let h = 5 - 0. Suppose -4*l + 2*q + 24 = 0, -h*q - 11 = -3*l - 0*q. Suppose -11 - 1 - 8 + 18*y - 3*y**2 - l = 0. Calculate y.
3
Suppose 4*y - 3*l - 5 = 17, 5*y + 2*l - 16 = 0. Find w such that 4 - 5/4*w**y + 13*w**2 - 15*w - 3/4*w**3 = 0.
-4, 2/5, 1, 2
Let l(k) be the first derivative of k**5/15 + 2*k**4/3 