16, -1, 0, 2/19, 2/5
Suppose 0*h + 4*h - 80 = 0. Let w(l) = -14*l + 334. Let b be w(23). Find q, given that -216*q + 473*q**2 - b*q**3 + h - 374*q**2 + 28 = 0.
1/4, 4
Let l(n) be the third derivative of n**8/33600 - n**7/6300 - 7*n**6/3600 - n**5/150 + 2*n**4 + 165*n**2. Let k(h) be the second derivative of l(h). Factor k(i).
(i - 4)*(i + 1)**2/5
Let n(h) be the second derivative of h**6/60 - 16*h**5/45 - 13*h**4/36 + 22*h**3/9 - 72*h**2 - 6*h + 2. Let d(z) be the first derivative of n(z). Factor d(w).
2*(w - 11)*(w + 1)*(3*w - 2)/3
Let w = 24697/1866 + 497/311. Factor 0 - 7/6*r**3 - w*r**2 + 13/3*r.
-r*(r + 13)*(7*r - 2)/6
Solve 6/5*k**3 - 66/5*k**2 + 2/5*k**4 - 48/5 + 106/5*k = 0.
-8, 1, 3
Let n(u) be the first derivative of -2*u**6/3 + 92*u**5/5 - 107*u**4 + 340*u**3/3 - 318. Determine w so that n(w) = 0.
0, 1, 5, 17
Let f(n) be the second derivative of n**4/54 - 95*n**3/9 + 284*n**2/9 - n + 221. Solve f(c) = 0.
1, 284
Let p(m) be the second derivative of m**7/280 + 7*m**6/120 + m**3/3 + 54*m**2 - 63*m. Let t(u) be the second derivative of p(u). Find z, given that t(z) = 0.
-7, 0
Factor -2/7*v**3 - 103968/7*v + 912/7*v**2 + 0.
-2*v*(v - 228)**2/7
Let r(k) be the second derivative of -5/3*k**4 + 0 + 235*k + 1/2*k**5 + 5/2*k**3 - 2*k**2 + 0*k**6 - 1/42*k**7. Find s, given that r(s) = 0.
-4, 1
Find t, given that 70 - 115 - 44 - 113 - t**2 - 158 + 42*t = 0.
12, 30
Suppose 31180 + 29943 - 1818*g + 2*g**2 - 64767 = 0. Calculate g.
-2, 911
Let n(g) be the first derivative of -64 + 28*g - 20/3*g**2 + 4/9*g**3. Solve n(v) = 0.
3, 7
Let 131/2*x**3 + 0*x - 3/2*x**5 - 105/2*x**2 + 0 - 23/2*x**4 = 0. What is x?
-35/3, 0, 1, 3
Suppose 2*r = -2*g + 6, 5*g + 4*r - 190 + 174 = 0. Let m(y) be the second derivative of 0 + 5/6*y**g - 1/10*y**5 + 4*y**2 - 16*y - 8/3*y**3. Factor m(d).
-2*(d - 2)**2*(d - 1)
Let z(k) be the second derivative of 3*k**6/2 - 129*k**5/20 - 141*k**4/4 + 387*k**3/2 + 81*k**2 + 2043*k. Find h such that z(h) = 0.
-3, -2/15, 3
Let i(h) = -158*h**2 + 2754*h + 2772. Let p(o) = -17*o**2 + 306*o + 308. Let m(v) = -3*i(v) + 28*p(v). Factor m(g).
-2*(g - 154)*(g + 1)
Let j = 392 + -326. Find b such that j - 32*b - 190*b**3 - 220*b**2 + 95*b**4 + 59 - 11*b**5 + b**5 + 232*b = 0.
-1, -1/2, 1, 5
Find h such that -570 + 81/5*h**3 - 1149/5*h**2 + 3/5*h**4 + 783*h = 0.
-38, 1, 5
Factor -14/9*v**3 - 1/9*v**4 + 3640/9*v + 157/3*v**2 - 67600/9.
-(v - 13)**2*(v + 20)**2/9
Let k be 10 - (2/25)/(20/2495). Let p(o) be the second derivative of 0 - k*o**5 - 2/15*o**3 + 0*o**2 + 28*o - 1/10*o**4. Factor p(x).
-2*x*(x + 1)*(x + 2)/5
Let a(d) = -100*d**3 + 1215*d**2 - 6785*d + 330. Let u(p) = -11*p**3 + 135*p**2 - 754*p + 36. Let n(t) = -6*a(t) + 55*u(t). Let n(i) = 0. What is i?
0, 8, 19
Suppose -d - 11 = -2*z, 2*z = 5*z - 5*d + 1. Factor -16 - 2*w - 8*w**3 + 34*w - 2*w**4 + z*w**4 - 12*w**2 - 2*w**4.
4*(w - 2)*(w - 1)**2*(w + 2)
Let k(p) be the first derivative of -2*p**3 + 0*p - 1/2*p**6 + 6/5*p**5 + 3/2*p**2 - 53 + 0*p**4. Factor k(c).
-3*c*(c - 1)**3*(c + 1)
Let y(h) be the first derivative of 0*h + 90 - 52/3*h**3 + 3*h**4 + 8*h**2. Factor y(n).
4*n*(n - 4)*(3*n - 1)
Suppose 2*q = 22*q - 40. Factor -34*g**3 - 15 - 116*g - g**3 + g**4 - 12*g**q + 3*g**4 - 57 + 71*g**3.
4*(g - 2)*(g + 1)**2*(g + 9)
Let j = -1287 - -274. Let l = 1013 + j. Suppose l*p**4 + 4/9*p**3 - 2/9*p - 2/9*p**5 + 0 + 0*p**2 = 0. What is p?
-1, 0, 1
Let z = 29 - 28. Let i be 10/(z - 0 - 3). Let u(m) = -5*m**2 - 2*m - 5. Let p(y) = y**2 + 1. Let v(t) = i*u(t) - 30*p(t). Find w such that v(w) = 0.
1
Factor 0*b**2 + 1/6*b**5 + 1/3*b**4 + 0*b - 1/2*b**3 + 0.
b**3*(b - 1)*(b + 3)/6
Let f(h) be the third derivative of -h**6/30 + 7*h**5/3 + 76*h**4/3 + 104*h**3 + 566*h**2. Factor f(n).
-4*(n - 39)*(n + 2)**2
Suppose 616 - 16 = -10*z. Let g be 0 - (-234)/z - (-2 + -2). Determine q, given that 1/5*q**2 + g*q**5 - 3/10*q + 1/5*q**3 + 1/10 - 3/10*q**4 = 0.
-1, 1
Let a = -426172 - -2983220/7. Let -4/7*v**5 + 48/7*v**2 + 8/7*v**3 - 36/7*v + 0 - a*v**4 = 0. Calculate v.
-3, 0, 1
Let c(s) be the first derivative of -s**6/480 - 3*s**5/40 - 5*s**4/8 - 113*s**3/3 - 154. Let k(j) be the third derivative of c(j). Let k(r) = 0. Calculate r.
-10, -2
Let b(g) be the second derivative of 3/5*g**5 - 1/15*g**6 - 3 + 0*g**2 + 2/3*g**4 - 8/3*g**3 - 1/21*g**7 - 8*g. Suppose b(x) = 0. What is x?
-2, 0, 1, 2
Let s(m) = 50 - 145 + 3 - 2*m. Let u be s(-46). Let 0*o - 1/7*o**5 + u - 2/7*o**2 - 5/7*o**3 - 4/7*o**4 = 0. Calculate o.
-2, -1, 0
Suppose 11*k = -2*f + 14*k + 22, -4*f + 2*k + 28 = 0. Suppose -111*p**3 + 21*p**f + 93*p**2 + 1557*p + 1539*p - 3114*p + 15*p**4 = 0. What is p?
-3, 0, 2/7, 1
Suppose 14*h - 1058 = 3030. Suppose -h = 9*t - 310. Suppose -20/3*l**3 + 4/3*l**5 - 4/3*l**t + 4/3*l**4 + 32/3*l - 16/3 = 0. What is l?
-2, 1
Suppose -514*u = 259*u - 807 - 1512. Solve 18/11*p**2 + 46/11*p + 24/11 - 2/11*p**4 - 6/11*p**u = 0.
-4, -1, 3
Let r(d) = -21*d**4 - 1156*d**3 - 22*d**2 + 1285*d. Let y(g) = 3*g**4 + 165*g**3 + 3*g**2 - 183*g. Let j(u) = 6*r(u) + 43*y(u). Factor j(t).
3*t*(t - 1)*(t + 1)*(t + 53)
Factor -1/7*f**4 - 41/7*f**2 - 20/7*f - 22/7*f**3 + 0.
-f*(f + 1)**2*(f + 20)/7
Let n(s) be the first derivative of s**5/10 + s**4/8 - s**3/2 - s**2/4 + s + 4169. Let n(f) = 0. What is f?
-2, -1, 1
Let d(i) be the first derivative of 14*i + 1/6*i**4 + 1/90*i**5 - 3 + 5/9*i**3 - 25/9*i**2. Let v(w) be the first derivative of d(w). Factor v(m).
2*(m - 1)*(m + 5)**2/9
Solve 3/4*w**2 - 1839/2 + 1833/4*w = 0.
-613, 2
Let d(v) be the second derivative of -v**6/15 + 41*v**5/5 - 1757*v**4/6 + 2960*v**3/3 + 4800*v**2 + 4*v - 602. Determine x, given that d(x) = 0.
-1, 3, 40
Let q(y) = -11*y**3 - 119*y**2 - 5*y - 15. Let o(b) = 27*b**3 + 297*b**2 + 12*b + 36. Let i(u) = -5*o(u) - 12*q(u). Suppose i(c) = 0. Calculate c.
-19, 0
Let p(d) be the third derivative of d**5/60 + 69*d**4/2 + 28566*d**3 - 314*d**2. Solve p(a) = 0 for a.
-414
Let q(k) be the second derivative of -4*k**6/15 + 7*k**5/10 + 61*k**4/6 + 32*k**3/3 - 60*k**2 + 4290*k. Let q(n) = 0. What is n?
-2, 3/4, 5
Let f = 288 - 336. Let m be 4 + ((-26)/6)/(f/(-36)). Factor 1/4*n**2 + 0 - 3/4*n**3 + 0*n + m*n**4 - 1/4*n**5.
-n**2*(n - 1)**3/4
Suppose 27370 = -249*r + 28117. Factor 0 - 2/17*b**4 - 288/17*b**2 - 48/17*b**r + 0*b.
-2*b**2*(b + 12)**2/17
Let g(s) = -s**2 - 8*s - 7. Let h be g(-6). Suppose -364*d + 39 + 1672*d**2 + 343*d**h - 132*d - 1680*d**3 - 637*d**4 + 28 - 19 = 0. What is d?
-2, 2/7, 3
Let j(i) be the second derivative of 5*i**4/12 + 2360*i**3/3 + 556960*i**2 + 95*i + 3. Let j(l) = 0. What is l?
-472
Let o(v) be the second derivative of 0*v**3 - 13*v - 8*v**2 - 1/180*v**4 + 0 - 1/450*v**5. Let n(w) be the first derivative of o(w). What is r in n(r) = 0?
-1, 0
Let i be 10/(-15)*(-9)/6. Let c(w) = w + 2. Let l(x) = -x**2 + 5*x - 10. Let j(n) = i*l(n) + 2*c(n). Factor j(b).
-(b - 6)*(b - 1)
Let h(p) be the first derivative of -3*p**4/16 - 51*p**3/4 + 81*p**2 - 165*p - 633. Determine l, given that h(l) = 0.
-55, 2
Find w, given that 2*w**3 + 15*w**3 - 19*w - 24*w**5 - 13*w**4 + 61*w**2 + 25*w**5 - 27*w - 20*w = 0.
-2, 0, 1, 3, 11
Let b(m) be the second derivative of m**9/22680 - m**7/3780 + m**4/2 - m**3/2 + 115*m. Let p(k) be the third derivative of b(k). Factor p(r).
2*r**2*(r - 1)*(r + 1)/3
Let s(w) = 5*w**3 - 2*w + 2. Let t be s(1). Suppose t*q + 3 - 13 = 0. What is i in 16*i + 4*i**q - 41 + 41 = 0?
-4, 0
Let d(v) be the second derivative of 15/14*v**3 + 6 + v + 1/4*v**4 - 1/140*v**5 + 0*v**2 - 1/210*v**6. Let d(b) = 0. Calculate b.
-3, 0, 5
Suppose -4*w - 3*h = 19, 162*w - 156*w = -4*h - 24. Find t, given that 0 + 0*t + 2*t**3 - 2*t**w - 3/2*t**5 + 5/2*t**4 = 0.
-1, 0, 2/3, 2
Let z(v) be the second derivative of -v**6/6 + 11*v**5/2 - 6655*v**3/3 + 73205*v**2/2 - 144*v - 4. Factor z(a).
-5*(a - 11)**3*(a + 11)
Let m(u) be the first derivative of u**4/24 + 13*u**3/3 + 169*u**2 - 29*u + 29. Let r(f) be the first derivative of m(f). Factor r(p).
(p + 26)**2/2
Let z(k) be the third derivative of 5/24*k**3 + 25/24*k**4 + 0*k + 0 + 25/12*k**5 + 14*k**2. Factor z(u).
5*(10*u + 1)**2/4
Let d = -490 - -490. Suppose 1 + 11 = -4*y, 0 = 2*m - y - 959. Factor -481*a**5 + 6*a**3 - 3*a + d*a**2 + 0*a**2 + m*a**5.
-3*a*(a - 1)**2*(a + 1)**2
Determine r so that 82*r**