or k(d).
-2*d**2*(d - 1)*(d + 3)/9
Let a(n) = -n**3 + 2*n - 1. Let k(s) = 7*s**3 + 24*s**2 - 40*s + 14. Let g(f) = -2*a(f) + k(f). Suppose g(p) = 0. What is p?
-4, 2/3
Factor 1632*t - t**2 + 10558474 - 2*t**2 - 10780426.
-3*(t - 272)**2
Factor -171*r + 274*r - 88*r**3 - 54*r**2 - 648 + 41*r**3 + 44*r**3 + 302*r.
-3*(r - 3)**2*(r + 24)
Let j(t) = 3*t**3 + t**2 + 2. Let c(q) = -7*q**3 + 650*q**2 - 105621*q - 213862. Let w(g) = -3*c(g) - 6*j(g). Factor w(l).
3*(l - 327)**2*(l + 2)
Suppose 5*n + v - 21 = 0, -8*n = -7*n + v - 13. Factor -2/5*p**n + 2 - 8/5*p.
-2*(p - 1)*(p + 5)/5
Let g(h) be the second derivative of -h**6/135 + 229*h**5/90 - 6835*h**4/27 + 64064*h**3/27 - 25088*h**2/3 - 8772*h. Find v, given that g(v) = 0.
2, 3, 112
Let l(u) = 2*u**2 + 9*u - 35. Suppose 0*k - 56 = 8*k. Let x be l(k). Determine w, given that 4/5*w**5 - 16/5*w - 8/5*w**2 + x + 36/5*w**3 - 22/5*w**4 = 0.
-1/2, 0, 2
Let q(u) = 90 - 6*u**2 - u**2 + 12*u**2 + 84 - 8*u**2 - 13*u. Let v be q(-10). Factor 2*w + 1/4*w**2 + v.
(w + 4)**2/4
Let g(m) be the first derivative of 4*m + 13/2*m**2 - 17 + 3*m**3. Let d(f) = 22*f**2 + 32*f + 10. Let s(q) = -5*d(q) + 12*g(q). Let s(y) = 0. Calculate y.
-1
Suppose 4*b - 55 - 117 = -2*u, -2*b = -4*u + 304. Suppose 0 = u*t - 97*t. Factor 2/15*y**2 - 4/15*y + t.
2*y*(y - 2)/15
Let t = 809220 - 809216. Suppose -47/4*m**3 + 47*m - 9/4*m**t + 10 + 13/2*m**2 = 0. Calculate m.
-5, -2, -2/9, 2
Let o(s) = -25*s + 173. Let p be o(7). Let i be ((-28)/42)/(p*(-14)/(-36)). Determine n so that i*n - 2/7*n**2 + 8/7 = 0.
-1, 4
Suppose 1076/15*h - 48 - 2/15*h**3 - 118/5*h**2 = 0. Calculate h.
-180, 1, 2
Let f(m) = 24*m**2 + 657*m - 1311. Let j(i) = 13*i**2 + 328*i - 653. Let z(y) = 5*f(y) - 9*j(y). Find x, given that z(x) = 0.
-113, 2
Let n be 4/21*(-7 - 2415/(-138)). Let 44/13*s - 46/13 + 2/13*s**n = 0. What is s?
-23, 1
Let q = -19073 - -19559. Solve 21/4*v**3 + q + 1647*v - 375/2*v**2 = 0.
-2/7, 18
Let z(i) = i**3 - 5*i**2 - 3*i - 13. Let r be z(6). Solve 85*u**3 - 4*u**r - 93*u**3 + 6*u**5 = 0.
-2, 0, 2
Let y(s) be the second derivative of -s**5/40 + 17*s**4/24 - 14*s**3/3 + 13*s**2 + 66*s + 3. Factor y(q).
-(q - 13)*(q - 2)**2/2
Suppose -6806*z**3 + 13627*z**3 + 1776 - 6817*z**3 - 132*z**2 - 640*z = 0. What is z?
-6, 2, 37
Let r(v) = 38*v**2 + 250*v - 11. Let l(c) = 7*c**2 + 51*c - 2. Let i(j) = 33*l(j) - 6*r(j). Factor i(q).
3*q*(q + 61)
Let a be 36/10*22/(-33)*2725/(-2180). Solve 0 - 16/3*r + 0*r**2 + r**a - 1/6*r**4 = 0 for r.
-2, 0, 4
What is f in 178*f**5 - 259*f - 1514*f**2 - 64*f**5 - 13 + 24*f**5 - 873*f**4 - 57*f**5 - 2222*f**3 = 0?
-1, -1/9, 13
Solve -162/5 + 1047/5*l + 39/5*l**2 = 0 for l.
-27, 2/13
Let a(u) = -u**3 - 18*u**2 + 13*u - 54. Let i be a(-19). Let v = -58 + i. Factor 8*m + 27*m + 49 + 23 - 22 + 5*m**v.
5*(m + 2)*(m + 5)
Let k(l) be the second derivative of 9*l**4/2 - l**3/2 - 182*l. Let k(n) = 0. What is n?
0, 1/18
Let g(b) = b**3 - 19*b**2 + 19*b - 12. Let l be g(18). Let i be (l/14)/((-12)/(-252)). Let i*k**2 - 9*k**2 + 5*k - 3*k**3 + 4*k - 6 = 0. Calculate k.
-2, 1
Let s(a) be the first derivative of -a**6/180 - a**5/60 - a**4/72 + 192*a - 122. Let u(v) be the first derivative of s(v). Solve u(n) = 0 for n.
-1, 0
Let i(x) be the second derivative of -x**6/540 - x**5/15 - x**4 - 18*x**3 - 33*x + 1. Let d(r) be the second derivative of i(r). Factor d(b).
-2*(b + 6)**2/3
Let i(h) be the second derivative of h**4/30 + 8*h**3/3 + 336*h**2/5 - 571*h. Factor i(g).
2*(g + 12)*(g + 28)/5
Let x(k) be the first derivative of 4*k**3 - 2*k**4 - 36 - 12/5*k**5 + 0*k + 4*k**2. Factor x(m).
-4*m*(m - 1)*(m + 1)*(3*m + 2)
Let a = -49 - -51. Let k be a/(-2)*3 - -7. Determine b so that -104*b**3 - 84*b - 4*b**5 + 136*b**2 + 36*b**k + 20 - 5*b**4 + 5*b**4 = 0.
1, 5
Let n(x) = 2*x**2 - 28*x - 62. Let c(t) = -t + 11. Let q be c(9). Let h(k) = k**2 + 19*k + 85 - 44 - 3*k**q + k**2. Let g(z) = -8*h(z) - 5*n(z). Factor g(u).
-2*(u + 3)**2
Let f(m) = -8*m**4 - 132*m**3 - 20*m**2 + 6*m - 14. Let b(g) = 3*g**4 + 44*g**3 + 7*g**2 + g + 5. Let h(v) = 14*b(v) + 5*f(v). Factor h(z).
2*z*(z - 22)*(z - 1)*(z + 1)
Let p(s) be the third derivative of -7/120*s**6 - 1/8*s**4 - 1/140*s**7 + 94*s**2 + 0 + 0*s + 0*s**3 - 17/120*s**5. Factor p(w).
-w*(w + 1)*(w + 3)*(3*w + 2)/2
Let h(i) be the first derivative of -10*i**2 + 1/780*i**6 + 0*i**4 + 0*i + 0*i**3 + 27 - 1/39*i**5. Let x(f) be the second derivative of h(f). Factor x(j).
2*j**2*(j - 10)/13
Let h(q) be the third derivative of q**5/330 + 71*q**4/44 - 1782*q**2. Factor h(t).
2*t*(t + 213)/11
Let h(z) be the second derivative of -3*z**5/20 - 17*z**4/18 + 413*z**3/18 - 15*z**2 + 3173*z. Factor h(i).
-(i - 5)*(i + 9)*(9*i - 2)/3
Let -10/19*t**2 - 2/19*t**3 - 14/19*t - 6/19 = 0. Calculate t.
-3, -1
Let q(g) be the third derivative of g**8/84 + 4*g**7/21 + 4*g**6/15 - 2*g**5/3 - 3*g**4/2 - 9*g**2 - g. Find v such that q(v) = 0.
-9, -1, 0, 1
Let t be 60/450 - ((-6)/(-55) + 0). Let m(u) be the second derivative of 0 - 1/66*u**4 + 0*u**3 + 8*u + 0*u**2 + 3/110*u**5 + t*u**6. Let m(x) = 0. What is x?
-1, 0, 1/4
Let f(c) be the second derivative of 1/70*c**5 - 119*c + 2/21*c**4 + 0*c**2 + 4/21*c**3 + 0. Factor f(i).
2*i*(i + 2)**2/7
Solve -27*g**2 - 66*g**3 + 190*g**2 + 200*g**2 - 4*g**4 + 21*g**2 + 82*g**3 = 0 for g.
-8, 0, 12
Let n(b) be the first derivative of -128*b**2 - 17*b**4 - 320/3*b**3 - 4/5*b**5 + 0*b + 80. Factor n(o).
-4*o*(o + 1)*(o + 8)**2
Suppose -6*j = 29 - 101. Solve 63*p**2 - 3*p**3 - 11*p**3 - 18*p**3 - 8*p**4 + j*p + 20*p**5 - 55*p**2 + 0*p**4 = 0.
-1, -3/5, 0, 1
Let h(t) be the second derivative of -t**6/15 + t**5 - 8*t**4/3 + 3*t + 112. Determine b so that h(b) = 0.
0, 2, 8
Factor -74*b**4 + 134 + 10 - 236*b - 104*b**3 + 91*b**4 - b**5 + 280*b**2 - 107*b + 7*b.
-(b - 6)**2*(b - 2)**2*(b - 1)
Factor 520 + 2332/3*a - 4*a**2.
-4*(a - 195)*(3*a + 2)/3
Let q(d) be the second derivative of d**7/483 + 2*d**6/345 - d**5/115 - 4*d**4/69 - 7*d**3/69 - 2*d**2/23 - 1150*d. Factor q(l).
2*(l - 2)*(l + 1)**4/23
Let x = 20192 - 100942/5. Solve 6/5*z**4 - 3*z + 6/5*z**3 - 16/5*z**2 + 1/5*z**5 + x = 0 for z.
-3, -2, 1
What is z in 2/7*z**2 + 1284/7 - 62*z = 0?
3, 214
Determine l, given that 48/5 - 73/5*l**3 + 3*l**4 - 142/5*l - 1/5*l**5 + 153/5*l**2 = 0.
1, 2, 3, 8
Let r = -59779/3 + 19931. Factor r*k**3 - 16/3 - 12*k**2 - 2/3*k**4 + 40/3*k.
-2*(k - 2)**3*(k - 1)/3
Let j(s) be the second derivative of s**4/12 + 179*s**3/6 - 90*s**2 - 3*s + 269. What is g in j(g) = 0?
-180, 1
Find o, given that -224 - 86/5*o**2 + 2/5*o**3 + 592/5*o = 0.
4, 35
Let i(f) = -4*f**2 + 176*f + 428. Let a(d) = -14*d**2 + 706*d + 1693. Let u(q) = -4*a(q) + 15*i(q). Factor u(r).
-4*(r + 2)*(r + 44)
Suppose -55*l + 52*l + 18 = -m, 3*l = 18. Let t(k) be the second derivative of 6*k + 0*k**2 - 1/50*k**5 + m - 1/75*k**6 + 0*k**3 + 1/15*k**4. Factor t(v).
-2*v**2*(v - 1)*(v + 2)/5
Let n(z) be the third derivative of -z**8/336 - z**7/210 + 7*z**6/60 + 7*z**5/15 - z**4/3 - 16*z**3/3 - 1455*z**2. Let n(p) = 0. Calculate p.
-2, 1, 4
Let y = -7108/21 - -2388/7. Factor -2/3*j**3 + 0 - y*j - 4*j**2 + j**4 + 1/3*j**5.
j*(j - 2)*(j + 1)*(j + 2)**2/3
Let j(h) = -2*h**3 + 2*h - 1. Let m(q) = -12*q**3 + 5172*q**2 - 1674424*q + 1669260. Let l(z) = -4*j(z) + m(z). Let l(y) = 0. What is y?
1, 646
Find b such that -6 - 36*b**3 - 28*b**3 + 4*b**2 + 63*b**3 - b = 0.
-1, 2, 3
Let r = -3477/79 - -24418/553. Suppose r*c**2 - 24/7 + 23/7*c = 0. What is c?
-24, 1
Let t(l) be the first derivative of -l**4/2 + 13*l**2 - 24*l + 688. Factor t(u).
-2*(u - 3)*(u - 1)*(u + 4)
Suppose 10*o = 58 + 42. Suppose -o*q - 3*q + 26 = 0. Determine x, given that 0*x - 1/2*x**5 + 4*x**q - 6*x**3 + 3*x**4 + 0 = 0.
0, 2
Suppose 17 = 3*d - 4*a, 5*d = -6*a + 3*a - 20. Let k be (2 - d) + -2 - -3*1. Suppose 103*t**4 - 53*t**4 - 48*t**k - 2*t**3 = 0. What is t?
0, 1
Let h(s) be the first derivative of -s**5/60 + s**4/16 + 71*s**2/2 + 41. Let x(k) be the second derivative of h(k). Find d, given that x(d) = 0.
0, 3/2
Let s(v) = -v**3 - 27*v**2 - 27*v - 22. Let m be s(-26). Factor 74*o**m - 3*o - 3 - 77*o**4 - 12*o**3 - 2*o - 7*o - 18*o**2.
-3*(o + 1)**4
Let b = 62326 - 62294. Determine i, given that 1/7*i**3 - 29/7*i**2 + b*i - 28 = 0.
1, 14
Let w(j) be the second derivative of -j**5/80 -