s d?
-8, 0
Let s be (178 + -1)/((-15)/(-10)). Let k = 124 - s. Factor -19 + 3*i**2 + k*i**3 + 9*i**2 + 7 + 2*i - 8*i**3.
-2*(i - 6)*(i - 1)*(i + 1)
Suppose 14 = -x - v + 52, 2*x - 3*v - 61 = 0. Let u = 37 - x. What is f in -7*f**2 - 10*f**2 + 21*f**2 - f**u + 6*f = 0?
-2, 0
Suppose 92/3*y - 26/3*y**2 - 19/3*y**3 - 1/3*y**5 - 56/3 + 10/3*y**4 = 0. Calculate y.
-2, 1, 2, 7
Suppose 55 = 28*s + 47*s - 11*s - 265. Determine q, given that 127/6*q**2 + 25/3*q - 381/2*q**4 - 15/2*q**s + 0 - 445/6*q**3 = 0.
-25, -2/5, -1/3, 0, 1/3
Let n(v) be the first derivative of -32/11*v - 1/33*v**3 + 3/2*v**2 - 15. Factor n(g).
-(g - 32)*(g - 1)/11
Let o = -35593 - -1031997/29. Let t = 716/87 + o. Find u, given that 4/3*u + 0 + t*u**2 = 0.
-1, 0
Suppose -32*q = -68*q - 92*q. Let x(p) be the third derivative of -7/3*p**4 + q - 98/3*p**3 + 0*p + 13*p**2 - 1/15*p**5. Find v, given that x(v) = 0.
-7
Suppose 16*z - 5 = -8*z - 5. Let k(f) be the second derivative of 1/75*f**6 + 1/15*f**3 + 0 - 1/30*f**4 + 17*f - 1/50*f**5 + z*f**2. Factor k(x).
2*x*(x - 1)**2*(x + 1)/5
Let m(l) be the first derivative of -58 + 0*l + 0*l**3 + 20*l**4 - 5/2*l**2. Determine k so that m(k) = 0.
-1/4, 0, 1/4
Let p(l) be the third derivative of l**8/1344 - 17*l**7/420 + 3*l**6/5 + 17*l**5/120 - 289*l**4/96 - 4656*l**2. Suppose p(c) = 0. What is c?
-1, 0, 1, 17
Let u(x) = x**3 - 11*x + 5. Let v(b) = b**3 + b**2 - 10*b + 4. Let g = 16 - 24. Let d = g + 4. Let f(c) = d*u(c) + 5*v(c). Factor f(r).
r*(r - 1)*(r + 6)
Suppose -2/11*b**2 + 0 - 2*b = 0. Calculate b.
-11, 0
Let j(y) = 11*y**2 + 944*y + 103076. Let n(f) = -10*f**2 - 940*f - 103074. Let o(g) = -8*j(g) - 9*n(g). Let o(b) = 0. Calculate b.
-227
Let u(g) = -4*g**2 + 35*g - 67. Let a = 94 + -12. Let w(p) = -11 - 11*p - 124 - 5*p**2 - 3*p**2 + a*p. Let h(y) = -7*u(y) + 3*w(y). Factor h(s).
4*(s - 4)**2
Let f(h) = -2*h**2 - 3*h + 11. Let i(m) = 2*m**2 + m - 11. Let d(g) = -4*f(g) - 3*i(g). Determine o, given that d(o) = 0.
-11/2, 1
Determine u, given that -3115*u**3 + 1770957 - 1770997 + 590*u - 400*u**4 - 2289*u**2 + 320*u**5 + 524*u**2 = 0.
-2, -1, 1/8, 4
Factor 1108/3*p**2 + 2228/3*p - 4/3*p**3 + 372.
-4*(p - 279)*(p + 1)**2/3
Let w(a) = 43*a**2 + 4502*a - 2513291. Let r(d) = -5*d**2 - 2*d + 1. Let l(n) = 18*r(n) + 2*w(n). Factor l(m).
-4*(m - 1121)**2
Let a = 156064 + -156062. Let 4/3 + 0*c - 1/3*c**a = 0. Calculate c.
-2, 2
Factor 71*s**3 + 9*s**3 - 2*s**5 + 3*s**5 + 4*s**4 - 20*s**3 - 23*s**4.
s**3*(s - 15)*(s - 4)
Let v(m) = 14*m**2 + 379*m + 27. Let z be (-2)/(12/81*(-14)/(-28)). Let a be v(z). Let a*u**3 + 0*u**2 - 3/5*u**4 + 0 - 1/5*u**5 + 0*u = 0. Calculate u.
-3, 0
Let r be (-8 - 2211/(-268))*4*2. Factor 9/2*n - 3/2*n**r + 0.
-3*n*(n - 3)/2
Let m(p) be the first derivative of -5*p**6/21 + 64*p**5/35 - 9*p**4/14 - 12*p**3/7 - 4408. Determine o, given that m(o) = 0.
-3/5, 0, 1, 6
Let m(j) be the third derivative of -j**8/84 - 6*j**7/35 - 23*j**6/30 - 7*j**5/15 + 4*j**4 + 32*j**3/3 + 7*j**2 + 23. Suppose m(u) = 0. What is u?
-4, -1, 1
Let p be -3 + (-19)/((-133)/168). Let a be 11/((-77)/p) - -5. Let 36/5*r**a + 26/5*r**4 - 14/5*r - 6/5*r**5 - 44/5*r**3 + 2/5 = 0. Calculate r.
1/3, 1
Let u be 3/(1/2*2). Let v(m) be the first derivative of 2*m + 25*m + 5*m**2 - 3*m**u + 4*m**3 - 10 + 4*m**2. Factor v(q).
3*(q + 3)**2
Let i be (-6)/(-9) - (34/12 + -3). Let p(t) be the third derivative of 0 + 15*t**2 - 10/3*t**3 - 1/12*t**5 + i*t**4 + 0*t. Factor p(z).
-5*(z - 2)**2
Let m(r) be the second derivative of -1/8*r**5 + 7 + 2*r + 35/24*r**4 - 55/12*r**3 + 25/4*r**2. Determine s, given that m(s) = 0.
1, 5
Let k(m) = 140*m + 23102. Let d be k(-165). What is a in -a**d - 2/3*a**3 - 4/3 + 1/3*a**4 + 8/3*a = 0?
-2, 1, 2
Let h(k) be the third derivative of k**8/2016 - 11*k**7/3780 + k**6/540 + k**4/4 - 4*k**3/3 + 32*k**2. Let z(n) be the second derivative of h(n). Factor z(q).
2*q*(q - 2)*(5*q - 1)/3
Let i(m) be the third derivative of -17*m**2 + 18*m**3 + 0 + 13/3*m**4 + 0*m - 1/15*m**5. Suppose i(f) = 0. What is f?
-1, 27
Let n(d) be the first derivative of 21/4*d**4 + 18*d**3 - 194 + 12*d**2 - 9/5*d**5 + 0*d. Factor n(q).
-3*q*(q - 4)*(q + 1)*(3*q + 2)
Find y such that -418/5*y**2 - 72*y + 0 + 18/5*y**4 - 42/5*y**3 + 2/5*y**5 = 0.
-9, -4, -1, 0, 5
Let g(l) be the second derivative of l**5/4 + 55*l**4/4 - 675*l**3/2 - 76545*l**2/2 - 641*l + 4. Factor g(q).
5*(q - 21)*(q + 27)**2
Let g(m) be the second derivative of m**5/5 - 5*m**4 + 94*m**3/3 - 66*m**2 - 73*m + 29. Solve g(d) = 0 for d.
1, 3, 11
Suppose -6*c**4 + 1089/2 + 39*c**3 - 13/2*c**2 - 1485/4*c + 1/4*c**5 = 0. What is c?
-3, 2, 3, 11
Let r be ((9/4)/((-6)/(-16)))/3. Factor -6 - 6 + 7 - 5*k**r + 10*k**2.
5*(k - 1)*(k + 1)
Let m(u) be the second derivative of u**7/630 - u**6/360 - 53*u**4/12 + 4*u + 2. Let o(l) be the third derivative of m(l). What is y in o(y) = 0?
0, 1/2
Let w(m) = 3*m - 15. Let i(c) = -c + 5. Let u(v) = -17*i(v) - 6*w(v). Let p be u(-3). Factor -l**2 - p*l**2 - 141 + 7*l**2 + 28*l + 43.
-2*(l - 7)**2
Suppose 158 = -2*m + 4*o, 0 = 5*m - 4*o + 331 + 52. Let d be -11 + (-1005)/m - 1*2. Factor -4/5*l + d*l**3 + 0 + 2/5*l**2.
2*l*(l - 1)*(l + 2)/5
Let f be (216/21 + -10)/(48/42). Let t(z) be the second derivative of 15/2*z**2 + f*z**4 + 26*z + 0 + 3*z**3. Factor t(y).
3*(y + 1)*(y + 5)
Factor 263169 - 30098*k - 30547*k + 59619*k + k**2.
(k - 513)**2
Suppose 0 = h - 4*h + 2*f + 40, 3*h - 5*f - 55 = 0. Find q, given that 240*q**3 - 176*q**2 - 119*q**2 + 13*q**5 - h*q**5 - 5*q**2 + 57*q**4 = 0.
-10, 0, 1
Let m = -28/821 - -4161/1642. Factor -1/2*j**2 + 2*j + m.
-(j - 5)*(j + 1)/2
Let b = 215 - 213. Determine m, given that 38 - 67 + 29 + 16*m + b*m**2 = 0.
-8, 0
Let a(o) be the second derivative of -o**7/28 - 23*o**6/20 + 51*o**5/40 + 1831*o**4/8 - 904*o**3 + 1344*o**2 + 192*o. Solve a(p) = 0 for p.
-16, 1, 7
Solve -50*z**3 - 8/3*z**4 - 244/3*z**2 + 0 - 34*z = 0.
-17, -1, -3/4, 0
Let x = 229 - 197. Solve -27*h**3 + x*h + 72*h**3 - 14*h**2 - 22*h**3 - 24 - 21*h**3 = 0 for h.
2, 3
Let 1014*g**2 + 241340450 + 2/5*g**3 + 856830*g = 0. What is g?
-845
Let z = -44 + 52. Let g(k) = -k + 10. Let l be g(z). Suppose 2*o - 2*o**2 + 898*o**3 - 3*o + l - o - 896*o**3 = 0. What is o?
-1, 1
Let j(m) be the third derivative of m**9/12096 + 5*m**8/4032 + m**7/504 - m**6/18 + m**5/30 + 63*m**2. Let n(h) be the third derivative of j(h). Factor n(c).
5*(c - 1)*(c + 2)*(c + 4)
Find l, given that -1/7*l**2 - 435/7 + 92/7*l = 0.
5, 87
Let o(w) be the second derivative of w**9/7560 - w**8/1680 + w**7/1260 - 13*w**4/12 - w**3/3 - 85*w. Let i(m) be the third derivative of o(m). Factor i(a).
2*a**2*(a - 1)**2
Factor -233523/5 + 1674/5*o - 3/5*o**2.
-3*(o - 279)**2/5
Let t = -426 + 430. Suppose -17 = -3*h + 2*d, 5*h + 5*d - 24 = t*d. Find v such that -5*v**4 + 5/3 + 10/3*v**3 - 5*v + 5/3*v**h + 10/3*v**2 = 0.
-1, 1
Factor -5808 + 38*l**2 - 471*l + 42*l**2 + 40*l**2 + 3*l**3 + 810*l + 585*l.
3*(l - 4)*(l + 22)**2
Let k = -49 - -54. Factor u**3 - 16*u + 10 - k*u**2 + 0*u**3 + 8*u + 2.
(u - 6)*(u - 1)*(u + 2)
Let m(v) = v**3 - 20*v**2 - 3*v + 58. Let o be m(20). Let n be (-1 + 0)*(o + -4 + 4). Factor 3/4*w**4 + 1/4*w**5 + 0*w + 3/4*w**3 + 0 + 1/4*w**n.
w**2*(w + 1)**3/4
Suppose 1 = -2*d - 5*c + 10*c, 5*d + 4*c - 80 = 0. Let s = -6 - -12. Factor -10 - 15*q + 4 + d*q**2 - s*q.
3*(q - 2)*(4*q + 1)
Let f(h) be the third derivative of h**8/168 - 149*h**7/105 + 1406*h**6/15 - 2738*h**5/15 + 5*h**2 - 289*h. Determine c so that f(c) = 0.
0, 1, 74
Let n(u) be the second derivative of u**5/20 + 17*u**4/12 + 5*u**3 + 177*u + 4. Suppose n(g) = 0. What is g?
-15, -2, 0
Let m(q) be the first derivative of 3*q**4/4 - 441*q**3 + 73260*q**2 - 145200*q - 3311. Find x, given that m(x) = 0.
1, 220
Determine k so that -43*k**2 - 5575*k**4 - 5555 + 794*k**2 - 5578*k**5 + 22250*k**3 + 22225*k + 5583*k**5 - 34101*k**2 = 0.
1, 1111
Factor -2/5*t**2 + 2/15*t - 16/3*t**3 + 0.
-2*t*(5*t + 1)*(8*t - 1)/15
Let l(t) = 23*t**2 + 376*t. Let n(f) = 19*f**2 + 376*f. Let h(k) = 5*l(k) - 6*n(k). Find b such that h(b) = 0.
0, 376
Let a(r) = 4*r**3 - 13*r**2 - 45*r + 45. Let j(v) = -15*v**3 + 52*v**2 + 176*v - 180. Let q(h) = -11*a(h) - 3*j(h). Determine y, given that q(y) = 0.
-3, 1, 15
Suppose 6*o**2 + 221*o + 416*o**3 - 826*o**2 + 29*o - 4*o*