74)
Let j(b) be the first derivative of -b**4/10 - 296*b**3/5 - 3738. Find t, given that j(t) = 0.
-444, 0
Suppose 2/9*i**4 - 142/9*i**2 + 20/9*i**3 + 40/3*i + 0 = 0. What is i?
-15, 0, 1, 4
Let r(p) be the third derivative of -5*p**8/336 + 5*p**7/42 - 7*p**6/24 + p**5/4 - 1302*p**2. Find f such that r(f) = 0.
0, 1, 3
Let l(f) be the third derivative of 13*f**5 - 5*f**4/24 + 868*f**2. Factor l(r).
5*r*(156*r - 1)
Let a = 3369 + -3355. Let o(t) be the third derivative of -20/3*t**3 - 35/6*t**4 + 23/24*t**6 + a*t**2 + 1/6*t**7 + 0 + 0*t + 1/2*t**5. Solve o(s) = 0 for s.
-2, -2/7, 1
Factor 47*n**2 + n**4 + 1264*n + 15*n**3 + 1287*n + 10*n**3 - 2528*n.
n*(n + 1)**2*(n + 23)
Let y(n) be the first derivative of -8*n - 14 + 0*n**2 - 5/6*n**3 + 5/12*n**4. Let l(c) be the first derivative of y(c). Factor l(t).
5*t*(t - 1)
Let y be (-15 + 2410/160)/((-2)/(-1)). Let b(w) be the second derivative of -13*w + 0*w**2 + 0 + 1/16*w**3 + y*w**5 + 1/12*w**4. Let b(p) = 0. Calculate p.
-1, -3/5, 0
Let x(m) be the first derivative of -m**5/5 + 11*m**4/4 + 172*m**3/3 - 190*m**2 - 762. Factor x(j).
-j*(j - 19)*(j - 2)*(j + 10)
Suppose -q = 4*q - 5*u - 35, 2*q = -5*u. Let r(y) be the second derivative of 0 + 2*y**3 - 3/20*y**q + 3*y - 1/4*y**4 + 6*y**2. Factor r(g).
-3*(g - 2)*(g + 1)*(g + 2)
Let q(j) = 4*j**2 + 2. Let d(n) = -7*n**2 + 2*n - 3. Let u(r) = r + 4. Let h be u(-1). Let l(g) = h*q(g) + 2*d(g). Suppose l(k) = 0. What is k?
0, 2
Suppose -1/2*c**5 + 72*c**2 + 59/2*c**3 - 218*c + 120 - 3*c**4 = 0. What is c?
-10, -4, 1, 6
Let d be (3 + (-192)/66)*2 + 36/(-198). Let i(p) be the third derivative of -1/15*p**5 + 1/3*p**4 - 1/30*p**6 + 2*p**2 + 0*p**3 + 0 + d*p. Factor i(n).
-4*n*(n - 1)*(n + 2)
Suppose 1706*y = -1738*y + 3487*y. Let y - 5/2*t**2 + 25/2*t = 0. What is t?
0, 5
Let m be (7 - 3) + 2*-1. Let t = 2/782707 - -1565392/8609777. Solve 2/11*h**m + 0*h - t = 0.
-1, 1
Let b = -47752 + 2578733/54. Let r = b + 5/27. Suppose r*k + 1/2*k**4 - 3/2*k**2 - 1/2*k**3 - 1 = 0. What is k?
-2, 1
Let -148/7*a**2 + 92/7 - 226/7*a - 6/7*a**3 = 0. What is a?
-23, -2, 1/3
Let z = -63 - -70. Let v(f) = -f**2 - 16*f + 9. Let l(s) = -3*s**2 - 49*s + 24. Let g(c) = z*v(c) - 2*l(c). Let g(j) = 0. Calculate j.
-15, 1
Let a(n) = n**5 - 3*n**4 + n**2 + n - 1. Let d(u) = 11*u**5 - 39*u**4 - 22*u**3 + 145*u**2 - 71*u - 1. Let f(q) = 2*a(q) - 2*d(q). Find b such that f(b) = 0.
-2, 0, 3/5, 2, 3
Factor 0 + 31/6*s**3 - 85/2*s**2 + 75/2*s - 1/6*s**4.
-s*(s - 15)**2*(s - 1)/6
Let u(v) = 4632 + 6*v**2 - 65*v + 4700 - 9273. Let g(q) = 13 - 7*q + 0 + 3*q**2 + 16 - 25*q. Let j(x) = -5*g(x) + 2*u(x). Solve j(t) = 0 for t.
1, 9
Suppose 23*c + 6759 = -5293. Let u = c - -529. Factor 3/5*a**u + 0 + 0*a**2 + 0*a**4 - 6/5*a**3 + 3/5*a.
3*a*(a - 1)**2*(a + 1)**2/5
Let b(d) be the third derivative of -d**8/20160 + d**7/1680 + d**6/180 + 31*d**5/30 + 6*d**2. Let s(y) be the third derivative of b(y). Factor s(z).
-(z - 4)*(z + 1)
Let t be (0 - (-378)/(-30)) + (-24 + 16 - -21). Suppose 32/5 + t*l**2 + 16/5*l = 0. Calculate l.
-4
Let -609/4*o - 3/4*o**2 + 0 = 0. Calculate o.
-203, 0
Let j(y) = y**2 + 5*y - 21. Let g be j(4). Let b(k) = -5*k + 75. Let u be b(g). Factor -1/10*i**2 + u - 1/10*i.
-i*(i + 1)/10
Let a(c) be the second derivative of -1/8*c**4 - 675*c**2 + 7 - 15*c**3 - 11*c. Factor a(b).
-3*(b + 30)**2/2
Let p = -3936 + 3939. Let x(b) be the third derivative of 1/4*b**p - 1/240*b**6 + 0 - 9*b**2 + 0*b + 1/48*b**4 - 1/40*b**5. Factor x(w).
-(w - 1)*(w + 1)*(w + 3)/2
Suppose c - 16 = -2*w, -w - 4 = -4*c - 3. Factor -w*p**3 + 11*p**3 - 31*p + 15*p.
4*p*(p - 2)*(p + 2)
Let s = -44 - -72. Suppose -s*u = -33*u + 20. Let -5*p**u + 4*p**4 + 4*p**3 + 5 - 5 - 3*p**2 = 0. What is p?
0, 1, 3
Let j(t) = t**4 - 875*t**3 - 21413*t**2 + 4807*t. Let n(v) = -1751*v**3 - 42826*v**2 + 9613*v. Let f(l) = 9*j(l) - 5*n(l). Factor f(m).
m*(m + 49)**2*(9*m - 2)
Let a(o) = 38*o**3 - 143*o**2 - 288*o - 15. Let d(c) = 10*c**3 - 36*c**2 - 72*c - 4. Let g(w) = -4*a(w) + 15*d(w). Solve g(r) = 0.
-2, 0, 18
Let i be (15/(-100))/(11/(-44)). Let v = -620 + 622. Find o, given that 0*o**v - i*o**3 - 1/5*o**4 + 0 + 4/5*o = 0.
-2, 0, 1
Determine s, given that 24000 + 176878 + 2046*s + 116880 - 85043 + 116128 + 3*s**2 = 0.
-341
Let v(z) be the first derivative of -2*z**5/35 + 88*z**4/7 + 710*z**3/21 + 178*z**2/7 + 220. Let v(n) = 0. What is n?
-1, 0, 178
Suppose 4*f - 4 = 3*o, -7*f = -10*f + o - 2. Let k be f/7 - (-112)/49. Determine d, given that 3*d**2 - 4*d**k + 4*d**3 + 9*d**2 = 0.
-2, 0
Let y be (16/120 + 2/5)*972/81. Find c, given that 26/5*c**3 + 18/5*c**2 + 6/5*c**5 + 8/5 - 26/5*c**4 - y*c = 0.
-1, 1/3, 1, 2
Let j(f) = 15*f**5 - 166*f**4 - 38*f**3 - 3*f**2 - 3*f - 3. Let p(r) = 17*r**5 - 165*r**4 - 38*r**3 - 4*r**2 - 4*r - 4. Let u(q) = 4*j(q) - 3*p(q). Factor u(i).
i**3*(i - 19)*(9*i + 2)
Suppose -265*x + 44 = -254*x. Factor -8 - 37*p**3 - 9*p**4 - x*p + 14*p**4 + 30*p**2 + 14*p**3.
(p - 2)**2*(p - 1)*(5*p + 2)
Solve -m**4 - 7*m - 1745*m**3 + 1741*m**3 + m**2 + 11*m = 0.
-4, -1, 0, 1
Suppose -b = -5*l - 40, 0 = -5*b - 172*l + 177*l + 60. Let c(j) be the first derivative of j**b + 5/4*j**4 + 0*j**3 + 0*j**2 + 15 + 0*j. Factor c(s).
5*s**3*(s + 1)
Let i be (-5 - (-11 + 4))*14. Solve -1132*s**5 - 64*s**3 - i*s + 66*s**4 - 136*s**2 + 1096*s**5 + 198*s**4 = 0.
-1/3, 0, 1, 7
Let n(y) be the first derivative of 3*y**5/140 + 5*y**4/28 + y**3/2 + 9*y**2/14 - 43*y - 21. Let k(g) be the first derivative of n(g). Factor k(j).
3*(j + 1)**2*(j + 3)/7
Let j = -70065 + 350406/5. Factor j*s**2 - 21/5*s - 2/5.
(3*s - 1)*(27*s + 2)/5
Let w(a) be the second derivative of -4913*a**7/63 + 3179*a**6/5 - 6511*a**5/5 - 3749*a**4/9 - 151*a**3/3 - 3*a**2 + a - 179. Factor w(y).
-2*(y - 3)**2*(17*y + 1)**3/3
Let r = 107 + 68. Let m be 4/14 + (-25)/r. Find n, given that -m - 1/7*n**3 + 1/7*n**2 + 1/7*n = 0.
-1, 1
Let v(c) be the third derivative of 4*c**7/105 - 101*c**6/60 - 79*c**5/30 + 13*c**4/6 + 794*c**2. Factor v(b).
2*b*(b - 26)*(b + 1)*(4*b - 1)
Let u(i) be the second derivative of i**6/30 - 3*i**5/10 + 7*i**4/12 + i**3 - 4*i**2 - 1379*i. Determine w so that u(w) = 0.
-1, 1, 2, 4
Suppose -18495*a**2 - 12856765/4 - 270*a**3 - 844605/2*a = 0. Calculate a.
-137/6
Let o(y) be the second derivative of y**7/630 - 8*y**6/45 - 65*y**4/6 - 163*y. Let d(f) be the third derivative of o(f). What is u in d(u) = 0?
0, 32
Let f(r) = 20*r**3 + 34*r**3 + 19*r**4 + 1 + 4 + 11*r**5 - 36*r**3. Let g(v) = 6*v**5 + 9*v**4 + 9*v**3 + 3. Let y(w) = -3*f(w) + 5*g(w). Factor y(m).
-3*m**3*(m + 1)*(m + 3)
Let c = -38556/5 + 7715. Factor -17/5 + 7*v + 1/5*v**3 - c*v**2.
(v - 17)*(v - 1)**2/5
Let q(r) = 7*r - 5. Let m be q(2). Let h = -6 + m. Factor 3*l**2 + l**2 - 12*l**4 + 3*l**h + 3*l**2 - l**2 - 9*l**5.
-3*l**2*(l + 1)**2*(3*l - 2)
Let s = 3/81470 - -293289/81470. Determine w, given that s - 3/5*w - 3*w**2 = 0.
-6/5, 1
Let w(i) = i**3 - 8*i**2 - 6*i - 22. Let n be w(9). Suppose -d - 120 = -n*d. Factor -8 + 70*y**3 - 2 + 45*y + 5*y**5 - 80*y**2 - d*y**4 + 0*y**5.
5*(y - 2)*(y - 1)**4
Suppose -2*w = -75*p + 77*p - 34, -4*w - 44 = -4*p. Solve -12/7*x**2 + 16/7 - 4/7*x**w + 0*x = 0 for x.
-2, 1
Suppose -13 = 5*a - 23. Suppose 6*h**2 - 598*h - 18 + 2*h**3 - 2*h**2 + a + 590*h = 0. What is h?
-2, 2
Suppose -5*f + 19 + 1 = 0. Let h(l) = -5*l + 97. Let d be h(19). Factor 0*m**2 - 9*m + f*m - 5*m**d.
-5*m*(m + 1)
Find z such that -128/9*z + 20/9*z**4 + 32/9*z**3 - 4/9*z**5 + 256/9 - 176/9*z**2 = 0.
-2, 1, 4
Let q(s) = s**2 - 3*s + 5. Suppose 12*d - 15 = 7*d. Let k be q(d). Factor -y - 11 - 3*y**2 + 35 - k*y.
-3*(y - 2)*(y + 4)
Let f(y) be the second derivative of 75*y**3 + 0*y**2 - 1/15*y**6 - 85/2*y**4 - 108*y + 1 + 31/10*y**5. Factor f(k).
-2*k*(k - 15)**2*(k - 1)
Let o(t) be the third derivative of 1/420*t**7 + 0 + 0*t - 1/120*t**5 + 0*t**3 - 41*t**2 - 1/240*t**6 + 1/48*t**4. Let o(c) = 0. What is c?
-1, 0, 1
Suppose -5*u = -u + 4*v + 992, -4*u - 5*v = 993. Let w = u - -626. Find b, given that 376*b - w*b - 13*b**2 - 6 - 9*b**4 + 3*b**3 + 28*b**2 = 0.
-1, -2/3, 1
Let z be (-96)/16*(-74)/333. Factor -10/3*d - 4/3*d**2 + z + 10/3*d**3.
2*(d - 1)*(d + 1)*(5*d - 2)/3
Determine h, given that -330*h + 45/2*h**3 + 5/2*h**5 + 109*h**2 - 18*h**4 + 252 = 0.
-14/5, 2, 3
Let p = 19 + -1