 13
Let a(m) be the first derivative of 1/9*m**2 - 1/18*m**4 + 0*m - 292 - 1/45*m**5 + 1/27*m**3. Find f, given that a(f) = 0.
-2, -1, 0, 1
Let o(u) be the third derivative of u**7/420 + u**6/80 - 4*u**5/15 + 5*u**4/4 - 8*u**3/3 - 61*u**2 - 10*u. Factor o(j).
(j - 2)**2*(j - 1)*(j + 8)/2
Let b(t) be the second derivative of 3*t**4/20 + 124*t**3/5 - 249*t**2/10 + 4492*t. Factor b(y).
3*(y + 83)*(3*y - 1)/5
Let t = 20 - 92/5. Let n(r) = 519*r + 2081. Let m be n(-4). What is l in -16/5*l**m - t*l - 114/5*l**3 + 76/5*l**4 + 0 + 56/5*l**2 = 0?
0, 1/4, 1/2, 2
Factor 392/9 + 242/9*d**3 + 11770/9*d**2 - 4304/9*d.
2*(d + 49)*(11*d - 2)**2/9
Let z(n) be the second derivative of -1/100*n**5 + 1/210*n**7 + 4 + 7*n + 0*n**6 + 0*n**3 + 0*n**4 + 0*n**2. Find f, given that z(f) = 0.
-1, 0, 1
Let i = 1418/7 + -202. Factor -2/7*l**2 - 2/7*l + i.
-2*(l - 1)*(l + 2)/7
Let d be -6 + 2 + 6 - 0. Factor d*l - 988*l**2 + l**3 + l + 991*l**2 + 1.
(l + 1)**3
Let v = -138 + 144. Factor -20*u**3 - 7*u**4 - 2*u**2 + v*u**4 + 25*u**3 - 8*u.
-u*(u - 4)*(u - 2)*(u + 1)
Let j(d) be the second derivative of -d**7/21 - 406*d**6/15 - 5508*d**5 - 419175*d**4 - 820125*d**3 - 185*d - 5. Solve j(w) = 0 for w.
-135, -1, 0
Suppose -6720/11*g - 8*g**2 + 28800/11 + 2/11*g**4 + 56/11*g**3 = 0. What is g?
-20, 6
Let u(g) = g**5 + g**3 - 2*g**2 - g. Let y(h) = -4*h - 6*h**5 + 12*h**4 + 6 - 10 + 2*h**5 + 8*h**2. Let j(n) = -8*u(n) - y(n). Factor j(d).
-4*(d - 1)*(d + 1)**4
Let f(a) be the first derivative of -52/3*a - 76/3*a**2 - 68 + 4/3*a**3. Factor f(g).
4*(g - 13)*(3*g + 1)/3
Let u(o) be the third derivative of o**5/12 + 35*o**4/8 - 115*o**3/3 - 1097*o**2. Let u(s) = 0. What is s?
-23, 2
What is l in 58/3 + 172/9*l - 2/9*l**2 = 0?
-1, 87
Let u = -41195 - -3831049/93. Let d = u + 70/31. What is k in -10*k - 32/3*k**5 + 62/3*k**3 - 44/3*k**2 + 16*k**4 - d = 0?
-1, -1/4, 1, 2
Let u = -6560446/7 - -937282. Solve -1362944/7 - u*o**2 + 2/7*o**3 + 46464/7*o = 0.
88
Let w = 172 - 172. Suppose -15 = -3*a + 5*d, 4*a - a - 2*d - 6 = w. Solve -4/7*v**3 + 4/7*v + 0 + a*v**2 = 0 for v.
-1, 0, 1
Suppose m = -f + 2*f - 25, 5*f - 67 = 3*m. Let w = 31 + m. Let 24 + 20*d**3 + 23*d**2 - 9*d**w - 18*d**3 + 32*d = 0. Calculate d.
-3, -2
Find m, given that -369*m**3 + 166*m**4 - 56*m**4 - 58*m**4 - 49*m**4 = 0.
0, 123
Let g(q) be the first derivative of q**4/2 - 70*q**3/3 + 392*q**2 - 2744*q - 628. Find m, given that g(m) = 0.
7, 14
Factor 35*v**3 - 14*v**4 - 75*v**2 - 235115*v**5 + 49*v**4 + 235120*v**5.
5*v**2*(v - 1)*(v + 3)*(v + 5)
Let c = -1677 - -2962. Let f = -1282 + c. Factor 7/5*v**4 - 23/5*v**f - 22/5*v**2 + 0 + 8/5*v.
v*(v - 4)*(v + 1)*(7*v - 2)/5
Let v(w) be the second derivative of -2704/7*w**2 + 166*w - 1/105*w**6 - 51/35*w**5 - 2497/42*w**4 + 1768/7*w**3 + 0. Factor v(h).
-2*(h - 1)**2*(h + 52)**2/7
Let u(a) be the first derivative of 5*a**4/8 + 11*a**3/6 - a**2/2 - 4*a + 573. Find q, given that u(q) = 0.
-2, -1, 4/5
Let w(p) = 4*p**3 + 24*p**2 - 10*p - 21. Let n(v) = 11*v**3 + 70*v**2 - 27*v - 62. Let t(g) = -3*n(g) + 8*w(g). Factor t(b).
-(b - 1)*(b + 1)*(b + 18)
Let s(f) be the third derivative of -f**8/1680 - 24*f**7/175 - 5597*f**6/600 - 989*f**5/10 - 1587*f**4/5 + 3241*f**2. Determine h so that s(h) = 0.
-69, -4, -2, 0
Let h(b) be the first derivative of 12*b + 1085*b**3 - 276 + 192*b**2 + 2883/4*b**4. Factor h(d).
3*(d + 1)*(31*d + 2)**2
Let t be -64 + (-16371)/(-4080)*16. Factor -20*y - t*y**2 - 500.
-(y + 50)**2/5
Let c(m) be the second derivative of 2*m - 1/120*m**6 - 9/80*m**5 - 9/4*m**2 - 9 - 13/8*m**3 - 29/48*m**4. Factor c(y).
-(y + 1)*(y + 2)*(y + 3)**2/4
Let q(z) be the second derivative of -8/33*z**4 + 0*z**2 + 0 - 3/110*z**5 + 1/33*z**7 + 47*z + 16/165*z**6 - 4/33*z**3. Solve q(l) = 0.
-2, -1, -2/7, 0, 1
Suppose 2*t + 47 = -5*w, -4*t - 5*w = 78 - 39. Factor -16838/13*y**3 - 50/13*y**5 + 52294/13*y**2 + 10648/13 + 1610/13*y**t + 3872*y.
-2*(y - 11)**3*(5*y + 2)**2/13
Let d(a) be the second derivative of -65*a + 0 - 3/5*a**2 + 1/20*a**4 + 1/10*a**3. Factor d(c).
3*(c - 1)*(c + 2)/5
Factor -63*v**4 + 2592 - 77*v**2 + 38*v**4 - 28*v**3 + 35*v**4 - 355*v**2 + v**5 - 432*v + 4*v**3.
(v - 6)*(v - 2)*(v + 6)**3
Let g = 94 - 82. Suppose 0 = 3*p - 4*i - 6, i + 8 = -8*p + g*p. Factor 5/3 - 10*k + 40/3*k**p.
5*(2*k - 1)*(4*k - 1)/3
Let a(r) be the first derivative of -2*r**5/5 - 21*r**4/2 + 140*r**3/3 - 48*r**2 + 608. Factor a(l).
-2*l*(l - 2)*(l - 1)*(l + 24)
Let p(a) = a**2 + 26*a + 177. Let l be p(-13). Factor -l*u + 241*u**2 + 234*u**2 - 474*u**2 + 16.
(u - 4)**2
Let x = -1059805/4 - -265066. Factor 3/4*m**3 + x*m - 117/2*m**2 - 57.
3*(m - 76)*(m - 1)**2/4
Let a(l) = l**3 + 38*l**2 + 41*l + 144. Let r be a(-37). Let u be ((-56)/(-98))/(r/(-14)). Factor 1/2*g + 0 - 3/2*g**3 + u*g**5 - 2*g**4 + g**2.
g*(g - 1)**2*(2*g + 1)**2/2
Let a(d) be the first derivative of 1/7*d**2 - 2/7*d + 2/21*d**3 - 1/14*d**4 - 13. Factor a(r).
-2*(r - 1)**2*(r + 1)/7
Suppose 1689/4*g + 3/4*g**2 + 0 = 0. Calculate g.
-563, 0
Determine x so that 23*x**4 + 535*x**3 - 660*x**3 - 282*x + 22*x**4 + 16*x**2 - 5*x**5 + 119*x**2 + 232*x = 0.
0, 1, 2, 5
Let r = -36590 + 73185/2. Find o, given that 1/2*o**4 + 0 + 0*o + 2*o**2 + r*o**3 = 0.
-4, -1, 0
Find m such that 30/11*m**4 + 0 - 30/11*m**2 + 32/11*m + 2/11*m**5 - 34/11*m**3 = 0.
-16, -1, 0, 1
Let y(g) be the first derivative of -g**4/16 - 7*g**3/2 - 60*g**2 - 200*g + 789. Factor y(m).
-(m + 2)*(m + 20)**2/4
Factor -154/3*y - 32/3*y**2 + 2/3*y**3 - 40.
2*(y - 20)*(y + 1)*(y + 3)/3
Let w(p) = 668*p - 6678. Let h be w(10). Factor -2704/5 - 1/5*v**h - 104/5*v.
-(v + 52)**2/5
Let f(k) = -21*k**4 + 78*k**3 + 52*k**2 - 33*k. Let d(s) = 10*s**4 - 38*s**3 - 25*s**2 + 17*s. Let h(u) = -14*d(u) - 6*f(u). Suppose h(p) = 0. Calculate p.
-1, 0, 4/7, 5
Let w = 2345/7039 + 4/21117. Factor 1/3 - 4/3*n**3 + 2*n**2 - 4/3*n + w*n**4.
(n - 1)**4/3
Let i(y) = y**3 + 31*y**2 - 2*y - 7. Let x be i(-31). What is a in -2*a + x*a**2 - 1 + 57*a**2 - 113*a**2 = 0?
-1
Suppose -4*z + 0*z = -2*a - 16, a = -4*z + 10. Determine w so that 5*w**z + 4*w**5 + 0*w**3 - w**3 + 8*w**4 = 0.
-1, 0
Suppose 0 = -8555*d + 7743*d + 3248. Solve -1 - 3/2*c**3 + 31/8*c**2 - 3/4*c - 5/8*c**d = 0.
-4, -2/5, 1
Let a be (11 + -11)*(14/4 - 2)/3. Let u(b) be the second derivative of -1/14*b**4 + a + 1/14*b**3 + 3/7*b**2 - 3*b - 3/140*b**5. Factor u(r).
-3*(r - 1)*(r + 1)*(r + 2)/7
Let i(y) = -y**4 - y**3 + y + 1. Let a(n) = -8*n**4 - 60*n**3 - 132*n**2 + 4*n + 4. Let c(x) = a(x) - 4*i(x). Suppose c(f) = 0. What is f?
-11, -3, 0
Factor 54415 + 29020 + 174097*c + 907*c**2 + 5*c**3 - 13497 - 1003*c**2 - 1772*c**2.
(c - 187)**2*(5*c + 2)
Suppose 2*k - 8 + 4 = 0. Determine s, given that -298*s + 287*s - 3*s**2 + 4*s**k - 12 = 0.
-1, 12
Let h = 14830 - 14828. Suppose -4*x + 0*x = -p - 57, 0 = -x - 4*p + 27. Suppose -11*i**h - 5*i**3 - x - 27*i**2 + 13*i**2 - 35*i = 0. Calculate i.
-3, -1
Suppose 44 = -3*c - 2*b, 0 = -2*b + 6*b + 16. Let m be ((-12)/9)/(8/c). Factor 802 - 2*x**m + 18*x - 802.
-2*x*(x - 9)
Suppose -2/13*p**2 + 0 - 106/13*p = 0. What is p?
-53, 0
Factor 2/11*s**3 - 120/11*s + 34/11*s**2 + 0.
2*s*(s - 3)*(s + 20)/11
Let o = 3707 - 3707. Let y(k) be the third derivative of 1/15*k**5 + 0*k**4 + o*k**6 - 1/3*k**3 + 12*k**2 + 0 + 0*k - 1/105*k**7. Solve y(d) = 0 for d.
-1, 1
Let o(x) be the third derivative of -1/12*x**5 + 0*x + 0 + 71*x**2 + 0*x**3 + 5/6*x**4. Factor o(u).
-5*u*(u - 4)
Let a(m) be the third derivative of 0*m + 1/12*m**5 + 5*m**2 + 0 + 25/3*m**3 - 55/24*m**4. Suppose a(o) = 0. Calculate o.
1, 10
Factor -5609 - 89*u + 5189 - 15*u - 4*u**2.
-4*(u + 5)*(u + 21)
Let w(o) be the second derivative of -o**5/50 - 37*o**4/3 - 11284*o**3/5 + 69192*o**2/5 + o - 137. Find p such that w(p) = 0.
-186, 2
What is q in q**2 - 4 + 1/7*q**3 - 4/7*q = 0?
-7, -2, 2
Let a(m) = -3*m**2 + 300*m - 684. Let i(c) = c - 10. Let p(l) = a(l) - 12*i(l). Factor p(f).
-3*(f - 94)*(f - 2)
Let r be (-90)/14*273/(-130). Let 3/4*g**2 + r - 33/4*g = 0. Calculate g.
2, 9
Factor 294 - 146*f - 1/2*f**2.
-(f - 2)*(f + 294)/2
Determine v, given that 41/2*v**2 - 3 + 4*v**3 - 43/2*v = 0.
-6, -1/8, 1
Let w be (7*(-76)/28)/(-3). Let n(x) be the third derivative of -11*x**2 + 13/5*x**5 - w*x**4 + 8*x**3 + 1/21*x**7 - 11/20*x**6 + 0*x + 0. Fact