e n, given that h(n) = 0.
-4, -2, 2
Let q(i) be the first derivative of -i**6/30 + 3*i**5/5 - 8*i**2 - 11. Let p(j) be the second derivative of q(j). Find o, given that p(o) = 0.
0, 9
Determine c, given that -3373*c + 12 + 3*c**2 - 3375*c + 6760*c = 0.
-2
Let z = -18 - -19. Let j(l) = -8*l + 10. Let x be j(z). Factor 0 + 2/7*y**x - 2/7*y**3 + 0*y.
-2*y**2*(y - 1)/7
Let k be 23/4 - (-24)/(-32). Suppose -6*u + k = 5. Factor 3/4*r + u + 3/4*r**2.
3*r*(r + 1)/4
Let b(o) be the third derivative of o**8/672 - 4*o**7/315 - 11*o**6/240 - 7*o**5/180 - 40*o**2 - o. Find k such that b(k) = 0.
-1, -2/3, 0, 7
Let j = 624 + -621. Let z(w) be the first derivative of 1/7*w**j - 3/35*w**5 - 3/28*w**4 + 6 + 0*w + 3/14*w**2. What is d in z(d) = 0?
-1, 0, 1
Let z(c) = 13*c - 143. Let a be z(11). Suppose a = 21*w - 61 - 2. Factor -45/4*u**2 - 375/4 + 225/4*u + 3/4*u**w.
3*(u - 5)**3/4
Let k(z) be the second derivative of -1/30*z**4 + 0 + 0*z**2 + 1/15*z**3 + 9*z. Factor k(u).
-2*u*(u - 1)/5
Let t = -36 + 42. Suppose 0 = 10*x + 8*x - t*x. Determine u so that -1/7*u - 1/7*u**2 + x = 0.
-1, 0
Let -3/4*p - 1/2 + 1/4*p**2 + 1/4*p**4 + 3/4*p**3 = 0. What is p?
-2, -1, 1
Let g(i) be the second derivative of 27*i**5/20 - 3*i**4/2 + i**3/2 - 16*i. Factor g(n).
3*n*(3*n - 1)**2
Let y = 12 + -16. Let l(o) = o**3 - 8*o**2 + 8*o. Let t(b) = b**2 - b. Let s(g) = y*t(g) - l(g). Factor s(n).
-n*(n - 2)**2
Let a(q) be the third derivative of 2/105*q**5 + 0*q**4 + 0 + 1/210*q**6 + 3*q**2 + 0*q**3 + 0*q. Find z, given that a(z) = 0.
-2, 0
Suppose 2*b + 2*y = 12, 4*b + 2*y - 33 + 11 = 0. Let f be 16/5 + (-1)/b. Let 102*v**4 + 8*v**f + 4 - 98*v**4 - v**5 - 8*v**2 - 4*v - 3*v**5 = 0. Calculate v.
-1, 1
Let y(j) be the second derivative of -j**8/16800 + j**7/3150 + j**6/1800 - j**5/150 - 17*j**4/12 + 15*j. Let f(k) be the third derivative of y(k). Factor f(i).
-2*(i - 2)*(i - 1)*(i + 1)/5
Let b be ((-1)/(-3))/(4/4). Let f(t) = -3*t**3 - t**2 + 7*t + 7. Let o be f(-1). Factor 4/3*l**4 + b*l**3 - 4*l**o - 11/3*l - 2/3.
(l - 2)*(l + 1)**2*(4*l + 1)/3
Let a(n) be the second derivative of -n**6/5 - 7*n**5/2 - 26*n**4/3 - 20*n**3/3 + 2*n + 23. Find q, given that a(q) = 0.
-10, -1, -2/3, 0
Let g(d) be the second derivative of d**7/2520 + d**6/720 - 5*d**4/6 - 8*d. Let r(x) be the third derivative of g(x). Let r(h) = 0. Calculate h.
-1, 0
Let f(j) be the third derivative of 0 + 0*j - 1/720*j**6 + 1/180*j**5 - 1/144*j**4 + 0*j**3 - 21*j**2. Factor f(i).
-i*(i - 1)**2/6
Suppose -16*l + 85 = -107. Factor -15*v - l + 9/2*v**2.
3*(v - 4)*(3*v + 2)/2
Let q(z) = -z**2 + 3*z + 12. Let p be q(5). What is o in -2*o**2 - 12*o**3 + 3*o**4 - 7*o**4 - 6*o**p = 0?
-2, -1, 0
Let y(z) = -2*z**3 + 4*z**2 + 3*z - 3. Let m be ((-4)/(-4) - 5)/(-2). Let r(h) = h**m - 5*h + 3 - 4 + 7*h - h**3 - h. Let s(f) = 12*r(f) - 4*y(f). Factor s(j).
-4*j**2*(j + 1)
Let c(s) be the first derivative of -4*s**3/3 + 22*s**2 - 33. Factor c(n).
-4*n*(n - 11)
Let l(q) be the first derivative of 0*q**2 + 0*q**3 + 0*q**4 + 0*q - 1/3*q**6 + 7 - 2/5*q**5. Factor l(a).
-2*a**4*(a + 1)
Suppose 55 = -76*w + 50*w + 37*w. Suppose 0*b - w*b**3 - 5*b**2 + 0 - 5/4*b**4 = 0. What is b?
-2, 0
Let c(n) be the third derivative of n**6/420 + 2*n**5/105 + 5*n**4/84 + 2*n**3/21 + n**2 - 54*n. Let c(s) = 0. Calculate s.
-2, -1
Let m be ((-540)/48 - -12)/(3/2). Let y(g) be the first derivative of -m*g**2 + 0*g + 12/5*g**5 - 3/2*g**6 - 4/3*g**3 + 1/2*g**4 - 3. Factor y(r).
-r*(r - 1)**2*(3*r + 1)**2
Let s(u) be the third derivative of -1/150*u**6 + 0*u + 0 + 3/25*u**5 + 1/15*u**4 + 2/105*u**8 - 12/175*u**7 + 0*u**3 + 8*u**2. Solve s(i) = 0.
-1/2, -1/4, 0, 1, 2
Let i(t) be the third derivative of -t**7/504 + t**6/24 - 3*t**5/8 + t**4/8 + 7*t**2. Let p(w) be the second derivative of i(w). Solve p(n) = 0 for n.
3
Let p = 98 + -68. Let -6*n + p*n**2 - 15*n**3 - 12*n**3 - 3*n**2 = 0. What is n?
0, 1/3, 2/3
Let m be ((-609)/145)/(12/(-16)). Factor 0 - m*a**3 - 2/5*a + 13/5*a**2 + 4*a**4.
a*(2*a - 1)**2*(5*a - 2)/5
Let t = -30265/7 - -4324. Factor 0 - 1/7*h**5 - t*h**4 - 1/7*h**2 + 0*h - 3/7*h**3.
-h**2*(h + 1)**3/7
Let f(o) = -2*o**4 + 41*o**3 + 30*o**2 + 8*o - 7. Let s(t) = -t**4 + 40*t**3 + 29*t**2 + 6*t - 6. Let a(d) = 6*f(d) - 7*s(d). Factor a(j).
-j*(j + 1)*(j + 6)*(5*j - 1)
Suppose 0 = q + 5, 0*q + 2*q - 2 = -2*o. Suppose -8*r = -3*r - o*r. Suppose 0 + 14/5*i**4 + 4/5*i**3 + r*i + 2*i**5 + 0*i**2 = 0. Calculate i.
-1, -2/5, 0
Let q = 469/4 + -117. Let i(y) be the first derivative of 1/2*y + 1/8*y**4 - 5 - 1/6*y**3 - q*y**2. Factor i(v).
(v - 1)**2*(v + 1)/2
Let l(d) be the second derivative of 29*d**6/15 - 27*d**5/10 - d**4/3 - 51*d - 3. Factor l(m).
2*m**2*(m - 1)*(29*m + 2)
Factor -3/8*j**3 + 31/8*j**2 - 6 - 25/4*j.
-(j - 8)*(j - 3)*(3*j + 2)/8
Let j(h) be the first derivative of 5*h**3/3 - 45*h**2/2 + 100*h + 110. Factor j(l).
5*(l - 5)*(l - 4)
Let z be 32/336 - 484/(-21). Determine g so that -z - 2/7*g**2 + 36/7*g = 0.
9
Let v(i) be the first derivative of 2/5*i**3 + 4*i - 17/5*i**2 - 16. Find n, given that v(n) = 0.
2/3, 5
Let j(i) be the first derivative of i**6/6 - 18*i**5/5 + 4*i**4 + 6*i**3 - 17*i**2/2 - 43. Determine t so that j(t) = 0.
-1, 0, 1, 17
Factor -2/5*d**3 - 96/5*d + 72/5 + 26/5*d**2.
-2*(d - 6)**2*(d - 1)/5
Suppose -w - 3 + 9 = 0. Let n(x) = -2*x**3 - 13*x**2 + 9*x + 17. Let l be n(-7). Let 9*t + 7*t + w*t**2 + 3*t**l - 13*t = 0. What is t?
-1, 0
Let c(r) = 44*r**2 - 30*r - 152. Let k(f) = -5*f**2 + 3*f + 17. Let y(l) = 6*c(l) + 52*k(l). Factor y(s).
4*(s - 7)*(s + 1)
Suppose 4*w + 4*b - 32 = 0, 5*w + 6*b = 2*b + 35. Determine k so that -w*k + k + 3*k - 21*k**2 - 7*k = 0.
-2/7, 0
Let -257*n**2 - 130*n**3 - 204*n**4 + 8 + 10*n**5 + 0 + 341*n**2 - 8 = 0. Calculate n.
-1, 0, 2/5, 21
Suppose 3*u = 5*u. Let g(o) be the third derivative of u*o + 0 - 1/6*o**4 + 4*o**2 - 1/3*o**3 - 1/30*o**5. Factor g(v).
-2*(v + 1)**2
Solve -434*d**2 + 35*d**3 - 69*d**3 + 23760*d - 21198 + 36*d**3 - 2130 = 0 for d.
1, 108
Let m = -10 + 25. Suppose m = q + 4*q. Solve 3*u**q - 24*u**2 + 30*u**3 + 63*u**5 + 11*u**3 - 8*u**3 + 150*u**4 = 0 for u.
-2, -2/3, 0, 2/7
Let z = 65 + -39. Let b be 2/(-4) - (-65)/z. Factor -m**2 + 2*m + 4 - 7*m**b - 2*m**3 + 2*m**4 + 2*m**2.
2*(m - 2)*(m - 1)*(m + 1)**2
Factor 40*u**2 + 27*u**3 - 6*u**3 - 13*u**3 - 7*u**3 - 9*u + 48*u.
u*(u + 1)*(u + 39)
Let c(t) be the second derivative of 0 - 15*t + 0*t**2 + 5/3*t**3 + 1/4*t**5 + 5/4*t**4. Factor c(m).
5*m*(m + 1)*(m + 2)
Suppose 9*n = 32 - 23. Let w(o) be the first derivative of -n + 1/5*o**4 - 2/25*o**5 + 0*o**2 + 0*o - 2/15*o**3. Find k, given that w(k) = 0.
0, 1
Factor 8/7 - 4/7*k**2 + 4/7*k.
-4*(k - 2)*(k + 1)/7
Let w be ((-4)/(-6))/(7/((-210)/(-4))). Let -190*o**2 - 20*o - 10 - 514*o**w + 200*o**4 + 594*o**5 + 5*o**3 - 65*o = 0. What is o?
-2, -1, -1/4, 1
Suppose -8 = -4*u, -4*d + 3*u + 54 = d. Let r(c) = 2*c - 22. Let a be r(d). Suppose 0 - 2/3*w**a - 4/3*w = 0. What is w?
-2, 0
Let s = 872/3 + -289. Let n(j) be the third derivative of -7/60*j**6 - s*j**4 - 23/30*j**5 + 0*j - 4/3*j**3 - j**2 + 0. Let n(g) = 0. What is g?
-2, -1, -2/7
What is u in -1728/5 - 864/5*u - 108/5*u**2 - 4/5*u**3 = 0?
-12, -3
Suppose 0 = 5*s + 5*h - 30, 0*h + 12 = 4*s - 2*h. Find a such that 20*a + 5*a**3 - 4*a**5 - 21*a**3 + 24*a**2 + 637*a**4 - 661*a**s = 0.
-5, -1, 0, 1
Let g(z) = 2*z**5 - 2*z**4 - 6*z**2 + 3*z + 6. Let m(l) = -l**5 + l**4 + 2*l**2 - l - 2. Let y(f) = 2*g(f) + 6*m(f). Factor y(o).
-2*o**4*(o - 1)
Let o(m) be the first derivative of -15 + 1/20*m**5 + 0*m + 0*m**2 + 0*m**4 - 1/12*m**3. Factor o(y).
y**2*(y - 1)*(y + 1)/4
Let k be (-1)/2*3*8/(-2). Suppose -5*a - b + 5 = 0, -4*a + k + 14 = 4*b. Factor -1/3*l**3 + a + 1/3*l**4 - 2/3*l**2 + 0*l.
l**2*(l - 2)*(l + 1)/3
Let a(g) be the second derivative of -g**8/3360 + g**7/1260 + g**6/180 - 11*g**4/12 - 4*g. Let f(k) be the third derivative of a(k). Factor f(v).
-2*v*(v - 2)*(v + 1)
Let z = 39396 + -275770/7. Factor -2/7*w**2 + z*w**4 - 10/7*w**3 + 10/7*w + 0.
2*w*(w - 5)*(w - 1)*(w + 1)/7
Suppose 0 = 2*q + 3*c + 15, 19*q - 5*c = 15*q + 25. Let i = 3 + -1. Factor -2/11*d**4 + q*d - 2/11*d**i + 0 - 4/11*d**3.
-2*d**2*(d + 1)**2/11
Suppose -3*p - 5*x - 95 = 40, 2*p - 5*x + 90 = 0. Let k be (-10 + 1)*60/p. Determine q so that -17*q + 3*q**2