s**2*(s - 1)/4
Let y be (2/6)/(91/117). What is b in 0*b + y*b**2 - 6/7*b**3 + 3/7*b**4 + 0 = 0?
0, 1
Suppose l + 12 = -5*a, -3 = -4*l - 9*a + 6*a. Let i(d) be the third derivative of 0*d**l - 1/24*d**4 + 0 - 2*d**2 + 1/30*d**5 + 0*d. Find n such that i(n) = 0.
0, 1/2
Determine i so that -3/4*i - 5/4*i**2 + 1 + 1/4*i**4 + 3/4*i**3 = 0.
-4, -1, 1
Let f(q) be the third derivative of q**7/210 + q**6/240 - q**5/40 - q**4/48 + q**3/12 + 58*q**2. Factor f(o).
(o - 1)*(o + 1)**2*(2*o - 1)/2
Suppose 4*c + 9 = f, -3*f + 0*f = 9. Let u be (6/10)/((c/4)/(-1)). Find q, given that 0 + 1/5*q**3 + 0*q + 0*q**2 + u*q**5 + q**4 = 0.
-1, -1/4, 0
Let g(z) be the second derivative of -2*z**7/21 + 26*z**6/75 - 9*z**5/25 - z**4/15 + 4*z**3/15 + 3*z - 17. Factor g(r).
-4*r*(r - 1)**3*(5*r + 2)/5
Let o = 0 - -2. Suppose 2*t + 2 = o*d, 2*t + 9 = 5*t + d. Factor 3*n**4 + 0*n**4 - 4*n**2 - t*n**4 + 3*n**2.
n**2*(n - 1)*(n + 1)
Let s(h) be the second derivative of 11*h - 1/24*h**4 + 1/24*h**3 + 0*h**2 + 1/80*h**5 + 0. Determine d, given that s(d) = 0.
0, 1
Let f(v) be the third derivative of 1/114*v**4 - 5/3192*v**8 + 0*v + 0*v**3 + 1/285*v**7 - 7/570*v**5 + 11*v**2 + 1/380*v**6 + 0. What is l in f(l) = 0?
-1, 0, 2/5, 1
Let n(v) be the second derivative of v**4/20 + 2*v**3 - 63*v**2/10 - 737*v. Let n(w) = 0. What is w?
-21, 1
Let a(w) = -w**5 + 66*w**4 - 1290*w**3 - 4357*w**2 - 4485*w - 1530. Let y(u) = u**4 + 3*u**2 + 1. Let t(f) = -4*a(f) - 36*y(f). Suppose t(l) = 0. Calculate l.
-1, 39
Let w = -166/5 + 508/15. Find s such that w*s**3 - 2*s**2 - 2/3 + 2*s = 0.
1
Let w(v) be the first derivative of 4*v**5/5 - 5*v**4/2 - 16*v**3/3 + 17*v**2 - 12*v - 47. Find x, given that w(x) = 0.
-2, 1/2, 1, 3
Let r(l) be the third derivative of 1/16*l**4 - 10*l**2 + 3/80*l**5 + 0 - 3/8*l**3 - 1/80*l**6 + 0*l. What is a in r(a) = 0?
-1, 1, 3/2
Let f(k) be the third derivative of k**5/420 - k**4/4 + 21*k**3/2 + 94*k**2. Factor f(t).
(t - 21)**2/7
Let v(a) = -a**4 + 45*a**3 - 58*a**2 - 100*a - 4. Let t(x) = x**4 + x**2 + x + 1. Let u(h) = 4*t(h) + v(h). Solve u(c) = 0 for c.
-16, -1, 0, 2
Let p be (535/(-1070) - ((-6)/4 - -1))/(-2). Factor -2/3*q**4 + 2*q**2 + 0 + 4/3*q**3 + p*q.
-2*q**2*(q - 3)*(q + 1)/3
Determine t, given that 25*t + 0 + 7*t**3 - 2*t**3 + 7 - 2 + 20*t**2 + 5 = 0.
-2, -1
Solve -22/3 - 72*f**3 - 63*f - 16/3*f**4 - 457/3*f**2 = 0.
-11, -2, -1/4
Suppose 3*m = -b - 5, 0 = 4*b - m - 21 - 24. Factor -3 + b*g + 2*g**2 - 3*g**2 - 2*g - 4*g.
-(g - 3)*(g - 1)
Solve -5*m**4 - 126*m**2 - 2*m**2 + 16*m**3 - 32*m**2 + 49*m**3 + 100*m = 0 for m.
0, 1, 2, 10
Let a = 458 - 454. Find y such that -12/5 + 16/5*y - 9/5*y**3 + y**2 + 1/5*y**5 - 1/5*y**a = 0.
-2, 1, 3
Let i(j) be the second derivative of -j**6/105 + 93*j**5/70 - 961*j**4/14 + 29791*j**3/21 - 6*j - 3. Solve i(b) = 0.
0, 31
Let c(d) = d**4 + d**3 - 1. Let w(p) = 2*p**5 + 39*p**4 - p**3 - 72*p**2 + 2*p + 33. Let i(t) = 6*c(t) - 2*w(t). Determine a, given that i(a) = 0.
-18, -1, 1
Suppose -5*x + 0*x = -40. Let k(r) = -14*r**2 + 6. Let p(z) = 0 + 3 - 7 + 9*z**2. Let h(l) = x*p(l) + 5*k(l). Let h(c) = 0. What is c?
-1, 1
Let b be -4 - 1*(4 + -1). Let g = b + 15. Factor 2*i**2 + 24*i + 24*i + g - 40*i.
2*(i + 2)**2
Let a(x) be the third derivative of -x**7/420 - 9*x**6/80 - 31*x**5/24 - 103*x**4/16 - 15*x**3 - 228*x**2 + x. Factor a(z).
-(z + 1)*(z + 3)**2*(z + 20)/2
Let p(u) = -2*u**2 - 25*u + 51. Let o(h) = 12*h**2 + 176*h - 356. Let b(s) = -3*o(s) - 20*p(s). Find q, given that b(q) = 0.
3, 4
Let i(t) = -t**3 - 5*t**2 - 223*t - 874. Let k be i(-4). Solve 0 + 5/2*g**3 - 1/2*g**4 - k*g**2 + 0*g = 0.
0, 1, 4
Let q = 30139/8610 + -2/4305. Let t(s) be the first derivative of q*s**4 + 4/5*s**5 + 6 + 14/3*s**3 + 2*s**2 + 0*s. Suppose t(a) = 0. What is a?
-2, -1, -1/2, 0
Solve -6*c**2 + 7*c**3 + 6 - 17*c**3 + 3*c + 7*c**3 = 0.
-2, -1, 1
Let a(v) be the third derivative of -v**6/360 - v**5/9 - 25*v**4/18 + 39*v**2 - v. Factor a(l).
-l*(l + 10)**2/3
Find t, given that -34/7*t**3 + 6*t**2 + 4/7 + 10/7*t**4 - 22/7*t = 0.
2/5, 1
Let n(c) be the third derivative of -c**7/525 - c**6/150 + c**5/150 + c**4/30 - 211*c**2. What is t in n(t) = 0?
-2, -1, 0, 1
Let b(g) be the first derivative of g**5/5 + 13*g**4/4 + 17*g**3 + 35*g**2/2 - 100*g + 184. Find y, given that b(y) = 0.
-5, -4, 1
Let x(y) = -3*y + 5*y - 21 + 11. Let p be x(7). Determine g, given that -p - 2 - 12*g - 6 - 3*g**2 + 0 = 0.
-2
Let b(g) be the second derivative of g**5/20 - g**4/3 - 11*g**3/6 - 3*g**2 - 40*g. Factor b(n).
(n - 6)*(n + 1)**2
Let j(t) be the third derivative of 0 + 0*t**5 + 0*t**3 + 6*t**2 + 0*t - 1/120*t**6 + 0*t**4. What is h in j(h) = 0?
0
Let p = 2119 + -158923/75. Let a(r) be the second derivative of 0 - 2/5*r**2 + 0*r**4 - 4/15*r**3 + 2/25*r**5 + p*r**6 + 4*r. Factor a(l).
4*(l - 1)*(l + 1)**3/5
Suppose -345 = 35*j - 415. Factor 0*r - 2/9*r**3 - 2/9*r**j + 2/9*r**4 + 0 + 2/9*r**5.
2*r**2*(r - 1)*(r + 1)**2/9
Suppose -7*a + a = 0. Let p(w) be the third derivative of -1/60*w**5 + 0*w + 2*w**2 + a*w**4 + 0 + 1/6*w**3. Factor p(n).
-(n - 1)*(n + 1)
Factor 4/5*s**3 - 2/5*s + 0*s**2 + 0*s**4 - 2/5*s**5 + 0.
-2*s*(s - 1)**2*(s + 1)**2/5
Suppose -3 = 6*o - 15. Let c be 19/4 + (-72)/18. Determine d so that 0 + c*d**o - 1/4*d**3 - 1/2*d = 0.
0, 1, 2
Suppose -10 - 2*b + 25/2*b**2 - 1/2*b**5 + 5/2*b**3 - 5/2*b**4 = 0. Calculate b.
-5, -2, -1, 1, 2
Suppose 20*t - 4 = 21*t. Let c be (t + (3 - 2))/(-5). Let c*i**2 + 18/5*i + 27/5 = 0. Calculate i.
-3
Determine f, given that 0 + 4/5*f + 4/5*f**3 + 8/5*f**2 = 0.
-1, 0
Let o = -236 - -238. Let u(z) be the first derivative of 0*z + 2/25*z**5 - 1/5*z**4 + 1 + 2/15*z**3 + 0*z**o. Factor u(x).
2*x**2*(x - 1)**2/5
Suppose -4*k - b = -1 + 3, 0 = k - 2*b - 4. Suppose k = 3*j + 2*d - 44, 7*d = 5*j + 3*d - 88. Factor -j*i - 16/3 - 20/3*i**2.
-4*(i + 2)*(5*i + 2)/3
Find u, given that 3 + 7*u - 7*u**3 - 17/4*u**2 + 5/4*u**4 = 0.
-1, -2/5, 1, 6
Let d be (-2)/34 - (-6)/102. Let u(v) be the second derivative of 4*v + 0 + d*v**2 + 1/50*v**5 + 1/30*v**4 + 0*v**3. Factor u(o).
2*o**2*(o + 1)/5
Let a = -19079/4 + 4770. Factor 0 + l**3 - 3/2*l + 1/4*l**4 + a*l**2.
l*(l - 1)*(l + 2)*(l + 3)/4
Factor -363/4*m + 15/2*m**3 - 3/8*m**4 + 0 - 231/8*m**2.
-3*m*(m - 11)**2*(m + 2)/8
Suppose 3*p - 3*s - 5 - 4 = 0, 5*s - 1 = -3*p. Factor -9/2*u**p + 9/2 - 12*u.
-3*(u + 3)*(3*u - 1)/2
Let h be ((-6)/(-9))/(14/84). Let u(a) be the first derivative of h + 2/15*a**3 + 3/5*a**2 + 4/5*a. Let u(v) = 0. What is v?
-2, -1
Let k(p) be the first derivative of -p**7/280 + 3*p**5/40 - p**4/4 + 3*p**3/8 + 6*p**2 - 29. Let h(i) be the second derivative of k(i). Factor h(x).
-3*(x - 1)**3*(x + 3)/4
Let d(c) = c**3 - c**2 - c - 1. Let i(m) = -9*m**3 + 6*m + 3. Let q(z) = z**3 - 25*z**2 - 28*z + 53. Let u be q(26). Let w(x) = u*i(x) + 3*d(x). Factor w(h).
-3*h*(h + 1)*(2*h - 1)
Factor 165/7*n**2 + 3/7*n**3 - 339/7*n + 171/7.
3*(n - 1)**2*(n + 57)/7
Suppose -76880 + 454390*c**2 - 454395*c**2 + 24*c + 1216*c = 0. What is c?
124
Let b(d) be the first derivative of -1/16*d**6 - 3/40*d**5 + 0*d**2 + 0*d**3 + 3/16*d**4 + 0*d + 37. Suppose b(i) = 0. What is i?
-2, 0, 1
Let f(n) be the first derivative of n**4/5 + 44*n**3/15 + 78*n**2/5 + 36*n + 7. Suppose f(g) = 0. What is g?
-5, -3
Let f = 1166/9 - 8153/63. What is r in -2/7*r - f*r**4 + 0 + 3/7*r**2 + 0*r**3 = 0?
-2, 0, 1
Let r(b) be the third derivative of 0*b + 1/3*b**4 - 2/15*b**6 + 1/5*b**5 + 25*b**2 - 8/105*b**7 - 2/3*b**3 + 0. Factor r(d).
-4*(d + 1)**2*(2*d - 1)**2
Let j be (-10)/80*0/12. Factor -1/2*k**4 + j*k**3 + 0 + 3/2*k**2 - k.
-k*(k - 1)**2*(k + 2)/2
Let n = -281 + 287. Let g(k) be the first derivative of -23/6*k**3 - 4*k**2 + 67/8*k**4 + 119/10*k**5 + 2*k + 7 + 49/12*k**n. Determine w so that g(w) = 0.
-1, 2/7
Let b(d) = 1505*d**2 + 3815*d + 2465. Let v(i) = -251*i**2 - 636*i - 411. Let r(j) = -6*b(j) - 35*v(j). Factor r(o).
-5*(7*o + 9)**2
Let k(l) be the second derivative of l**4/8 + l**3 + 3*l**2 + 115*l. Factor k(h).
3*(h + 2)**2/2
Let s = -25 - -27. Suppose -6*w + 1436 = -s*w. Factor -3*c**4 + 3 + 359*c**2 - 6*c**3 - w*c**2 + 6*c.
-3*(c - 1)*(c + 1)**3
Let a = -24 - -26. Let p(f) = 21 - 4*f - 27 + 3*f**3 - 4*f**a - f. Let b(t) = t**3 - 1. Let j(v) = 4*b(v) - p(v). Suppose j(c) = 0. What is c?
-2, -1
Find b