. Let b be u(-5). Suppose 2/7*f**b - 2/7*f + 0 = 0. Calculate f.
0, 1
Let s(t) be the third derivative of t**6/900 + t**5/450 - t**4/180 - t**3/45 + 41*t**2 + 2. Determine j so that s(j) = 0.
-1, 1
Let 2/7*d + 1/7 - 4/7*d**2 + 3/7*d**4 - 2/7*d**3 = 0. Calculate d.
-1, -1/3, 1
Let d(b) = -54*b - 51. Let l be d(-6). Let i be (6 - l/49)/((-3)/(-8)). Factor -i*z - 16/7*z**2 + 0 - 10/7*z**3 - 2/7*z**4.
-2*z*(z + 1)*(z + 2)**2/7
Factor 47/5*x - 1/5*x**2 + 0.
-x*(x - 47)/5
Suppose -8*k - 13*k = -2*k. Let m(z) be the second derivative of 1/15*z**3 - 1/60*z**4 + 0 + k*z**2 - 4*z - 1/100*z**5. Factor m(s).
-s*(s - 1)*(s + 2)/5
Suppose 3*i - 57 = -14*i - 2*i. Factor -p**2 + 4 + 2*p - 1/2*p**i.
-(p - 2)*(p + 2)**2/2
Let j(w) be the third derivative of 1/24*w**3 - 1/280*w**7 + 1/120*w**5 - 1/24*w**4 + 0 + 1/120*w**6 + 0*w - 29*w**2. Find f, given that j(f) = 0.
-1, 1/3, 1
Suppose 12 + 21 = 11*d. Let m(p) be the second derivative of 0*p**2 + 1/12*p**4 - 1/6*p**7 + 0 + 1/3*p**d - 3/4*p**5 + 19/30*p**6 + 3*p. Factor m(z).
-z*(z - 1)**3*(7*z + 2)
Let i be ((-228)/(-22) + -10)/((-3)/(-6)). Determine n, given that -2/11*n - 8/11*n**4 + i*n**2 + 0 + 2/11*n**3 = 0.
-1, 0, 1/4, 1
Let r(p) be the third derivative of -6/5*p**6 - 8*p**3 + 9/10*p**7 - 22/5*p**5 - 2*p**2 + 0*p + 10*p**4 + 27/112*p**8 + 5. Solve r(h) = 0 for h.
-2, 1/3, 2/3
Let p be 98/114 + 1/(-3). Let m = 973/10 - 18347/190. Suppose -p*r - m*r**2 + 4/19 = 0. Calculate r.
-1, 2/7
Let g be (1 + 1/2)/(13/(520/30)). Factor 5/7*j - 1/7*j**g - 6/7.
-(j - 3)*(j - 2)/7
Let q(s) be the first derivative of s**6/720 - s**4/12 - s**3 + s**2/2 - 52. Let t(x) be the third derivative of q(x). Factor t(b).
(b - 2)*(b + 2)/2
Let r(j) be the first derivative of -j**6/12 - j**5/10 + 3*j**4/8 + j**3/6 - j**2/2 + 2. Solve r(c) = 0 for c.
-2, -1, 0, 1
Factor -19776 - 26*j + 774*j - 58*j + 59451 + 3*j**2.
3*(j + 115)**2
Let g(t) be the first derivative of -5*t**6/3 - 15*t**5 - 45*t**4/2 + 5*t**3/3 + 15*t**2 - 32. What is p in g(p) = 0?
-6, -1, 0, 1/2
Let u(p) = -5*p**3 - 90*p**2 - 167*p + 2422. Let i(k) = -10*k**3 - 180*k**2 - 335*k + 4845. Let g(j) = -2*i(j) + 5*u(j). Factor g(m).
-5*(m - 4)*(m + 11)**2
Factor -5*i**5 + 20*i**2 + 10*i**2 + 5*i - 10*i**4 - 20*i**2.
-5*i*(i - 1)*(i + 1)**3
Let 14/11*m**3 - 10/11*m**2 - 14/11*m - 2/11*m**4 + 12/11 = 0. What is m?
-1, 1, 6
Find a such that 44*a**4 + 31 + 4*a + 4*a**5 + 3656*a**2 - 3744*a**2 - 8*a**3 + 13 = 0.
-11, -1, 1
Let h(l) be the third derivative of l**6/480 + l**5/48 - l**4/96 - 5*l**3/24 - l**2 + 39. Let h(a) = 0. What is a?
-5, -1, 1
Let i(o) be the first derivative of 3*o**6/2 - 26*o**5/5 - o**4 + 40*o**3/3 - 709. What is f in i(f) = 0?
-10/9, 0, 2
Let r be ((-1)/15)/((-8)/(-620)) - (-2640)/440. Factor r*l - 2/3 - 1/6*l**2.
-(l - 4)*(l - 1)/6
Let y(p) = -p**3 + 2*p**2 + 1. Let h(w) = -4*w**3 - 2096*w**2 + 371712*w - 21807096. Let l(q) = h(q) - 8*y(q). Factor l(r).
4*(r - 176)**3
Let a(w) be the second derivative of -w**7/1540 + w**6/660 - w**5/660 + 13*w**4/12 - 9*w. Let u(b) be the third derivative of a(b). Factor u(f).
-2*(3*f - 1)**2/11
Let w(c) be the second derivative of c**5/30 - c**4/12 - 21*c**2/2 + 2*c. Let n(x) be the first derivative of w(x). Factor n(i).
2*i*(i - 1)
Suppose -5*a - 31 = 6*m - 4*m, 0 = -3*m + 2*a - 94. Let b = m + 31. Suppose 0 + 8/5*u**2 + 0*u - 2/5*u**b = 0. What is u?
0, 4
Suppose -1 = -d + 1. Solve 33*t**3 + 8*t + 87*t**2 - d*t - 48*t**2 = 0 for t.
-1, -2/11, 0
Let s = -47373/7 + 6768. Factor -18/7 + s*u + 6/7*u**2.
3*(u + 2)*(2*u - 3)/7
Let c(v) be the first derivative of 1 + v + 1/18*v**4 - 2/9*v**3 + 1/3*v**2. Let o(p) be the first derivative of c(p). Solve o(k) = 0.
1
Suppose 0 = -3*d - 3*z + 12, d = 6*d - 5*z - 40. Let v = d - 2. Let 4*l + 3*l**2 - v*l**2 + 3*l**2 - 2*l**3 = 0. What is l?
-1, 0, 2
Let -14023*g**2 - 7*g**4 + 14063*g**2 - 3*g**4 + 5*g**3 - 20*g = 0. Calculate g.
-2, 0, 1/2, 2
Let v be 18/15 - (-1)/(-5) - 5. Let r be -5 + (-1595)/(-315) - v/18. Factor 0*h + 0 + 0*h**2 - r*h**4 + 2/7*h**3.
-2*h**3*(h - 1)/7
Let o be ((-1)/(-6))/(-1) - 429/378. Let f = o + 379/63. Suppose -36/7*k + 75/7*k**4 + 90/7*k**3 - f*k**2 + 12/7 = 0. What is k?
-1, 2/5
Let z be 2 + ((-16)/4 - -2). Suppose -4*n - 2*o - 2 = 0, 4*o = -z*n + 4*n - 28. Factor -10*x**2 + 4*x - 4 + 21*x**2 - 7*x**n - 4*x**3.
-4*(x - 1)**2*(x + 1)
Suppose 4*c - 48 = 44. Suppose -h + 3*m = -3 - 6, -5*m - c = -3*h. Factor v**5 - v + 2*v**2 + h*v**2 - 2*v**4 + 0*v**2 - 6*v**2.
v*(v - 1)**3*(v + 1)
Determine d, given that 384 - 16*d + 1/6*d**2 = 0.
48
Let v be 0*((-396)/(-22))/(-36). Factor -2/17*k**4 + 0 + 0*k**2 + v*k - 8/17*k**3.
-2*k**3*(k + 4)/17
Let m be 5 - (-6)/(0 + -3). Suppose q**m + q**4 + 113*q - 2*q**2 - 113*q = 0. Calculate q.
-2, 0, 1
Let a be -1*(-1 + (1 - 0)). Suppose -2*c + 6 = -w, a = 4*w + 6*c - 2*c - 12. What is m in w*m + 0 - 2/9*m**3 + 0*m**2 = 0?
0
Suppose 5*u - 3*n = 21, -9 + 1 = -2*u + n. Factor 88*y**2 + 4*y**4 + 59 - 271*y**u + 137 - 336*y + 319*y**3.
4*(y - 1)**2*(y + 7)**2
Let g be -21*((-10)/(-6) - 2). Suppose -x = -g + 3. Let x - 2*d**2 + 4*d**2 - 6*d + 0*d**2 + 0*d = 0. What is d?
1, 2
Let z(d) be the first derivative of 3*d**5/40 - d**4/2 + d**3 + 7*d**2/2 + 4. Let t(h) be the second derivative of z(h). Suppose t(i) = 0. What is i?
2/3, 2
Factor 39*a**2 - 105*a**2 + 27*a**2 + 36*a**2 - 24 - 30*a + 3*a**3.
3*(a - 4)*(a + 1)*(a + 2)
Let d(r) be the second derivative of r**4/30 + 7*r**3/15 - 8*r**2/5 - 2*r - 5. Determine m, given that d(m) = 0.
-8, 1
Let p(k) be the first derivative of -1/5*k**2 + 4/5*k + 1/10*k**4 - 4/15*k**3 + 13. Let p(d) = 0. What is d?
-1, 1, 2
Let q(t) = 139*t**3 + 797*t**2 - 3475*t - 611. Let k(s) = -28*s**3 - 159*s**2 + 695*s + 122. Let c(y) = -11*k(y) - 2*q(y). Determine a, given that c(a) = 0.
-8, -1/6, 3
Suppose 0 + 4/5*b**2 + 0*b - 2/5*b**3 = 0. Calculate b.
0, 2
Let p(u) = -3*u**3 + u**2 - 4*u - 5. Let i be (-4)/(-2)*5/(-10). Let b be p(i). Factor 1/2*c + b*c**2 + 0.
c*(6*c + 1)/2
Let a(k) = k**2 - 4*k + 3. Let j(y) = y - 1. Let i(z) = -5*a(z) + 15*j(z). Suppose i(w) = 0. What is w?
1, 6
Let l(t) = -t**3 + 15*t**2 - 48*t + 61. Let p(q) = -q**2 + 1. Let h(k) = -4*l(k) - 12*p(k). Factor h(z).
4*(z - 4)**3
Let d(f) be the first derivative of 4*f**3/3 + 70*f**2 + 136*f - 235. Factor d(q).
4*(q + 1)*(q + 34)
Suppose -85 = -24*z - 24 + 11. Factor -6/13 + 2/13*t**z + 6/13*t**2 - 2/13*t.
2*(t - 1)*(t + 1)*(t + 3)/13
Let j be (-1 + 24/40)/(2/(-20)). Let y(m) be the first derivative of 0*m + 2*m**2 + 8/3*m**3 - 8 + m**j. Find g such that y(g) = 0.
-1, 0
Factor 2/7 + 2/7*y**2 - 4/7*y.
2*(y - 1)**2/7
Let t(z) be the second derivative of -z**7/168 - 17*z**6/480 - z**5/15 - z**4/24 - 8*z**2 + 14*z. Let h(j) be the first derivative of t(j). Factor h(n).
-n*(n + 1)*(n + 2)*(5*n + 2)/4
Determine a so that 2/3*a**4 + 0 + 4/3*a**3 - 14/3*a**2 + 8/3*a = 0.
-4, 0, 1
Suppose 0 = -2*y + 36. Let o be 24/(-16) + y/4. Factor -3*z**2 - 8*z + 3*z**4 - z**o + z**5 + 9*z - z.
z**2*(z - 1)*(z + 1)*(z + 3)
Let c(t) be the first derivative of 2/9*t**3 - 39 + 1/3*t**2 + 0*t. Find z, given that c(z) = 0.
-1, 0
Let t = -8317 - -8317. What is k in 1/10*k**3 + 8/5*k**2 + t + 32/5*k = 0?
-8, 0
Let c be -6*(-60)/(-9)*-1. Suppose -5 = x, 0 = -3*k + 4*x + 46 + c. Factor 2*o**3 - 35*o**3 - 6*o**2 + o**5 - k*o**5 - 48*o**4.
-3*o**2*(o + 1)**2*(7*o + 2)
Let h(m) = -m**3. Let u be ((-6)/(-9))/((-10)/15). Let b(j) = 5*j**4 + 53*j**3 + 180*j**2 + 80*j - 320. Let y(c) = u*b(c) + 2*h(c). Factor y(l).
-5*(l - 1)*(l + 4)**3
Let z(n) = -n**2 - 10*n - 11. Let q be z(-8). Find w such that -6*w + 0*w + 18*w**3 + 27*w**2 - 63*w**3 + 33*w**4 - 9*w**q = 0.
0, 2/3, 1
Let w = -8073 + 72659/9. Determine h so that 0*h + w*h**3 + 0 - 2/9*h**2 = 0.
0, 1
Let h(q) be the second derivative of -q**7/126 + q**6/45 + 3*q**5/5 + 43*q**4/18 + 77*q**3/18 + 4*q**2 + 12*q. Determine g so that h(g) = 0.
-3, -1, 8
Solve 6*d**5 + 0*d + 0*d**2 - 9/2*d**4 + 0 - 3/2*d**3 = 0 for d.
-1/4, 0, 1
Suppose 4*x = -n + 6, n + 3*x - 6 = -2*x. Suppose -6*d + 5*s = -2*d - 13, -n = -4*d - 2*s. Factor -2/11*f**3 + 2/11*f - 2/11 + 2/11*f**d.
-2*(f - 1)**2*(f + 1)/11
Let r(o) = -o**3 + 2*o**2 + 1. Let w(u) = -u**4 + 3*u**3 - u**2 + 13*u + 2. Let c(b) = -12*r(b) - 3*w(b). Find g, given that c(g) = 0.
-2, -1