et k = p - -3/131. Factor k*y**3 - 12/5*y - 3/5*y**4 - 12/5 + 9/5*y**2.
-3*(y - 2)**2*(y + 1)**2/5
Let s(a) be the first derivative of -a**4/4 - 26*a**3/3 + 27*a**2/2 - 208. Factor s(g).
-g*(g - 1)*(g + 27)
Let h(x) be the second derivative of x**5/10 + x**4 - 4*x**3/3 - 24*x**2 - 70*x. Find q, given that h(q) = 0.
-6, -2, 2
Let k(t) be the first derivative of t**6/60 - t**4/8 + t**3/6 - 10*t + 4. Let a(i) be the first derivative of k(i). Let a(m) = 0. What is m?
-2, 0, 1
Let -9*z**2 + 24 - 18*z**2 + 26620*z**4 - 6*z - 26617*z**4 + 6*z**3 = 0. Calculate z.
-4, -1, 1, 2
Let s(w) be the second derivative of 7/15*w**3 + 16*w - 1/6*w**4 - 2/5*w**2 + 0. Factor s(r).
-2*(r - 1)*(5*r - 2)/5
Let t be 66 - ((-14)/56 + 1/4). Let z = t - 63. Find h such that 2/11*h + 4/11*h**2 + 0 + 2/11*h**z = 0.
-1, 0
Let s be ((-27)/(-6)*-2)/(-1). Let l = 13 - s. Factor 8*i**2 + l*i**2 - 10*i**2.
2*i**2
Let r(l) be the first derivative of 7*l**6/66 + 138*l**5/55 + 505*l**4/22 + 3200*l**3/33 + 3375*l**2/22 - 1250*l/11 - 66. Find a, given that r(a) = 0.
-5, 2/7
Let y(k) be the third derivative of -k**8/24 - 2*k**7/21 + k**6/140 + 2*k**5/21 - k**4/21 - 13*k**2. Solve y(v) = 0.
-1, 0, 2/7
Let g(a) be the third derivative of 4*a**7/1575 + 16*a**6/225 - a**5/150 - 47*a**4/180 + 16*a**3/45 - 2*a**2 - 46. What is v in g(v) = 0?
-16, -1, 1/2
Let r be 34/(-12)*(-244)/2074. Solve r*i**4 - 1/3*i**2 - 1/3*i**3 + 1/3*i + 0 = 0.
-1, 0, 1
Factor 18*t**2 + 7*t**2 - 12*t**3 - 9*t**2 - 4*t**4.
-4*t**2*(t - 1)*(t + 4)
Let y(k) be the first derivative of 2/39*k**3 + 1 + 8/13*k - 5/13*k**2. Factor y(m).
2*(m - 4)*(m - 1)/13
Let g be (-31)/(-11) + (-554)/(-3047). Determine s so that 92/3*s**2 + 16 + 4/3*s**4 - 32/3*s**g - 112/3*s = 0.
1, 2, 3
Factor -30*v**3 + 7*v**4 - 3*v**4 + 18*v**3 - 24*v**3.
4*v**3*(v - 9)
Let x(k) be the third derivative of k**5/15 + k**4 - 14*k**3/3 - 243*k**2. Suppose x(j) = 0. Calculate j.
-7, 1
Let b be (-2 - (-2 + 3))*1698/54. Let j = -94 - b. Factor -2/3 + j*t + 2/3*t**2 - 1/3*t**3.
-(t - 2)*(t - 1)*(t + 1)/3
Let s(m) be the second derivative of -m**7/210 - m**6/75 + m**5/50 + 2*m**4/15 + 7*m**3/30 + m**2/5 - 8*m - 4. What is r in s(r) = 0?
-1, 2
Let j = -106 - -109. Let a(c) be the first derivative of 3/2*c**2 + 3/4*c**4 - 4 + 0*c - 2*c**j. Determine n, given that a(n) = 0.
0, 1
Solve -46*l - 2*l**2 + 36*l + 7 + 23*l = 0 for l.
-1/2, 7
Let z = 1097/2 - 560. Let r = -11 - z. Factor 9/2*q**3 + 0 + r*q**2 + 5/2*q**5 - 13/2*q**4 - q.
q*(q - 1)**3*(5*q + 2)/2
Factor 957*n**2 - 963*n**2 + n**3 - 8*n - 2*n**3.
-n*(n + 2)*(n + 4)
Let v(y) be the third derivative of 0*y**3 + 0*y - 1/20*y**5 + 1/70*y**7 - 5*y**2 - 1/8*y**4 + 1/40*y**6 + 0. Factor v(l).
3*l*(l - 1)*(l + 1)**2
Let n(z) be the first derivative of -z**4/6 - 8*z**3/9 - z**2/3 + 4*z - 124. Find g, given that n(g) = 0.
-3, -2, 1
Suppose 4*k - 5*w = 599 - 30, -562 = -4*k - 2*w. Let y = 144 - k. Find x, given that x + 1/2*x**2 + 0 - 5/2*x**y - 1/2*x**4 + 3/2*x**5 = 0.
-1, -2/3, 0, 1
Let f(g) be the first derivative of 2*g**6/15 - g**5/5 - g**4/3 + 2*g**3/3 - 19*g - 37. Let s(v) be the first derivative of f(v). Factor s(n).
4*n*(n - 1)**2*(n + 1)
Let n(m) be the first derivative of -m**6/30 + m**5/6 + m**4/3 + m**3/3 - 15. Let y(o) be the third derivative of n(o). Factor y(z).
-4*(z - 2)*(3*z + 1)
Let q(f) be the first derivative of f**5 + 5/2*f**4 - 5/3*f**3 - 5*f**2 + 0*f + 25. Let q(x) = 0. What is x?
-2, -1, 0, 1
Let i = -1053 + 1053. Factor 2/17*z**2 + i - 2/17*z.
2*z*(z - 1)/17
Let k = 580 + -572. Let u(j) be the third derivative of 1/40*j**6 + 1/48*j**4 + 0 + 5*j**2 + 1/105*j**7 + 1/30*j**5 + 0*j**3 + 1/672*j**k + 0*j. Factor u(z).
z*(z + 1)**4/2
Let k = 31205/2268 + -5/567. Let a = 287/20 - k. Suppose -a*i**3 + 0*i - 1/5*i**5 + 0 + 3/5*i**4 + 1/5*i**2 = 0. What is i?
0, 1
Let o(p) be the third derivative of -2*p**6/15 + p**5 + 2*p**4/3 - 5*p**2 - 2. Let o(t) = 0. What is t?
-1/4, 0, 4
Let t(h) be the second derivative of -7/5*h**5 - 16/15*h**6 + 0 + 2*h - 2/7*h**7 + 0*h**3 - 2/3*h**4 + 0*h**2. Solve t(r) = 0 for r.
-1, -2/3, 0
Let l(q) = 5*q**2 - 5*q - 20. Let g(u) = 27*u**2 - 26*u - 101. Let r(s) = 6*g(s) - 33*l(s). Factor r(t).
-3*(t - 6)*(t + 3)
Let s(y) be the third derivative of 7*y**5/15 + 2*y**4/3 - 2*y**3 - y**2 + 15*y. Factor s(x).
4*(x + 1)*(7*x - 3)
Let r(z) be the third derivative of z**7/1365 + z**6/390 + z**5/390 - 3*z**2 + 92*z. Factor r(s).
2*s**2*(s + 1)**2/13
Let z(n) = -3*n**2 + 11*n. Let p = 2 + -2. Let t(q) = p*q**2 + q**2 - 5*q + q**2 - q**2. Let v(j) = 5*t(j) + 3*z(j). Factor v(x).
-4*x*(x - 2)
Suppose 0 + 1/2*o**3 + o**2 - 3/2*o = 0. What is o?
-3, 0, 1
Let g(k) = -k**3 + k**2 + 1. Let b(v) = -112*v**4 - 77*v**3 + 57*v**2 + 20*v - 11. Suppose -9 + 0 = 3*c. Let d(r) = c*g(r) - b(r). Let d(n) = 0. What is n?
-1, -1/2, 2/7, 1/2
Let t = 1 + 3. Suppose -3*d + k = -4*d + 6, -5*k - 18 = -3*d. Suppose 3*w - w**2 + 7*w**2 + 0*w**4 - w**5 - 2*w**5 - d*w**t = 0. Calculate w.
-1, 0, 1
Let y(q) be the second derivative of -q**8/11200 - q**7/2100 - q**6/1200 - 10*q**4/3 + 15*q. Let v(w) be the third derivative of y(w). Solve v(l) = 0 for l.
-1, 0
Let o be 3/12*(-137 - -145). Let 0 + 2/15*k**5 + 2/15*k**3 + 0*k**o - 4/15*k**4 + 0*k = 0. What is k?
0, 1
Let c(p) = -5*p - 17. Let d be c(-4). Factor 34*f - 9*f + 27 - 2*f + 21*f**2 + 3*f**d + 22*f.
3*(f + 1)*(f + 3)**2
Let y(p) be the third derivative of p**7/126 + p**6/18 + p**5/12 + 22*p**2 - p. Suppose y(c) = 0. What is c?
-3, -1, 0
Let o(d) be the second derivative of d**6/660 + d**5/110 - 3*d**4/44 + 5*d**3/33 - 6*d**2 + 28*d. Let g(m) be the first derivative of o(m). Factor g(q).
2*(q - 1)**2*(q + 5)/11
What is u in 1/2*u**3 + 1/2*u**2 + 4 - 5*u = 0?
-4, 1, 2
Let 21/4*v**2 + 1/8*v**4 + 13/8 + 2*v**3 + 5*v = 0. What is v?
-13, -1
Let h(l) = -87*l - 33. Let q be h(-3). Let r = -1594/7 + q. Solve -r*c**2 - 6/7*c + 8/7 = 0.
-4, 1
Let w = 52/465 - -2/93. Let x(y) be the first derivative of 0*y**3 + 2/3*y + 1/3*y**4 + 6 - 2/3*y**2 - w*y**5. Let x(b) = 0. What is b?
-1, 1
Find z, given that 24/5*z**2 + 136/5 + 162/5*z - 2/5*z**3 = 0.
-4, -1, 17
Suppose n - 1 = 4*p - 3, 2*n - 5*p + 4 = 0. Let j(i) = -i**2 - i. Let l(q) = -8*q**2 - 16*q. Let z(v) = n*l(v) + 20*j(v). Find w, given that z(w) = 0.
0, 3
Let w(h) be the second derivative of h**4/6 - 10*h**3/3 - 24*h**2 + 198*h. Suppose w(o) = 0. What is o?
-2, 12
Suppose -j - o - 3 = 3, j - 2*o = -6. Let m be 0/(8/j + 26/(-39)). Factor 2/15*v + m + 0*v**2 - 2/15*v**3.
-2*v*(v - 1)*(v + 1)/15
Determine d, given that -25/2*d**2 + 27/2*d**4 - 1 + 15/2*d - 15/2*d**3 = 0.
-1, 2/9, 1/3, 1
Let l = -9 - 0. Let i = 12 + l. Let -5 - 4*x - 2 + 6 + 4*x**i + 4*x**2 - 3 = 0. Calculate x.
-1, 1
Let m = -286 + 278. Let t be 32/m + 11 + -6 + 1. Factor -4*f - t*f**2 - 1/3*f**3 - 8/3.
-(f + 2)**3/3
Suppose -2*i + 20 = 4*h, 4*h = 3*h - 5*i + 5. What is d in -76 + 5*d**2 + d**3 - h*d + 4*d**3 + 71 = 0?
-1, 1
Let s(k) be the second derivative of -2/15*k**3 - 1/5*k**4 - 1/25*k**6 - 1/210*k**7 + 40*k - 13/100*k**5 + 0*k**2 + 0. Factor s(t).
-t*(t + 1)**2*(t + 2)**2/5
Suppose 0 = -0*o - o + 3. Let -8*y**2 + 1 + 14*y**o - 1 - 18*y**3 = 0. Calculate y.
-2, 0
Let u(y) be the third derivative of y**8/4032 - y**7/112 + y**6/18 - 11*y**5/20 + 5*y**2. Let q(v) be the third derivative of u(v). Factor q(t).
5*(t - 8)*(t - 1)
Let c = -111 - -167. Let y = c - 54. Let 1 + 1/2*d**y - 3/2*d = 0. Calculate d.
1, 2
Factor 24 + 1/3*d**2 - 73/3*d.
(d - 72)*(d - 1)/3
Let y(w) be the first derivative of -w**4/18 - 2*w**3/27 + 4*w**2/9 + 8*w/9 - 231. Suppose y(q) = 0. Calculate q.
-2, -1, 2
Factor 182*t + 50*t**2 + 65*t - 20*t + 392 + 53*t.
2*(5*t + 14)**2
Factor 8/5*k**4 + 0*k - 4/5*k**2 + 14/5*k**3 + 0.
2*k**2*(k + 2)*(4*k - 1)/5
What is u in 21/2*u**2 + 105/4*u + 33/2 + 3/4*u**3 = 0?
-11, -2, -1
Let u be (-4)/2 - (-1 - 3). Suppose -s = 3*l - 10, -26 = -6*l + u*l + 5*s. Solve -9*c**4 + 6*c**3 - 23*c**l - 18*c**5 + 32*c**2 + 8*c + 4*c**5 = 0.
-2, -1, -2/7, 0, 1
Suppose 6*j - 420 = -6*j. What is a in -5 - j*a**2 + 63*a**2 - 33*a**2 + 10*a = 0?
1
Suppose 329*q - 110 = 307*q. Factor 0*t**2 + 0*t + 0 + 1/8*t**3 + 0*t**4 - 1/8*t**q.
-t**3*(t - 1)*(t + 1)/8
Let r be -1*-10*(-1)/(-2). Determine u, given that 2/3*u**r - 14/3*u**4 + 0 - 40/3*u**2 + 12*u**3 