t = -2664 - -2664. Factor -2/11*r**2 + t + 2/11*r.
-2*r*(r - 1)/11
Suppose 3*o - 24 = -3*b, 0*o - 4*o = 2*b - 26. Suppose v = -4*i - 4, 5*v - b*i - 43 = -2*i. Factor -v*q**3 - 6 + 9*q - 8*q**3 + 13*q**3.
-3*(q - 1)**2*(q + 2)
Let a(h) be the first derivative of h**6/45 + h**5/10 - h**4/9 - 4*h**3/3 - 8*h**2/3 - 23*h + 9. Let o(p) be the first derivative of a(p). Factor o(u).
2*(u - 2)*(u + 1)*(u + 2)**2/3
Let k(q) be the third derivative of q**6/270 + 2*q**5/45 - q**3 - 11*q**2. Let z(l) be the first derivative of k(l). Determine n, given that z(n) = 0.
-4, 0
Let z(a) = 3*a + 3. Let b be z(7). Let -49 - 15 - 3*d**2 + 16 + b*d = 0. Calculate d.
4
Let d(q) be the first derivative of 2*q**5/75 + q**4/30 - 8*q**3/45 - 4*q**2/15 + 188. Suppose d(x) = 0. What is x?
-2, -1, 0, 2
Let l(j) = 19*j**2 - 111*j + 70. Let g(z) = -z**2 - z. Let i(c) = -4*g(c) - l(c). Factor i(b).
-5*(b - 7)*(3*b - 2)
Let h(w) = w**3 + 2*w**2 - 7*w - 7. Let d be h(-3). Let q(f) be the second derivative of f**2 + 4*f - 1/10*f**d + 1/3*f**3 + 0 - 1/6*f**4. Factor q(u).
-2*(u - 1)*(u + 1)**2
Let o = -2143 - -2145. Factor 20/9*d - 4/9*d**3 - 4/9*d**o - 4/3.
-4*(d - 1)**2*(d + 3)/9
Let a(b) be the first derivative of 3/20*b**5 + b**3 + 3/4*b**4 - b + 5 + 0*b**2. Let o(m) be the first derivative of a(m). Let o(s) = 0. What is s?
-2, -1, 0
Determine g so that 4*g**2 - g**3 - 4*g**4 - 4*g + 9*g**3 + 6*g**5 - 3*g + g - 8*g**5 = 0.
-3, -1, 0, 1
Let g(a) be the second derivative of -a**6/120 - a**5/60 - 11*a**2/2 - 17*a. Let r(s) be the first derivative of g(s). Factor r(t).
-t**2*(t + 1)
Let p = -97 - -100. Suppose -15 + p = -6*w. Let -10/9*f + 8/9*f**4 + 10/9*f**3 - 2/3*f**w - 2/9 = 0. Calculate f.
-1, -1/4, 1
Let r(w) = w**2 - 2*w - 1. Let a(s) = 7*s**2 - 42*s + 29. Let q(b) = -a(b) + 3*r(b). Factor q(j).
-4*(j - 8)*(j - 1)
Factor -2/7*l**2 - 44402/7 - 596/7*l.
-2*(l + 149)**2/7
Let i(s) be the third derivative of s**6/3240 - s**5/360 - 5*s**3/6 + 5*s**2. Let a(c) be the first derivative of i(c). Let a(p) = 0. What is p?
0, 3
Let z(d) be the second derivative of -d**4 - 13*d + 0 + 2/3*d**3 + 8*d**2. Factor z(i).
-4*(i + 1)*(3*i - 4)
Suppose 0 = -5*r - 13 - 12, 4*y - 3*r - 103 = 0. Let g = -17 + y. Factor -6*n**2 + 5*n**g - 12*n**4 + 6*n**3 - n**5 - n**5 + 9*n**3.
3*n**2*(n - 2)*(n - 1)**2
Let w(b) = b**3 + 5*b**2 + 3*b - 1. Let h be w(-4). Factor -r**3 - 2*r**3 + 0*r**5 + 9*r**4 - 3*r**h - 3*r**5.
-3*r**3*(r - 2)*(r - 1)
Let m(s) be the second derivative of -6*s**6/5 - 15*s**5/4 - 13*s**4/4 + s**3/2 + 3*s**2/2 - 113*s. Let m(v) = 0. Calculate v.
-1, -1/3, 1/4
Suppose 49*c = 54*c + 130. Let n = 28 + c. Factor 2/3*y**3 + 16/3 + 4*y**n + 8*y.
2*(y + 2)**3/3
Let q(j) be the first derivative of j**4/8 + 3*j**3/2 + 15*j**2/4 - 3*j - 17. Let r(v) be the first derivative of q(v). Determine u so that r(u) = 0.
-5, -1
Let g(q) = 11*q**4 - 3*q**3 - 30*q**2 + 4*q - 6. Let v(c) = -11*c**4 + c**3 + 29*c**2 - 4*c + 5. Let b(a) = 5*g(a) + 6*v(a). Factor b(y).
-y*(y - 1)*(y + 2)*(11*y - 2)
Suppose 15*y**3 - 90 + 2*y**3 - 67*y - 15*y**2 + 30*y**3 + 5*y**4 - 2*y**3 - 78*y = 0. Calculate y.
-9, -1, 2
Let f(a) be the second derivative of -a**7/42 + 37*a**6/30 + 77*a**5/20 + 13*a**4/4 + 433*a. Solve f(b) = 0.
-1, 0, 39
Let c = -35 + 37. Suppose 4*v = -c + 18. Determine r, given that -1/5*r**5 + 0 + 0*r**3 + 2/5*r**2 + 1/5*r - 2/5*r**v = 0.
-1, 0, 1
Let h = 1035/34 - 492/17. Determine a so that -15/2*a + 9 + h*a**2 = 0.
2, 3
Suppose -3*d + 4*d = -p, 0 = -3*d - 5*p. Let b(a) be the third derivative of -1/21*a**4 + 0*a**3 - 8*a**2 + d - 1/15*a**5 + 0*a. Factor b(l).
-4*l*(7*l + 2)/7
Suppose 47*f + 208 = 73*f. Let c(t) be the first derivative of f + 4*t - 2*t**2 - 13/3*t**3 - 5/4*t**4. Factor c(p).
-(p + 1)*(p + 2)*(5*p - 2)
Let w(j) be the first derivative of j**6/900 - j**4/60 - 10*j**3/3 - 16. Let t(m) be the third derivative of w(m). Factor t(d).
2*(d - 1)*(d + 1)/5
Let h be -1 + (2 - (-19 + 0)). Let a be (-1)/h + (-8)/(-32). Find w such that 0 - 2/5*w**2 + 0*w + 0*w**4 - a*w**5 + 3/5*w**3 = 0.
-2, 0, 1
Let f = 13 - 11. Let 4*x**2 - 2*x**4 - f*x**4 + 4*x**5 + 6*x**4 - 4*x**3 - 6*x**4 = 0. What is x?
-1, 0, 1
Suppose -10*a**5 - 38*a**2 + 44*a**3 - 76*a - 32*a**5 + 22*a**2 - 100*a**4 + 8 + 74*a**5 + 108*a**2 = 0. What is a?
-1, 1/8, 1, 2
Let m(i) be the third derivative of -23*i**6/120 - 77*i**5/10 - 195*i**4/2 - 100*i**3/3 + 89*i**2 + 3*i. Factor m(r).
-(r + 10)**2*(23*r + 2)
Let c(k) be the first derivative of -3*k**4/16 - 13*k**3/4 + 24*k**2 - 51*k - 330. Let c(q) = 0. Calculate q.
-17, 2
Suppose 0 = -111*p + 62*p + 98. What is d in 0 - 8/7*d - 4/7*d**p + 4/7*d**3 = 0?
-1, 0, 2
Let k be (-4)/14 - (-10)/245*7. Let i(c) be the first derivative of -2/9*c**3 + 0*c + k*c**2 + 2. Solve i(r) = 0.
0
Let w(s) be the second derivative of 7*s**6/75 - 23*s**5/50 + 2*s**4/3 - 4*s**3/15 - 77*s. Let w(d) = 0. Calculate d.
0, 2/7, 1, 2
Let d be (1293 + -1 + 2)/(-5). Let f = -258 - d. Determine k so that f*k + 1/5*k**2 + 3/5 = 0.
-3, -1
Let r(f) be the first derivative of 0*f - 1/18*f**6 + 0*f**4 + 0*f**2 + 0*f**3 - 1/15*f**5 + 8. Factor r(q).
-q**4*(q + 1)/3
Suppose -100*k - 25 = -105*k. Suppose -2*s + 6 = 2*q, -25 + 0 = -5*q + k*s. Factor -1/5*b**2 + 0 + 0*b - 1/5*b**q - 2/5*b**3.
-b**2*(b + 1)**2/5
Let j(l) = l**2 + 10*l - 21. Let q(z) = 10*z - 21. Let d(r) = -5*j(r) + 4*q(r). Let h(w) = 10*w**2 + 20*w - 41. Let x(g) = -11*d(g) - 6*h(g). Factor x(i).
-5*(i - 1)*(i + 3)
Let s = 17329 - 103949/6. Factor -5/3 - s*c - 5/6*c**3 - 10/3*c**2.
-5*(c + 1)**2*(c + 2)/6
Let -2/7*y**5 - 6/7*y**4 + 46/7*y**3 + 4*y - 66/7*y**2 + 0 = 0. Calculate y.
-7, 0, 1, 2
Suppose -23/7*n - 1/7*n**3 + 13/7*n**2 + 11/7 = 0. What is n?
1, 11
Let x = 22 - 20. Determine s, given that 9*s**4 + 3*s**5 + 0*s**4 - 136*s**3 - 9*s**x + 133*s**3 = 0.
-3, -1, 0, 1
Let i(r) be the third derivative of -r**5/15 - 35*r**4/6 + 24*r**3 - 2*r**2 - 2*r. Factor i(s).
-4*(s - 1)*(s + 36)
Let t = 25924/59731 + 2/2597. Suppose t*d + 8/23 + 2/23*d**2 = 0. What is d?
-4, -1
Let x(s) be the first derivative of -s**3/5 - 9*s**2 + 145. Determine n so that x(n) = 0.
-30, 0
Let a(x) be the first derivative of 0*x - 3/25*x**5 + 9/20*x**4 + 0*x**3 - 29 + 0*x**2. Suppose a(w) = 0. Calculate w.
0, 3
Let i(m) be the third derivative of -m**6/360 - m**5/9 - m**4/2 + 132*m**2. Factor i(w).
-w*(w + 2)*(w + 18)/3
Let q(i) be the first derivative of i**8/2520 - i**7/420 + i**6/180 - i**5/180 - 11*i**3/3 + 10. Let f(z) be the third derivative of q(z). Solve f(s) = 0 for s.
0, 1
Let r(z) = 270*z**2 - 3925*z + 3645. Let t(x) = -x**3 + 271*x**2 - 3923*x + 3645. Let l(v) = 4*r(v) - 5*t(v). Factor l(c).
5*(c - 27)**2*(c - 1)
Let i = 31/7 + 1/14. Let z(n) be the first derivative of 6*n + i*n**2 - 8 - 21/4*n**4 - 9/5*n**5 - 3*n**3. Let z(g) = 0. What is g?
-1, 2/3
Let y be 581/28 - 2*1/(-8). Factor 0*m**2 + 0*m**2 + 3*m**2 - y*m + 9 + 9*m.
3*(m - 3)*(m - 1)
Let a(h) = -h**3 + h + 1. Let r(s) = 3*s**4 + 179*s**3 + s + 1. Let g(m) = a(m) - r(m). Find d, given that g(d) = 0.
-60, 0
Let t(p) be the third derivative of 0 - 8*p**2 + 3/80*p**5 + 1/160*p**6 + 0*p + 3/32*p**4 + 1/8*p**3. Let t(f) = 0. What is f?
-1
Factor 2916/5*n + 2/5*n**5 + 0 - 58/5*n**4 + 594/5*n**3 - 486*n**2.
2*n*(n - 9)**3*(n - 2)/5
Let d(y) be the third derivative of y**6/24 + y**5/12 - 5*y**4/24 - 5*y**3/6 + 4*y**2 + 8*y. Find v such that d(v) = 0.
-1, 1
Suppose -22*n + 83 = -5. Factor -8/3*u + 4/3*u**2 + 8/3*u**3 - 2 + 2/3*u**n.
2*(u - 1)*(u + 1)**2*(u + 3)/3
Let q(h) be the second derivative of h**7/840 + h**6/80 + h**4 + 9*h. Let v(i) be the third derivative of q(i). Factor v(p).
3*p*(p + 3)
Suppose 153 = 6*q - 135. Let f be (-16)/q - (-34)/66. Factor 2/11*a**3 + 2/11*a**4 - 2/11*a**2 - f*a + 0.
2*a*(a - 1)*(a + 1)**2/11
Suppose 2*o - 79220 + 79216 = 0. Find d such that -1/2*d**4 - 3/2*d - 11/6*d**3 - 5/2*d**o - 1/3 = 0.
-1, -2/3
Let i(a) = 7*a**4 - 59*a**3 - 28*a**2. Let m(f) = 3*f**4 - 29*f**3 - 14*f**2. Let k(j) = -6*i(j) + 13*m(j). Find y, given that k(y) = 0.
-7, -2/3, 0
Let x(q) be the third derivative of q**6/420 - q**5/42 + q**4/28 + 3*q**3/7 - 112*q**2. Solve x(z) = 0 for z.
-1, 3
Let h(i) = i + 1. Let j = -27 - -30. Let l(q) = -3*q**2 + 15*q - 9. Let w(u) = j*h(u) - l(u). Suppose w(a) = 0. What is a?
2
Let x