 80. Let i(r) = n*z(r) - 3*x(r). Find o such that i(o) = 0.
9
Suppose 0 = 32*n - 40*n + 24. Let v(r) be the first derivative of r**n - 6/5*r - 11 + 9/10*r**2. Factor v(y).
3*(y + 1)*(5*y - 2)/5
Let u(d) be the first derivative of -2/21*d**3 + 13 + 8/7*d + 3/7*d**2. Find k such that u(k) = 0.
-1, 4
Let x(s) = s**2 - 1. Let u be (4 + -5)/1*3/(-3). Suppose -4*l - l = 10. Let y(n) = n**2 - 2. Let q(o) = l*x(o) + u*y(o). Factor q(w).
-w**2
Let s(b) be the first derivative of -9 + 0*b**2 + 0*b - 1/3*b**3. Find m such that s(m) = 0.
0
Let t(n) be the first derivative of 5/12*n**4 + 0*n - 12 + 1/9*n**3 + 4/15*n**5 + 0*n**2. Find c, given that t(c) = 0.
-1, -1/4, 0
Let u(s) be the second derivative of s**4/12 + 14*s**3/3 + 27*s**2/2 + 82*s. Let u(w) = 0. What is w?
-27, -1
Suppose k - 4*y - 19 = 0, 5*k - y - 11 = 8. Factor 3*m - m + k*m**2 - 6*m - 2*m + 3*m**3.
3*m*(m - 1)*(m + 2)
Let s be (8/56)/((-276)/(-42) - 7)*-18. Factor -s*w - 3/5 - 15*w**2.
-3*(5*w + 1)**2/5
Let i(d) be the third derivative of d**6/24 - 7*d**5/6 + 125*d**4/24 - 10*d**3 + d**2 + 188. Let i(r) = 0. Calculate r.
1, 12
Suppose 107 = 18*p + 17. Factor 3/5*h**4 + 2/5 - 13/5*h**3 - 17/5*h**2 + 4/5*h**p - 3/5*h.
(h - 2)*(h + 1)**3*(4*h - 1)/5
Suppose 4 = 2*b, 2*b = -0*d + d - 71. Determine z, given that 20 - d*z + 25*z**2 + 16*z + 11*z - 5*z**3 + 8*z = 0.
1, 2
Let f(p) = p**2 + 2*p - 3. Let d be f(-3). Factor 6*n + 3*n**2 + 12 + d*n**2 - 9.
3*(n + 1)**2
Let y(j) = -5*j**3 - 358*j**2 + 23071*j - 476663. Let t(f) = -3*f**3 - 178*f**2 + 11536*f - 238332. Let g(r) = -7*t(r) + 4*y(r). Find w, given that g(w) = 0.
62
Let b be (4*((-200)/48 + 4))/(-16). Let f(n) be the first derivative of 4 + 0*n**3 - 1/9*n**6 + 0*n**2 + 0*n - b*n**4 - 1/6*n**5. Find i such that f(i) = 0.
-1, -1/4, 0
Suppose 5*z + 15 = 5*b, 0 = 2*b + z + 2*z + 19. Let g(m) = m**2 + 3*m + 2. Let s be g(b). Solve s - 6/7*l - 2/7*l**2 = 0.
-3, 0
Let u = 6553/45969 + 2/6567. Find i, given that 2/7*i**2 + u*i**3 + 0*i + 0 = 0.
-2, 0
Let l(m) be the second derivative of -m**7/336 + m**6/60 + 3*m**5/80 - m**4/24 - 5*m**3/48 + 3*m - 43. Solve l(k) = 0 for k.
-1, 0, 1, 5
Let w = -341 - -804. Let o = w + -5087/11. Let 4/11 - 2/11*q**2 - o*q**3 + 6/11*q - 2/11*q**4 = 0. Calculate q.
-2, -1, 1
Factor l**2 + 3/4 + 13/4*l.
(l + 3)*(4*l + 1)/4
What is j in -2/7*j**3 + 10/7*j - 8/7*j**2 + 0 = 0?
-5, 0, 1
Let r(t) = -24 - 3*t**2 - 9*t - 35 - 3*t**3 + 54. Let m(s) = s**3 - s**2 + s + 1. Let u(v) = 2*m(v) + r(v). Factor u(a).
-(a + 1)**2*(a + 3)
Factor -2/3*f - 4/9 - 2/9*f**2.
-2*(f + 1)*(f + 2)/9
Let v(w) be the second derivative of w**7/56 - 3*w**6/20 - 9*w**5/10 - 13*w**4/8 - 9*w**3/8 + 51*w - 2. Find a, given that v(a) = 0.
-1, 0, 9
Let r be (-3 - 7) + 5 - (0 + -8). Let l(j) be the first derivative of 0*j**r + 2/5*j**5 + 0*j + 1/2*j**4 + 0*j**2 - 4. Factor l(f).
2*f**3*(f + 1)
Let n(a) be the third derivative of a**7/945 - a**6/60 + a**5/90 + 37*a**4/108 + 8*a**3/9 - 231*a**2. Factor n(x).
2*(x - 8)*(x - 3)*(x + 1)**2/9
Let h = 1500 + -1497. Let x(o) be the third derivative of -1/18*o**h + 1/36*o**4 + 1/60*o**5 + 0*o + 3*o**2 + 0. Factor x(d).
(d + 1)*(3*d - 1)/3
Let t(p) be the second derivative of p**8/336 + p**7/168 + p**3/3 + p. Let o(g) be the second derivative of t(g). Suppose o(c) = 0. What is c?
-1, 0
Let n = 12 - 9. Let w be 4*n/16*4. What is j in 3*j**2 + 5 - w - 2 = 0?
0
Let p(t) be the first derivative of t**6/300 + t**5/200 - t**4/24 + t**3/20 - 15*t + 11. Let z(j) be the first derivative of p(j). Solve z(l) = 0 for l.
-3, 0, 1
Let m = -59 + 62. Suppose 12 = 3*v + m*z, v - z = 4*z + 4. Determine d, given that -4/3*d**3 - 1/3*d**v - 4/3*d**2 + 0 + 0*d = 0.
-2, 0
Let t(v) be the first derivative of v**5/100 - v**4/20 + v**3/10 - v**2/10 - 12*v + 13. Let f(i) be the first derivative of t(i). Solve f(g) = 0 for g.
1
Suppose 43 - 45 = -z. Factor -3*o**z - 2*o**2 - 2*o**2 + 5*o**2 - 32 - 16*o.
-2*(o + 4)**2
Let i = 1/3963 - -7915/43593. Solve 2/11*x**2 - 10/11*x + 6/11 + i*x**3 = 0.
-3, 1
Let l(m) be the second derivative of -2/3*m**3 - 1/2*m**4 - 1/10*m**5 - 4*m - 1/120*m**6 + 0 + 0*m**2. Let j(u) be the second derivative of l(u). Factor j(g).
-3*(g + 2)**2
Let l(a) = -3*a**3 + 7*a**2 + 12*a - 2. Let t(o) = -35*o**3 + 85*o**2 + 145*o - 25. Let q(c) = -25*l(c) + 2*t(c). Determine s so that q(s) = 0.
-1, 0, 2
Let c(o) be the third derivative of o**7/420 - 3*o**6/80 + o**5/15 - 61*o**2. Factor c(k).
k**2*(k - 8)*(k - 1)/2
Let n(b) = 2*b**3 - b**2 - b + 1. Let k(r) = 13*r**3 - 14*r**2 + 13*r - 6. Let y(x) = k(x) - 6*n(x). Factor y(f).
(f - 4)*(f - 3)*(f - 1)
Factor -28*q - 2*q**4 - 174*q + 144 - 2*q**2 - 42*q**2 + 322*q - 22*q**3.
-2*(q - 2)*(q + 1)*(q + 6)**2
Suppose 3*k - 31 = -11*t + 6*t, -2*k = t - 9. Let n(c) be the first derivative of k*c**4 - 4 - 4*c**2 + 2*c - 2/3*c**3. Factor n(g).
2*(g - 1)*(g + 1)*(4*g - 1)
Let b(n) = -17*n**3 + 111*n**2 - 213*n - 68. Let z(t) = t**3 - 2*t**2 - t - 1. Let c(u) = -2*b(u) - 14*z(u). Determine q so that c(q) = 0.
-3/10, 5
Let d(n) be the first derivative of 372/11*n**2 - 3844/11*n**3 + 29791/22*n**4 - 17 - 16/11*n. Let d(f) = 0. Calculate f.
2/31
Let v be (3 + -3)/(-4)*(-2)/12. Determine i, given that 2/9*i**3 + 0*i**2 - 2/9*i + v = 0.
-1, 0, 1
Let c(t) be the second derivative of -t**6/20 + 3*t**5/40 + t**4/8 - t**3/4 + t + 12. Let c(a) = 0. Calculate a.
-1, 0, 1
Let p = 5 - 4. Let r = 2 + p. Suppose v - v**3 - 2*v**r + 2*v = 0. Calculate v.
-1, 0, 1
Let v(u) = 15*u**3 - 50*u**2 + 85*u - 40. Let i = -44 - -49. Let x(w) = 8*w**3 - 25*w**2 + 43*w - 20. Let c(k) = i*x(k) - 3*v(k). Determine r so that c(r) = 0.
1, 2
Let s(a) be the first derivative of a**3/3 - 2*a**2 + 5*a + 41. Let g be s(1). Factor n**g + 1/3 + 1/3*n**3 + n.
(n + 1)**3/3
Factor p + 10*p - p**3 - 52 - 8*p + 7*p**2 - 23 + 2*p.
-(p - 5)**2*(p + 3)
Let d = -19 + 21. Solve 5*a**2 - 7*a**3 - 12*a - 5*a**d - 2*a**3 + 24*a**2 = 0 for a.
0, 2/3, 2
Let r be 7 + ((-895)/150 - 1). Let l(i) be the third derivative of 0 + i**3 + 7*i**2 + 0*i - 1/3*i**4 + r*i**5. What is w in l(w) = 0?
1, 3
Let l(y) be the second derivative of y**6/1080 - y**5/120 - y**4/18 - 7*y**3/2 + 12*y. Let o(d) be the second derivative of l(d). Factor o(c).
(c - 4)*(c + 1)/3
Let 6*v**4 - 4 - 86/3*v**3 + 106/3*v**2 - 26/3*v = 0. Calculate v.
-2/9, 1, 3
Let p(q) = q**3 + 8*q**2 + 10*q - 7. Let x = 38 + -44. Let g be p(x). Find a such that 0 + 2/3*a**4 + 0*a**3 - 1/3*a + 1/3*a**g - 2/3*a**2 = 0.
-1, 0, 1
Let z be (-10)/(-18) + (29 + -27)/2. Factor 4/9*i + 2*i**3 + 0 - z*i**2 - 10/9*i**4 + 2/9*i**5.
2*i*(i - 2)*(i - 1)**3/9
Let b(p) be the second derivative of p**6/6 + p**5/20 - 5*p**4/12 - p**3/6 + 36*p. Solve b(t) = 0.
-1, -1/5, 0, 1
Suppose 144 = -13*f + 85*f. Factor 0 + 3/2*j**f + 0*j**4 - 9/4*j**3 + 3/4*j**5 + 0*j.
3*j**2*(j - 1)**2*(j + 2)/4
Let b(y) be the first derivative of -4*y**3/3 + 38*y**2 + 168*y + 153. Let b(p) = 0. What is p?
-2, 21
Suppose 3*w = 4*w. Suppose 8 = 4*i - n, 5*i - 3*n - 1769 = -1759. Factor 1/3*b**3 + 2/3*b**4 + w*b**i + 1/3*b**5 + 0 + 0*b.
b**3*(b + 1)**2/3
Let x(i) = -2*i**2 - 8*i + 11 + i**2 + 0*i**2 - 16. Let b be x(-7). Let 2/7*t + 0 - 2/7*t**b = 0. What is t?
0, 1
Let s = 4393/2 - 2195. Factor 9/4*k + 0*k**2 - 3/4*k**3 - s.
-3*(k - 1)**2*(k + 2)/4
Let w(p) be the first derivative of 0*p**2 + 0*p**3 + 18 + 0*p + 5/8*p**4. Determine j so that w(j) = 0.
0
Let c(y) = 2*y**2 + 37*y - 77. Let o be c(2). Let u(x) be the first derivative of 0*x**4 + 3*x + 3/5*x**o - 2*x**3 + 10 + 0*x**2. Solve u(a) = 0 for a.
-1, 1
Suppose 57*i - 183 = 45. Determine o so that 6/7*o**3 + 9/7*o**2 - 12/7 - 12/7*o - 3/7*o**i = 0.
-1, 2
Let n(j) be the second derivative of -j**5/4 - 65*j**4/4 - 665*j**3/2 - 1805*j**2/2 + 170*j. Factor n(g).
-5*(g + 1)*(g + 19)**2
Let r = -18 + 28. Suppose -5*y + r = -0*y. Factor -3*z**3 - z**3 + 2*z**5 + y - 5*z**2 + 2*z**4 + 0*z**2 + 2*z + z**2.
2*(z - 1)**2*(z + 1)**3
Let l(c) be the third derivative of -39*c**2 - 8/3*c**3 - 7/12*c**4 + 0*c + 0 + 1/30*c**5. Factor l(a).
2*(a - 8)*(a + 1)
Let k(r) = -r**2 + 14*r - 10. Suppose -4*w = j - 25, 0 = 4*j + w - 9 - 46. Let s be k(j). Factor 3*f**3 - 4*f**2 - 14*f**s - 5*f**3.
-4*f**2*(4*f + 1)
Let j(v) be the first derivative of 2*v**5/5 - 25*v**4/2 + 94*v**3 + 221*v**2 - 676*v + 446. 