et b(i) be the second derivative of d(i). Suppose b(y) = 0. Calculate y.
-1, 0, 1
Let t(a) be the third derivative of -2*a**7/21 + a**6/10 + 2*a**5/15 - 8*a**2. Let t(n) = 0. Calculate n.
-2/5, 0, 1
Let w = -3 + 5. Factor 2*n**4 + 3*n**w - 2*n**4 - n**2 + 2*n**4 - 4*n**3.
2*n**2*(n - 1)**2
Let b = 118051/6 - 19628. Let o = b - 47. Solve 0*g - 1/2*g**5 - 5/6*g**3 - 7/6*g**4 - o*g**2 + 0 = 0.
-1, -1/3, 0
Let w be (-19 + 22)*(-2)/9*-3. Factor 0*u**3 + 2/7*u**4 + 0 - 2/7*u**w + 0*u.
2*u**2*(u - 1)*(u + 1)/7
Suppose 0 = -48*a + 43*a + 20. Let o(b) be the first derivative of -2 + 1/20*b**5 + 1/16*b**a - 1/8*b**2 + 0*b - 1/12*b**3. Factor o(d).
d*(d - 1)*(d + 1)**2/4
Suppose 0 = -7*y - 16 + 51. Suppose -f = y*w - 14, -w - 1 = -2*f + 5. Factor -4/3 + 2/3*d**w - 2/3*d.
2*(d - 2)*(d + 1)/3
Factor -215/3*b**2 - 14/3*b**4 - 500/3 - 241/6*b**3 + 850/3*b - 1/6*b**5.
-(b - 1)**2*(b + 10)**3/6
Factor -1/4*y**3 + 0*y - 1/2*y**4 + 1/4*y**2 + 0.
-y**2*(y + 1)*(2*y - 1)/4
Let z = 105/4 - 24. Factor -5/4*s**3 + z*s**2 - 7/4*s + 1/2 + 1/4*s**4.
(s - 2)*(s - 1)**3/4
Let n(c) be the third derivative of c**8/2520 + c**7/378 + c**6/180 + c**5/270 + 5*c**3/6 - 3*c**2. Let t(w) be the first derivative of n(w). Solve t(q) = 0.
-2, -1, -1/3, 0
Let h = -10 + 12. Suppose h*m - l = l + 8, 8 = 2*m + 5*l. Let 0 + 2*i**2 + 2 + m*i - 8*i = 0. What is i?
1
Let d(i) be the second derivative of -i**5/10 - i**4/2 - i**3 - i**2 - 4*i. Find u such that d(u) = 0.
-1
Let q(y) be the second derivative of -5*y**4/12 - 5*y**3/2 + 10*y**2 - 4*y. Factor q(b).
-5*(b - 1)*(b + 4)
Suppose 5*k = -0*k - 35. Let n = 13 + k. Factor 0*y**4 - y**5 + 4*y**4 + 3*y**2 - n*y**3 - y + y**2.
-y*(y - 1)**4
Let q(w) be the second derivative of w**4/16 + 3*w**3/4 + 27*w**2/8 + 5*w. Find o, given that q(o) = 0.
-3
Let l = 32 + -30. Factor 3*c + 3/2*c**l + 3/2.
3*(c + 1)**2/2
Let c(y) = y**3 - 13*y**2 + 13*y - 10. Let f be c(12). What is t in -23*t**2 + t + 5*t + 10*t**3 - 2*t + 9*t**f = 0?
0, 2/5, 1
Let u = -2 + 2. Suppose p + 1 = -2*r - 2, -5*p - r + 12 = u. Solve 5*l**p - l**4 - 3*l**3 - l**2 - 4*l**3 = 0.
-1, 0
Let h(b) = 2*b**5 - 9*b**4 + 7*b**3 - 5*b**2. Let r(s) = s**5 - 5*s**4 + 4*s**3 - 3*s**2. Let a(m) = 6*h(m) - 10*r(m). Factor a(g).
2*g**3*(g - 1)**2
Let c(i) be the third derivative of i**7/1260 + i**6/270 + i**5/180 + i**3 - 6*i**2. Let z(s) be the first derivative of c(s). Factor z(d).
2*d*(d + 1)**2/3
Let x(j) be the second derivative of -j**4/4 + j**3 - 3*j**2/2 - 5*j. Factor x(l).
-3*(l - 1)**2
Suppose w + 2*j = 13, -3*w + 0*j - j = -19. Let d = w + 1. Factor -2*v**2 + d*v - 4 - 4 - 3 + 7.
-2*(v - 2)*(v - 1)
Let q(p) be the first derivative of -p**6/300 + p**5/150 + p**4/60 - p**3/15 - 2*p**2 + 1. Let u(b) be the second derivative of q(b). Solve u(x) = 0.
-1, 1
Factor -502*s**3 - 11*s + 69*s**2 - 7*s + 436*s**3 + 15*s**4.
3*s*(s - 3)*(s - 1)*(5*s - 2)
Let t(v) be the first derivative of 5*v**6/6 - v**5 - 5*v**4/2 + 10*v**3/3 + 5*v**2/2 - 5*v + 13. Suppose t(d) = 0. Calculate d.
-1, 1
Let s(g) = -2*g**2 + 11*g + 3. Let a(v) = 4*v**2 - 23*v - 7. Let p(b) = 3*a(b) + 7*s(b). Let p(x) = 0. Calculate x.
0, 4
Let m(u) be the second derivative of u**5/30 + u**4/18 - u**3/9 - u**2/3 - 4*u. Factor m(j).
2*(j - 1)*(j + 1)**2/3
Let q(g) = -g**2 + g + 6. Let p be q(3). Let y be (-5)/(-6) + (-4)/12. Factor 1/4*n + 1/4*n**2 - y*n**3 + p.
-n*(n - 1)*(2*n + 1)/4
Let n(c) = -98*c**2 - 43*c + 5. Let f(s) = 49*s**2 + 22*s - 2. Let y = -6 + 7. Suppose -23 = -4*p + y. Let m(v) = p*n(v) + 13*f(v). Solve m(z) = 0 for z.
-2/7
Let w = -17/6 - -10/3. Determine z so that -z**2 + 0 + w*z + 1/2*z**3 = 0.
0, 1
Let l(b) = 2*b**3 + 2*b**2 - 8*b. Let j(u) = 10*u**3 + 9*u**2 - 41*u. Let y(n) = -4*j(n) + 22*l(n). Suppose y(c) = 0. What is c?
-3, 0, 1
Let a = 5 + 4. Let r = 20 - a. Factor r*p**2 + 81*p**3 + 9*p**5 + 6*p + 28*p**2 + 12*p**5 + 69*p**4.
3*p*(p + 1)**3*(7*p + 2)
Find m such that 1/3*m**2 + 2/3*m + 0 = 0.
-2, 0
Suppose 0*q - 66 = -22*q. Determine t so that 0 + 2/5*t**2 - 2/5*t**q + 4/5*t = 0.
-1, 0, 2
Determine k so that 6/7*k**3 + 6/7*k**4 - 18/7*k**2 - 6/7*k + 12/7 = 0.
-2, -1, 1
Let o(z) = z**3 + z + 5. Let s be -2*1 + 2 + 0. Let j be o(s). Determine k so that -2*k**3 - 3*k**5 - 3*k**4 + 0*k**j + 2*k**5 = 0.
-2, -1, 0
Let w = 10258/6405 + -2/1281. Let 2/5*c**5 - 8/5*c**2 + 12/5*c**3 - w*c**4 + 2/5*c + 0 = 0. Calculate c.
0, 1
Let w(d) be the second derivative of -1/10*d**6 - 3/20*d**5 + 8*d + 1/2*d**3 + 0 + 1/4*d**4 + 0*d**2. Suppose w(b) = 0. What is b?
-1, 0, 1
Let m(j) be the first derivative of 2*j**2 + 2/3*j**3 + 4 + 2*j. Factor m(d).
2*(d + 1)**2
Let c(b) = b**3 + 5*b**2 - 28*b + 19. Let u(p) = 2*p**3 + 6*p**2 - 28*p + 18. Let s(r) = -2*c(r) + 3*u(r). Let s(v) = 0. What is v?
-4, 1
Let l = -5 + 7. Let c(d) be the first derivative of 2 + 8*d**l - 7/3*d**3 - 4*d. Solve c(q) = 0 for q.
2/7, 2
Let o = 251/3870 - 2/215. Let f(q) be the third derivative of 4/9*q**3 + 1/180*q**6 - 2*q**2 + 0 + o*q**5 + 2/9*q**4 + 0*q. Factor f(n).
2*(n + 1)*(n + 2)**2/3
Let h be (-6)/(-3) - 0/3. Let j(i) be the first derivative of -3*i**2 + 4*i + h + 2/3*i**3. Factor j(b).
2*(b - 2)*(b - 1)
Let w(y) be the first derivative of y**5/35 - 3*y**4/14 + 3*y**3/7 - 2*y**2/7 - 30. Factor w(m).
m*(m - 4)*(m - 1)**2/7
Let w(k) = k**2 + 3*k + 9. Let d be w(-4). Let i = d - 11. Factor 0 - 1/3*t**i + 0*t + 5/3*t**4 + 1/3*t**3 + t**5.
t**2*(t + 1)**2*(3*t - 1)/3
Let o(w) be the first derivative of -w**6/2700 - w**5/450 - w**4/180 - w**3 + 7. Let j(a) be the third derivative of o(a). Factor j(t).
-2*(t + 1)**2/15
Let 2/15 + 2/15*c**2 + 4/15*c = 0. What is c?
-1
Suppose -8*k = -7*k + 56. Let x be k/105*(-6)/8. Find m such that 2/5*m**3 - 3/5*m**4 - 1/5 + 4/5*m**2 - x*m = 0.
-1, -1/3, 1
Let g(v) = -4*v**2 - 16*v. Let q be g(-4). Factor -1/7 + 1/7*n**2 + q*n.
(n - 1)*(n + 1)/7
Let h(f) be the first derivative of -4*f**5/45 + 16*f**4/9 - 40*f**3/3 + 400*f**2/9 - 500*f/9 + 2. Factor h(j).
-4*(j - 5)**3*(j - 1)/9
Let p(b) be the first derivative of -b**3 - 1. Solve p(a) = 0.
0
Let y be (3/(-6))/((-3)/18). Let b = y - 1. Suppose 4*q**2 - q - 2*q**b - q**2 = 0. Calculate q.
0, 1
Factor -3/2*d - 1/2*d**2 + 2.
-(d - 1)*(d + 4)/2
Let h(b) be the third derivative of -3/32*b**4 - 1/12*b**3 - 4*b**2 - 1/20*b**5 - 1/96*b**6 + 0 + 0*b. Solve h(n) = 0 for n.
-1, -2/5
Find k, given that 8/13*k**3 - 20/13*k + 6/13*k**2 - 16/13 - 2/13*k**4 = 0.
-1, 2, 4
Let i(z) = 4*z**3 + 12*z**2 + 30*z + 22. Let v(n) = 9*n**3 + 23*n**2 + 59*n + 43. Let d(f) = 10*i(f) - 4*v(f). Find m, given that d(m) = 0.
-3, -2
Let o(y) be the third derivative of -y**6/30 - 2*y**5/15 + y**4/6 + 4*y**3/3 + 2*y**2. Factor o(k).
-4*(k - 1)*(k + 1)*(k + 2)
Suppose -8*h + 13*h = 0. Suppose -u - 4*u + 20 = h. Factor -3/4*f**3 - 1/2*f**2 + 0*f - 7/4*f**5 + 3*f**u + 0.
-f**2*(f - 1)**2*(7*f + 2)/4
Let v(n) = n**2 + 5*n - 10. Let s be v(-7). Factor 2*c**2 + 4*c + s - c + 3*c.
2*(c + 1)*(c + 2)
Suppose 5*t + 12 = 5*k + 4*t, 4*k - 18 = -2*t. Let m(c) = -c**3 + 9*c**2 - 10*c + 18. Let q be m(8). Factor -1/4*h**4 + 3/4*h - 1/4*h**q - 3/4*h**k + 1/2.
-(h - 1)*(h + 1)**2*(h + 2)/4
Let i be 1 + 2/16*-6. Determine r, given that -3/4*r**2 + i*r**3 + 0 + 1/2*r = 0.
0, 1, 2
Let f(x) be the second derivative of -x**5/110 + x**4/66 + 9*x. Determine c so that f(c) = 0.
0, 1
Let n(f) be the second derivative of -f**7/252 + f**6/90 - f**4/36 + f**3/36 - 6*f. Factor n(v).
-v*(v - 1)**3*(v + 1)/6
Let 0 - 1/5*l**5 + 0*l + 3/5*l**2 + 1/5*l**3 - 3/5*l**4 = 0. What is l?
-3, -1, 0, 1
Let n be 567/105 + (-4)/10. Let g(x) = -2*x**2 + 11*x - 3. Let j be g(n). Suppose -3/4*b**j - 3/4*b + 0 = 0. Calculate b.
-1, 0
Let t(l) be the second derivative of 16*l**6/135 - 44*l**5/45 + 59*l**4/18 - 154*l**3/27 + 49*l**2/9 - 24*l. Solve t(w) = 0 for w.
1, 7/4
Let l(p) be the first derivative of 0*p - 4/3*p**3 + 3 + 1/360*p**6 + 0*p**2 + 0*p**4 + 1/60*p**5. Let m(b) be the third derivative of l(b). Factor m(h).
h*(h + 2)
Suppose -3*c + 1 + 8 = 0. Let z(n) be the second derivative of 1/5*n**6 - n - 1/5*n**5 - n**2 + n**c - 1/21*n**7 + 0 - 1/3*n**4. Suppose z(y) = 0. What is y?
-1, 1
Let v(j) = -2*j**4 - 2*j**3 - 32*j**2 + 12*j + 12. Let f(a) = -a**4 - a**3 - 13*a**2 + 5*a + 5. Let u(m) = -12*f(m) + 5*v(m). Factor u(i).
2*i**2*(i - 1)*(i + 2)