e (1 - 1)/(3 - 5). Let i(a) be the second derivative of 0*a**3 + 1/18*a**4 + 0*a**2 + 0 + h*a**5 + a - 1/45*a**6. Let i(t) = 0. Calculate t.
-1, 0, 1
Let k be (-16)/(-64)*(-2)/(-2). Let w(c) be the third derivative of -3/20*c**5 + 2*c**2 + 0 + 0*c - 1/6*c**3 - k*c**4. Suppose w(f) = 0. What is f?
-1/3
Let i(d) be the third derivative of d**9/42336 - d**8/35280 + d**5/30 - 3*d**2. Let c(j) be the third derivative of i(j). Factor c(w).
2*w**2*(5*w - 2)/7
Suppose -l - 4 = -6. Let 4*d**3 + 27*d - 26*d**3 - 2*d**3 - l*d**2 - 3*d - 8*d**4 - 8 = 0. Calculate d.
-2, 1/2
Solve 4*y**2 - 12*y**4 + 0*y**5 + 3*y**5 + 5*y**5 = 0.
-1/2, 0, 1
Let r be (608/72 + -8)*(0 + 6). Let 2*j**2 - r - 7/3*j**4 + 28/3*j - 19/3*j**3 = 0. What is j?
-2, 2/7, 1
Let c(d) be the second derivative of d**6/40 + d**5/10 - d**4/8 - d**3 - d**2/2 + 5*d. Let y(b) be the first derivative of c(b). Find n, given that y(n) = 0.
-2, -1, 1
Let q(o) be the third derivative of -o**6/30 - 4*o**5/15 - 2*o**4/3 - 7*o**2. Let q(g) = 0. Calculate g.
-2, 0
Let z(b) be the first derivative of 2*b**3/9 - b**2/3 + 6. Factor z(m).
2*m*(m - 1)/3
Let d(l) be the first derivative of l**4/16 - l**2/8 + 5. Suppose d(h) = 0. What is h?
-1, 0, 1
Let l(z) be the first derivative of 0*z + 0*z**2 - 1/3*z**6 - 2/5*z**5 + 2/3*z**3 + 1/2*z**4 - 2. Factor l(p).
-2*p**2*(p - 1)*(p + 1)**2
Let h(w) be the second derivative of -2*w**6/15 - 3*w**5/5 - 2*w**4/3 + w. Factor h(d).
-4*d**2*(d + 1)*(d + 2)
Let b(k) = k**2 + 2. Let p = 10 - 7. Let m(l) = -8 - l**2 - 3*l**2 - p. Let d(r) = -11*b(r) - 2*m(r). Factor d(w).
-3*w**2
Let a = -2/31 - -41/155. Let c = -2 - -4. Find i such that 0*i - a*i**c + 0 = 0.
0
Let l(h) be the third derivative of -h**5/390 - 3*h**4/52 - 14*h**3/39 - h**2 - 12. Factor l(d).
-2*(d + 2)*(d + 7)/13
Suppose 2*u - 11 - 9 = 0. Let n = u - 5. Suppose -n*g**3 + 4*g**5 + 5*g**4 - 6*g**5 - g**2 + g + 2*g**3 = 0. Calculate g.
-1/2, 0, 1
Let a(r) = -9*r**4 + 24*r**2 - 27*r + 7. Let i(v) = 4*v**4 - 12*v**2 + 14*v - 4. Let j(k) = 2*a(k) + 5*i(k). Let j(n) = 0. Calculate n.
-3, 1
Let 0*v**2 + 0 + 0*v + 4/7*v**4 - 4/7*v**3 = 0. What is v?
0, 1
Let g(i) be the second derivative of -1/36*i**4 + 0*i**2 + 0*i**3 - 3*i - 1/60*i**5 + 0. Factor g(f).
-f**2*(f + 1)/3
Suppose 3*s - 5*s = n - 1, -5*s = -2*n - 16. Suppose -7 = -3*b + s. Factor 0 - 1/2*a**5 - 1/2*a + 2*a**2 + 2*a**4 - 3*a**b.
-a*(a - 1)**4/2
Let m(h) be the second derivative of 35*h**4/12 + 15*h**3/2 + 5*h**2 + 21*h. Factor m(j).
5*(j + 1)*(7*j + 2)
Let t = 73 - 217/3. Factor 0 - 2/9*h - 8/9*h**2 - t*h**3.
-2*h*(h + 1)*(3*h + 1)/9
Let n(k) be the first derivative of -1/10*k**5 - 4 + 2/3*k**3 - 1/2*k**4 + 0*k + 0*k**2 - 1/120*k**6. Let z(t) be the third derivative of n(t). Factor z(s).
-3*(s + 2)**2
Suppose 2/7*w**4 + 0 + 0*w + 10/7*w**2 + 12/7*w**3 = 0. What is w?
-5, -1, 0
Suppose -2*a + 7*a = 5*q + 5, 0 = 4*a + q - 19. Let z(b) be the first derivative of -a*b + 14/3*b**3 + 1 + 5*b**2. Solve z(t) = 0 for t.
-1, 2/7
What is z in -1/5*z**4 + 0 - 3/5*z**2 - 1/5*z - 3/5*z**3 = 0?
-1, 0
Factor -3/5*h**2 + 0*h + 0 - 1/5*h**3.
-h**2*(h + 3)/5
Let p(z) be the first derivative of z**6/14 - 6*z**5/35 - 9*z**4/28 + 4*z**3/7 + 6*z**2/7 + 38. Factor p(n).
3*n*(n - 2)**2*(n + 1)**2/7
Suppose -3*h - 13 = -2*i, -3*i + 20 = -4*h + 2. Suppose 7*d**2 - d**3 - 3*d**3 - 6*d**i = 0. What is d?
0, 1/4
Find h such that 0 + 17/9*h**2 + 2/9*h = 0.
-2/17, 0
Let p = -76 - -79. Let h(q) be the second derivative of -1/24*q**4 + 1/60*q**6 + 1/20*q**5 + 2*q - 1/6*q**p + 0*q**2 + 0. What is n in h(n) = 0?
-2, -1, 0, 1
Find l, given that -12 + 11*l + 14*l**2 - 3*l - 10*l**2 = 0.
-3, 1
Let x(s) = 8*s**2 + 3*s - 2. Let h be (-12)/3 + 1 - 1. Let v(d) = 9*d**2 + 3*d - 2. Let m(j) = h*x(j) + 3*v(j). Suppose m(p) = 0. Calculate p.
-1, 2/5
Let a = 8297/21 + -395. Let l(d) be the first derivative of -a*d**3 + 2 - 1/14*d**4 + 0*d**2 + 0*d. Factor l(h).
-2*h**2*(h + 1)/7
Factor -49/2*g**3 + 22/3*g + 7/3*g**2 + 4/3.
-(3*g - 2)*(7*g + 2)**2/6
Let t(p) be the third derivative of -p**6/420 + p**5/70 - p**4/42 - 13*p**2. Let t(c) = 0. Calculate c.
0, 1, 2
Let m(p) be the third derivative of -p**6/40 - p**5/5 - 3*p**4/8 - 7*p**2. Factor m(u).
-3*u*(u + 1)*(u + 3)
Let x be ((-3)/6 + 0)*36/(-6). Suppose g + 7 = -2*k, 0 = -g - 4*k - 3 - 12. Solve g + 1 + 2*o**3 - 2*o**2 - o + x*o**3 - 4*o**3 = 0 for o.
-1, 1, 2
Let p(u) be the third derivative of u**5/48 + u**4/48 - u**3/8 + 8*u**2. Factor p(d).
(d + 1)*(5*d - 3)/4
Let a = 1282/9 - 142. Let y(m) be the first derivative of 2/9*m**4 + a*m - 7/9*m**2 - 10/27*m**3 - 3. Let y(u) = 0. What is u?
-1, 1/4, 2
Let v(d) be the second derivative of d**4/4 + d**3 + 3*d**2/2 - 5*d. Factor v(c).
3*(c + 1)**2
Let z(w) be the first derivative of -w**4/16 - w**3/4 - 3*w**2/8 - w/4 + 8. Solve z(p) = 0.
-1
Let -4*x**4 - x**5 - 3*x**3 - 4*x**4 + 5*x**5 + 8*x**2 - x**3 = 0. What is x?
-1, 0, 1, 2
Let z(u) be the third derivative of u**8/6720 + u**7/1680 - u**6/120 - u**5/12 - 5*u**2. Let k(r) be the third derivative of z(r). Suppose k(v) = 0. What is v?
-2, 1
Let f(n) be the first derivative of n**6/9 + 2*n**5/3 + 3*n**4/2 + 14*n**3/9 + 2*n**2/3 - 39. Factor f(y).
2*y*(y + 1)**3*(y + 2)/3
Let b(s) be the third derivative of 0*s + 2*s**2 + 1/600*s**6 + 0 + 1/30*s**3 + 1/100*s**5 + 1/40*s**4. Factor b(w).
(w + 1)**3/5
Suppose 5*b = 2*v + 57 - 20, b = 4*v + 11. Let n = 9 - b. Solve 5*t**n + 8*t + 4*t**2 - 3 + 5 - t**2 = 0.
-1/2
Let c = 37 + -31. Let j(w) be the first derivative of -1/14*w**4 + 0*w**2 + 2 - 2/21*w**3 + 2/35*w**5 + 1/21*w**c + 0*w. Factor j(o).
2*o**2*(o - 1)*(o + 1)**2/7
Suppose 7/3*b**4 + 5/3*b**2 - 5*b**3 + 16/3*b - 1/3*b**5 - 4 = 0. What is b?
-1, 1, 2, 3
Suppose 0*p - 3*t - 9 = 2*p, 9 = p - 3*t. Factor p - 2/11*w**2 + 0*w.
-2*w**2/11
Factor 0 + 8*h + 12/5*h**2 - 4/5*h**3.
-4*h*(h - 5)*(h + 2)/5
Let l(t) be the second derivative of -t**5/5 - 11*t**4/12 - 5*t**3/6 + t**2 - 2*t. Factor l(i).
-(i + 1)*(i + 2)*(4*i - 1)
Let l be (-2)/(-2) - (-2 + 1). Suppose -l = 3*v - 11. Factor -q - 9*q**2 - v*q**3 + 7*q**2 + 2*q**3.
-q*(q + 1)**2
Let o(q) be the first derivative of -9*q**4/28 + 2*q**3/7 - q**2/14 - 1. Factor o(h).
-h*(3*h - 1)**2/7
Suppose n + 8 = 4*p - 3*n, 5*p - n - 18 = 0. Suppose 4 + 6*i**3 - 2*i**p - 6*i + 4*i**2 + 0*i**4 - 6*i**2 = 0. Calculate i.
-1, 1, 2
Let y = -59 - -296/5. Factor y*k**2 + 1/5 - 2/5*k.
(k - 1)**2/5
Let d(k) = k**5 - k**3 - k**2 - k + 1. Let b(n) = -20*n**3 + 8*n + 20*n**3 - 5*n**4 - 8 + 4*n**2 - 9*n**5. Let r(y) = 3*b(y) + 24*d(y). Factor r(h).
-3*h**2*(h + 1)*(h + 2)**2
Factor 0*u**4 + 1/7*u**5 + 1/7*u + 0 + 0*u**2 - 2/7*u**3.
u*(u - 1)**2*(u + 1)**2/7
Let j(t) = t**2 - 3*t - 7. Let y be 46/8 - 3/4. Let p be j(y). Factor 2*i**3 - p*i + i + i - i**5.
-i*(i - 1)**2*(i + 1)**2
Let t(o) be the third derivative of o**5/120 + o**4/4 + 3*o**3 - 5*o**2. Solve t(n) = 0.
-6
Let b(o) be the second derivative of 5*o**4/48 - 5*o**3/24 - 18*o. Determine l so that b(l) = 0.
0, 1
Factor -3 + 6*l**2 + 2*l**2 + 15*l + 10*l**2.
3*(l + 1)*(6*l - 1)
Let k = 94/15 - 25/4. Let m(x) be the second derivative of 0 + 0*x**2 + 1/84*x**7 - k*x**6 - 1/40*x**5 + 1/24*x**4 + 0*x**3 - 2*x. Factor m(y).
y**2*(y - 1)**2*(y + 1)/2
Let p(w) = w**2 - 3*w + 1. Let b be p(3). Suppose -5*t + 11 = b. Factor 2*a**4 + 0 + 2/3*a**5 + 0*a + 2/3*a**2 + t*a**3.
2*a**2*(a + 1)**3/3
Let r(c) be the third derivative of 1/48*c**4 - 3*c**2 + 1/210*c**7 + 0 + 0*c**3 + 0*c**6 + 0*c - 1/60*c**5 - 1/672*c**8. Factor r(l).
-l*(l - 1)**3*(l + 1)/2
Let u = -4 - -4. Let i = -28 - -32. Factor 4/5*b**2 + 0*b - 2/5 - 2/5*b**i + u*b**3.
-2*(b - 1)**2*(b + 1)**2/5
What is q in 24*q**4 + 40*q**2 - 68*q**3 - 64*q**2 + 14*q**2 - 8*q + 54*q**2 = 0?
0, 1/3, 1/2, 2
Determine m, given that 39/2*m + 3/2*m**2 + 0 = 0.
-13, 0
Let w(z) be the third derivative of z**6/24 - z**5/12 - 5*z**4/24 + 5*z**3/6 - 12*z**2. Factor w(t).
5*(t - 1)**2*(t + 1)
Let f = -15 - -20. Let l = -166 + 502/3. Determine r, given that 2/3*r**f - 2/3 + l*r**2 + 2/3*r - 2/3*r**4 - 4/3*r**3 = 0.
-1, 1
Let u = -3 + 8. Determine k so that 3*k**5 + 2*k**3 - 3*k**2 + k**4 - 3*k**4 - 5*k**u + 5*k**2 = 0.
-1, 0, 1
Suppose -5 - 6*k**2 + 3 + 5*k**2 + 3 = 0. What is k?
-1, 1
Let d(w) be the third derivative of -5*w**8/252 + 11*w**7/105 - 19