 + 17*l**5/60 + l**4/36 - 5*l**3/18 + l**2/6 - l. Let b(m) = 0. What is m?
-1/2, 1/4, 1
Let w = 1 - -2. Find i such that 0*i**3 + i**w + i**4 - 2*i**3 = 0.
0, 1
Let x(t) be the third derivative of -t**8/1120 - t**7/140 - t**6/60 - t**3/2 + t**2. Let o(s) be the first derivative of x(s). Factor o(c).
-3*c**2*(c + 2)**2/2
Suppose 2*k = 7*k - 15. Let m(n) = n**2 + n - 1. Let q(b) = 5*b**2 + 3*b - 5. Let r(j) = k*m(j) - q(j). Factor r(c).
-2*(c - 1)*(c + 1)
Let k(g) be the first derivative of -g**4 - 4*g**3/3 + 32*g**2 - 80*g + 35. Factor k(q).
-4*(q - 2)**2*(q + 5)
Let g(v) be the first derivative of v**6/240 - v**5/120 - v**4/48 + v**3/12 + v**2/2 + 3. Let d(y) be the second derivative of g(y). Solve d(i) = 0.
-1, 1
Let q(k) be the first derivative of k**8/1176 - k**7/735 - k**6/420 + k**5/210 + 3*k**2/2 + 1. Let c(b) be the second derivative of q(b). Factor c(s).
2*s**2*(s - 1)**2*(s + 1)/7
Suppose -3 = 3*p - 5*b - 18, -5*p + 12 = -4*b. Suppose p = 7*t - 6*t. Solve 0*n**2 - 2/9*n + 2/9*n**3 + t = 0 for n.
-1, 0, 1
Let p(x) be the second derivative of -x**5/120 - x**4/36 - x**3/36 + 4*x. Factor p(t).
-t*(t + 1)**2/6
Let d(w) be the first derivative of -w**3/3 - 8*w**2 - 15*w - 48. Determine j, given that d(j) = 0.
-15, -1
Let x(o) be the third derivative of o**7/140 + o**6/80 - o**5/40 - o**4/16 - 3*o**2. Solve x(a) = 0 for a.
-1, 0, 1
Let s(r) be the second derivative of -r**4/18 + 2*r**3/3 - 3*r**2 - 8*r. Factor s(j).
-2*(j - 3)**2/3
Let r(s) be the third derivative of -s**7/1470 - s**6/105 - s**5/28 + s**4/21 + 8*s**3/21 + 5*s**2. Solve r(k) = 0 for k.
-4, -1, 1
Suppose -2*w + 0 = -12. Let -4*b + 6*b**3 + 2*b**3 + 2*b**2 - 2*b**4 - w*b**5 + 0*b + 2*b**3 = 0. Calculate b.
-1, 0, 2/3, 1
Factor -2/3*u**2 - 2/3 - 5/3*u.
-(u + 2)*(2*u + 1)/3
Let t = 3/665 + 163/5985. Let s(x) be the second derivative of 0*x**2 - t*x**7 + 0 - 1/60*x**5 + 0*x**3 + 1/18*x**6 + x + 0*x**4. What is i in s(i) = 0?
0, 1/4, 1
Let g(n) be the third derivative of n**9/241920 + n**8/40320 + n**7/20160 - n**5/15 + n**2. Let f(i) be the third derivative of g(i). Factor f(b).
b*(b + 1)**2/4
Suppose 0 = 2*u + 5*p - 21, 2*p - 1 = -u + 8. Solve -18/7*o**2 - 54/7 - 2/7*o**u - 54/7*o = 0 for o.
-3
Suppose 13 = 3*u - 0*f - 2*f, 0 = 4*u - 5*f - 29. Determine j, given that 0 + j + j**5 + 10*j**3 - 10*j**2 - 5*j**4 - u + 4*j = 0.
1
Let b = -9 + 9. Let l(f) be the second derivative of 0*f**2 + 2*f + 1/100*f**5 + b*f**3 + 0 + 1/60*f**4. Solve l(k) = 0 for k.
-1, 0
Let w(f) be the second derivative of -f**5/70 - f**4/42 - 5*f. Factor w(u).
-2*u**2*(u + 1)/7
Let c(v) be the third derivative of -v**5/60 - v**4/12 + 3*v**2. Factor c(k).
-k*(k + 2)
What is m in 36/5*m + 3/5*m**4 + 48/5*m**2 + 21/5*m**3 + 0 = 0?
-3, -2, 0
Let m(d) be the second derivative of d**6/16 + 39*d**5/160 + d**4/8 - d**3/4 + 38*d. Solve m(y) = 0.
-2, -1, 0, 2/5
Let h(p) = 10*p**5 - 55*p**4 + 145*p**3 - 100*p. Let o(l) = l**5 - 6*l**4 + 16*l**3 - 11*l. Let w(c) = -6*h(c) + 55*o(c). Suppose w(v) = 0. Calculate v.
-1, 0, 1
Let t(n) = -2*n**2 - 7*n + 5. Let j be (1 + 1)*5/(-2). Let z(a) = -3*a**2 - 11*a + 8. Let m(d) = j*z(d) + 8*t(d). Determine o so that m(o) = 0.
-1, 0
Let k(u) be the second derivative of 0*u**2 + 1/36*u**4 + 1/90*u**6 + 0 + 0*u**3 + 1/30*u**5 + 3*u. Determine n, given that k(n) = 0.
-1, 0
Suppose 4*s - 2*s - 8 = 0. Let d(j) = 2*j + 1. Let u be d(1). Factor 2/7 - 2/7*n**s - 4/7*n + 4/7*n**u + 0*n**2.
-2*(n - 1)**3*(n + 1)/7
Let a = 8 - 4. Let g(d) = 8*d**3 - 6*d**2 + 2. Let n(c) = -c**3. Let h(i) = a*n(i) + g(i). Factor h(x).
2*(x - 1)**2*(2*x + 1)
Let p(g) be the second derivative of -1/28*g**4 + 5*g + 1/14*g**3 + 0 + 0*g**2. Suppose p(r) = 0. Calculate r.
0, 1
Let -2/15*u**4 + 8/15 + 8/15*u - 2/5*u**2 - 8/15*u**3 = 0. Calculate u.
-2, -1, 1
Find q, given that 2/11*q**3 + 2/11*q + 4/11*q**2 + 0 = 0.
-1, 0
Suppose 4*l + 294 = l. Let u = -488/5 - l. Determine y so that 2/5 - 6/5*y + 6/5*y**2 - u*y**3 = 0.
1
Let f(x) be the third derivative of x**8/84 - x**7/210 - x**6/10 - x**5/12 + x**4/12 - 72*x**2. Factor f(n).
n*(n - 2)*(n + 1)**2*(4*n - 1)
Factor 3*g**3 - 3*g + 23 - 17 + 3*g**2 - 9.
3*(g - 1)*(g + 1)**2
Let a(q) be the third derivative of q**5/105 + q**4/7 + 6*q**3/7 - 4*q**2. Suppose a(c) = 0. What is c?
-3
Factor -5/3*d - 2/3 - d**2.
-(d + 1)*(3*d + 2)/3
Let i be (-1)/2*-2*3. Let j be ((-8)/50)/(10/(-50)). Let -2/5*m**5 + 0*m**2 + j*m**4 - 2/5*m**i + 0*m + 0 = 0. Calculate m.
0, 1
Suppose -s - 4*j + 24 = 0, 41 + 7 = 4*s + 4*j. Factor n - 4 - 12*n**2 - 19*n + 6*n**2 + s*n**3.
2*(n - 2)*(n + 1)*(4*n + 1)
Determine o so that 0 + 6*o + 3/4*o**2 = 0.
-8, 0
Let l(i) be the second derivative of 3*i**5/130 + i**4/78 - i**3/13 - i**2/13 - 5*i. Suppose l(m) = 0. What is m?
-1, -1/3, 1
Let j(k) be the third derivative of 2*k**7/105 - 2*k**6/15 + 2*k**5/5 - 2*k**4/3 + 2*k**3/3 - 4*k**2. Factor j(u).
4*(u - 1)**4
Let w(q) be the third derivative of -q**7/70 - q**6/40 + q**5/10 + 56*q**2. Factor w(c).
-3*c**2*(c - 1)*(c + 2)
Let y(q) be the third derivative of -q**7/210 + q**6/20 - 13*q**5/60 + q**4/2 - 2*q**3/3 + 8*q**2. Factor y(i).
-(i - 2)**2*(i - 1)**2
Let t(a) = -4*a + 43. Let q be t(10). Factor -8/5*d - 1/5*d**q - 4/5 - d**2.
-(d + 1)*(d + 2)**2/5
Let r(i) be the first derivative of i**3/21 - 4*i/7 + 42. Factor r(t).
(t - 2)*(t + 2)/7
Let t(d) be the first derivative of 2*d**4 + 2*d + 4*d**3 + 4*d**2 - 2 + 2/5*d**5. Factor t(o).
2*(o + 1)**4
Suppose 0 = 2*d + 4*z + 13 - 1, -5*z - 37 = -3*d. Solve 4*i**3 + 2*i**d - 3*i + 2*i**2 + 3*i + 0*i**4 = 0 for i.
-1, 0
Let g = 63 + -57. Let o(y) be the third derivative of -1/45*y**5 - 1/180*y**g - y**2 + 0*y - 1/36*y**4 + 0 + 0*y**3. Factor o(z).
-2*z*(z + 1)**2/3
Suppose 5*a - 5*d = 0, 6 = 2*a + 3*d - 2*d. Solve 19/5*b**3 + 1/5*b**5 + 4/5 + 7/5*b**4 + 16/5*b + 5*b**a = 0 for b.
-2, -1
Let t = -8/29 + 173/522. Let q(c) be the second derivative of 0*c**3 + 0*c**2 + 0*c**5 + 1/45*c**6 - 3*c - t*c**4 + 0. Suppose q(k) = 0. What is k?
-1, 0, 1
Let x(o) = o**3 + o**2 - o + 2. Let b be x(0). Factor 2*v**3 + 4*v**3 - b*v - 2*v**5 - 2*v**3.
-2*v*(v - 1)**2*(v + 1)**2
Suppose a = -3*a + 8. Factor 6 - 13*n**3 - 24*n**a - 19*n**3 - 2 - 2.
-2*(2*n + 1)**2*(4*n - 1)
Let r(n) be the second derivative of n**5/50 - n**4/15 - 7*n**3/15 - 4*n**2/5 + 12*n. Find z, given that r(z) = 0.
-1, 4
Factor -16/3 + 8/3*f**2 + 0*f + 0*f**3 - 1/3*f**4.
-(f - 2)**2*(f + 2)**2/3
Let b = 616 - 1229/2. Suppose b - 3/4*m - 3/2*m**2 + 3/4*m**3 = 0. Calculate m.
-1, 1, 2
Suppose 1 = -2*u + 11. Suppose -2*x - 35 = -u*g, 4*x + 28 = 3*g - 7. Factor 0*y - 1/5*y**2 + 1/5*y**4 - 1/5*y**3 + 1/5*y**g + 0.
y**2*(y - 1)*(y + 1)**2/5
Let u(l) be the third derivative of l**10/252000 - l**9/50400 + l**8/33600 - l**5/15 - 2*l**2. Let d(t) be the third derivative of u(t). Solve d(r) = 0.
0, 1
Let y(o) = o**3 - 6*o**2 + 3*o + 5. Let p be y(5). Let b(q) = 4*q**2 - 7*q + 4. Let h(z) = -5*z**2 + 8*z - 5. Let k(w) = p*h(w) - 6*b(w). Solve k(l) = 0.
-1
Let c(q) be the first derivative of q**7/105 - q**5/15 + q**3/3 + 3*q**2/2 + 1. Let u(m) be the second derivative of c(m). Let u(b) = 0. What is b?
-1, 1
Let s(o) be the first derivative of 2*o**3/3 - 13*o**2/2 - 9*o - 2. Let b(x) = x**2 - 6*x - 4. Let k(g) = 9*b(g) - 4*s(g). Find u such that k(u) = 0.
0, 2
Factor 11*p - 2 - 24*p + 6*p**2 + 17*p - 8*p**3 - 8*p**4.
-2*(p + 1)**2*(2*p - 1)**2
Let n(k) = -k**5 - k**4 + 4*k**3 - 2*k**2 - 3. Let b(g) = g**3 - g**2 - 1. Let r be 4 - 4/2 - 14. Let f be 4*(-3)/r*2. Let q(u) = f*n(u) - 6*b(u). Factor q(o).
-2*o**2*(o - 1)*(o + 1)**2
Let j(z) = z + 0*z**2 + 2*z**2 + 0*z**2 - 1 - 3*z**2. Let q(p) = -2*p**2 + 5*p - 2. Let u(x) = -6*j(x) + 2*q(x). What is y in u(y) = 0?
-1
Find d such that -2/11*d**3 + 0*d**2 + 12/11 + 14/11*d = 0.
-2, -1, 3
Let y(i) be the third derivative of 0 - 7*i**2 + 0*i - 1/70*i**7 + 1/20*i**5 + 0*i**3 + 0*i**4 + 1/112*i**8 - 1/40*i**6. Factor y(q).
3*q**2*(q - 1)**2*(q + 1)
Let q = 15 - 8. Let g(n) be the third derivative of 1/48*n**4 + 0 + 1/40*n**5 + 1/80*n**6 + 0*n + 3*n**2 + 0*n**3 + 1/420*n**q. Solve g(t) = 0.
-1, 0
Factor 7*j**2 - 1 - 6*j**2 - j + j**3 + 0*j**2.
(j - 1)*(j + 1)**2
Factor -6/5 + 6/5*j**2 - 2/5*j**3 + 2/5*j.
-2*(j - 3)*(j - 1)*(j + 1)/5
Let c(s) = -4*s**3 + 2*s**2 + 10*s - 16. Let x(w) = 1