 0
Suppose -2*c + 7*c = -45. Let d = -4 - c. Determine k so that -41*k**3 + 4 + k**2 + 0*k**4 + 36*k**d - 5*k**4 + 16*k - 11*k**5 = 0.
-1, -2/5, 1
Let z = -34 + 32. Let i be z/7 - 135/(-252). Let 1/4*l**2 + 0*l**3 + 0*l - i*l**4 + 0 = 0. What is l?
-1, 0, 1
Suppose 4*j - 5*l = 14 - 3, 2*j + 4*l - 12 = 0. Let 1/2*n**3 - 1/2*n + 0 + 1/2*n**j - 1/2*n**2 = 0. Calculate n.
-1, 0, 1
Let h(m) be the first derivative of -3/7*m**2 - 1/21*m**3 - 9/7*m - 7. Let h(s) = 0. What is s?
-3
Suppose -3 = m + t, 0 = 12*m - 17*m + 5*t + 35. Suppose -1/4*x**m + 0 + 0*x - x**3 = 0. What is x?
-1/4, 0
Let z(k) be the second derivative of 2/3*k**3 + 5*k + 0*k**2 + 0 - 1/6*k**4 - 1/10*k**5. Factor z(w).
-2*w*(w - 1)*(w + 2)
Let l = 443/3660 - -3/244. Let f(q) be the first derivative of 1/5*q**2 - l*q**3 - 3 + 0*q. Factor f(x).
-2*x*(x - 1)/5
Let c(o) be the third derivative of 1/120*o**6 + 0*o**3 + 0*o + 1/8*o**4 - 8*o**2 - 1/12*o**5 + 1/210*o**7 + 0. Solve c(s) = 0.
-3, 0, 1
Let x be (-2)/24 + (-2)/(-8). Let g(c) be the third derivative of 2*c**2 - x*c**3 + 1/48*c**4 + 1/120*c**5 + 0 + 0*c. Solve g(v) = 0 for v.
-2, 1
Let s(f) be the third derivative of f**6/30 + f**5/5 - 3*f**2. Find l, given that s(l) = 0.
-3, 0
Let r(p) be the first derivative of p**6/10 - 3*p**4/20 + 5. Factor r(g).
3*g**3*(g - 1)*(g + 1)/5
Let t(u) = -u**3 - 7*u**2 - u - 5. Let c be t(-7). Let h = 1 + c. Factor -3*r**h + 2*r**5 - r**2 + 3*r**4 - 3*r**5 + 2*r**2.
-r**2*(r - 1)**3
Let f(o) be the second derivative of o**4/12 + 5*o**3/18 - o**2/3 - 5*o. Factor f(t).
(t + 2)*(3*t - 1)/3
Let s = 2/3 + -11/18. Let t(c) be the second derivative of 0 + s*c**4 + 2*c + 0*c**2 + 1/9*c**3. Let t(h) = 0. What is h?
-1, 0
Let f(t) = t**3 + 12*t**2 + 25*t - 15. Let g be f(-9). Find i such that 1/3*i**g + 0 + 0*i**2 + 0*i + 1/3*i**4 = 0.
-1, 0
Let c(a) be the second derivative of a**4/48 + a**3/8 + a**2/4 - 8*a. Factor c(t).
(t + 1)*(t + 2)/4
Let v = 234/11 - 1082/55. Factor 6/5*t**2 - v + 2/5*t**3 + 0*t.
2*(t - 1)*(t + 2)**2/5
Let f(i) = 16*i**2 - 223*i - 12. Let r be f(14). Suppose 1/3 - 1/6*z**r + 1/6*z = 0. Calculate z.
-1, 2
Let c be (8/50)/(37/130). Let n = -6/37 + c. Suppose -2/5*w**5 + 0*w**3 - 4/5*w**2 + n*w + 4/5*w**4 + 0 = 0. What is w?
-1, 0, 1
Let r(f) be the second derivative of -2*f**6/5 + f**5/10 + f**4/3 + 8*f. Factor r(c).
-2*c**2*(2*c + 1)*(3*c - 2)
Suppose 172*z - 174*z = 0. Suppose z*s - 1/4*s**2 + 1/4 = 0. What is s?
-1, 1
Factor -i**4 - 103*i**2 + 3*i**3 + i**3 + 104*i**2 - 4*i.
-i*(i - 4)*(i - 1)*(i + 1)
Let 4*l**2 - 29 - l**3 + 29 = 0. Calculate l.
0, 4
Factor 8/9*o**4 + 4/9*o**5 - 16/9*o**3 - 32/9*o**2 + 0*o + 0.
4*o**2*(o - 2)*(o + 2)**2/9
Let x(b) be the second derivative of -b**5/16 - 5*b**4/24 + 5*b**3/8 - 12*b. Factor x(g).
-5*g*(g - 1)*(g + 3)/4
Let x(b) = b - 5. Let r be x(7). Solve -4*a**r - a + 4*a**3 - 3*a + 6*a**4 - 2*a - 2 + 2*a**5 = 0.
-1, 1
Let t(k) = -k**3 + 11*k**2 - 13*k - 1. Let o be t(10). Let h = -29 - o. Suppose -1/2*w**h + 1/4*w**3 + 0 + 1/4*w = 0. Calculate w.
0, 1
Let q(n) be the third derivative of -n**6/240 - n**5/120 + n**4/48 + n**3/12 + n**2. Factor q(c).
-(c - 1)*(c + 1)**2/2
Suppose 5*d + z = d + 18, 8 = 4*z. Let c(s) be the first derivative of -1/4*s**d - 3 - s + 1/3*s**3 + 1/2*s**2. Suppose c(p) = 0. Calculate p.
-1, 1
Let g(z) be the first derivative of -2*z + 7/36*z**4 - 1 - 5/18*z**3 - 1/20*z**5 + 1/6*z**2. Let b(n) be the first derivative of g(n). Solve b(v) = 0.
1/3, 1
Suppose 4 + 6 = g - 5*l, 5*g = l + 2. Factor g + 2/7*t**2 + 4/7*t**3 + 0*t + 2/7*t**4.
2*t**2*(t + 1)**2/7
Let f(s) be the second derivative of 0*s**2 + 1/10*s**5 + 1/6*s**4 - 2/3*s**3 + 0 + 3*s. Factor f(r).
2*r*(r - 1)*(r + 2)
Factor -3*n**5 - 1 - 3*n - 1550*n**2 + 4*n**5 + 3*n**4 + 2*n**3 + 1548*n**2.
(n - 1)*(n + 1)**4
Solve 0 + 2*w**2 - 2/3*w + 2/3*w**4 - 2*w**3 = 0.
0, 1
Let f(z) be the third derivative of -7*z**5/120 + 5*z**4/48 + z**3/6 - z**2. Solve f(w) = 0 for w.
-2/7, 1
Let i(d) = 9*d**2 - 56*d + 180. Let m(f) = 55*f**2 - 335*f + 1080. Let n(z) = -25*i(z) + 4*m(z). Factor n(t).
-5*(t - 6)**2
Solve -5/4*v - 1/2*v**2 + v**4 - 1/2 + v**3 + 1/4*v**5 = 0.
-2, -1, 1
Factor 4/9*w**2 - 40/9*w + 100/9.
4*(w - 5)**2/9
Let r = -5 - -8. Factor -p**r - p + p**4 - 18*p**4 - 7*p**4 + 6*p**2 - 16*p**5.
-p*(p + 1)**2*(4*p - 1)**2
Let m = -47/3 - -347/21. Determine a, given that 6/7*a**4 + 0 - 2/7*a**3 - 2/7*a**5 - m*a**2 + 4/7*a = 0.
-1, 0, 1, 2
Let c(s) be the second derivative of -5*s**7/6 + 13*s**6/3 - 13*s**5/4 - 85*s**4/6 + 50*s**3/3 + 20*s**2 + 15*s. Find u such that c(u) = 0.
-1, -2/7, 1, 2
Let o(q) be the first derivative of 0*q + 0*q**4 - 3 + 1/720*q**6 - q**3 + 0*q**2 + 1/240*q**5. Let m(d) be the third derivative of o(d). Factor m(a).
a*(a + 1)/2
Let g be (-1656)/(-520) + ((-6)/(-5) - 1). Factor -10/13*v**5 - g*v**3 + 36/13*v**4 + 16/13*v**2 + 6/13*v - 4/13.
-2*(v - 1)**4*(5*v + 2)/13
Factor -r + 15*r - 4*r + r**2 - 7*r.
r*(r + 3)
Let c(p) be the third derivative of p**5/15 - 2*p**3/3 - 4*p**2. Find i such that c(i) = 0.
-1, 1
Let y(b) be the first derivative of -3*b**5/20 + 3*b**4/16 + 8. Factor y(u).
-3*u**3*(u - 1)/4
Let b(m) = m**3 + m**2 - m. Let f(q) = q**3 + q**2 - 3*q - 1. Let k be f(-2). Let a(c) = 2*c**3 + 3*c**2 - 4*c. Let v(l) = k*b(l) - a(l). Factor v(d).
-d*(d - 1)*(d + 3)
Determine h, given that -2/11*h**4 + 0 + 12/11*h**3 + 0*h + 14/11*h**2 = 0.
-1, 0, 7
Let c(h) be the first derivative of 63*h**4/4 - 13*h**3 - 41*h**2/2 + 7*h + 3. Let z(t) = -t - 1. Let g(n) = -c(n) + 5*z(n). Factor g(w).
-3*(w - 1)*(3*w + 2)*(7*w - 2)
Let y(u) be the second derivative of -1/3*u**3 + 2*u + 1/30*u**5 - u**2 + 0 - 1/60*u**6 + 1/12*u**4. Let f(k) be the first derivative of y(k). Factor f(h).
-2*(h - 1)**2*(h + 1)
Let o(f) be the third derivative of f**7/12600 + f**6/900 + f**5/150 - f**4/8 - 2*f**2. Let r(x) be the second derivative of o(x). Factor r(d).
(d + 2)**2/5
Let b(j) be the first derivative of j**4/36 - j**3/3 + 3*j**2/2 + 2*j - 1. Let v(w) be the first derivative of b(w). Factor v(x).
(x - 3)**2/3
Let v(j) be the third derivative of -j**5/240 - j**4/16 - 5*j**3/24 + 7*j**2. Let v(k) = 0. What is k?
-5, -1
Let x be 1*5 + 2/(-1). Determine b so that -b**4 + 2*b**3 + b**2 + 3*b**4 + 0*b**2 - x*b**2 - 2*b = 0.
-1, 0, 1
Let r be (-9 - -10)/(24/1). Let g(f) be the second derivative of 0 - 1/6*f**3 - f + r*f**4 + 1/4*f**2. What is q in g(q) = 0?
1
Factor -8/3*r**2 - 4/9*r**4 + 0*r + 0 + 20/9*r**3.
-4*r**2*(r - 3)*(r - 2)/9
Suppose 0 = i - 3*t - 12, 0 = 5*i - 10*i - 4*t - 16. Find z such that 2/11*z**2 + 0*z + i - 2/11*z**3 = 0.
0, 1
Let f = -555 - -557. Factor 1/2 + 1/4*b**4 + 9/4*b**f - 7/4*b - 5/4*b**3.
(b - 2)*(b - 1)**3/4
Suppose -4/7*b - 2/7 - 2/7*b**2 = 0. Calculate b.
-1
Let s = 14 - 18. Let n be (-6)/4*s/15. Factor -1/5*l**2 - n*l + 0.
-l*(l + 2)/5
Let t(v) = -12*v**3 + 36*v**2 - 30*v + 6. Let z(n) = 36*n**3 - 109*n**2 + 91*n - 18. Let h(k) = -8*t(k) - 3*z(k). Determine i so that h(i) = 0.
1/4, 1, 2
Let c(v) be the third derivative of -v**7/420 + v**6/120 - v**4/24 + v**3/12 + 28*v**2. Let c(g) = 0. What is g?
-1, 1
Let g(s) be the first derivative of s**2 + 11*s + 5. Let m be g(-4). Factor -2/9 - 4/9*f**m - 8/9*f - 10/9*f**2.
-2*(f + 1)**2*(2*f + 1)/9
Let g(h) = 2*h - 5. Let z be g(4). Suppose -z + 5 = j. Let -1/3*w**j - 2/3*w - 1/3 = 0. Calculate w.
-1
Let m(l) be the first derivative of 2*l**5/5 - 5*l**4/4 + l**3 + l**2/2 - l + 10. Factor m(d).
(d - 1)**3*(2*d + 1)
Let a(c) be the first derivative of c**9/1512 - c**8/420 + c**6/90 - c**5/60 - c**3/3 + 2. Let o(w) be the third derivative of a(w). Factor o(q).
2*q*(q - 1)**3*(q + 1)
Let t(v) be the first derivative of -v**3/9 + 20*v**2/3 - 400*v/3 - 7. Solve t(y) = 0 for y.
20
Let f(t) = -t**3 - 1. Let y(o) = -3*o**4 - 15*o**3 + 6*o**2 - 18. Let k(s) = 15*f(s) - y(s). What is u in k(u) = 0?
-1, 1
Let q be -6 + 4 + 24/10. Find c such that q - 4/5*c + 2/5*c**2 = 0.
1
Suppose -3*b + 3*n = 14 + 1, b - 19 = -5*n. Let k be 1*b/21*-6. Let 0*r + k - 2/7*r**2 = 0. Calculate r.
-1, 1
Let m = 4/273 - -478/4641. Factor 0 - 4/17*b**5 + 2/17*b**2 - 6/17*b**3 - 10/17*b**4 + m*b.
-2*b*(b + 1)**3*(2*b - 1)/17
Let i = 816 - 816. Determine k so that 9/4*k**4 + 9/4*k**3 + 3/4*k**5 + i*k + 0 + 3/4*k**2 = 0.
-1, 0
Factor -67*r**3 + 28*