, 1/3, 1
Let v = -50/119 + 14261/238. Let t = v - 58. Factor 1/2 - t*y**2 + y.
-(y - 1)*(3*y + 1)/2
Let n = 4 + -2. Factor 5*c**2 - 16*c - 2 + 4 - c**n + 10.
4*(c - 3)*(c - 1)
Factor 4 - 9 - 1 + 6*t**2 - t**3 - 2*t**3 + 3*t.
-3*(t - 2)*(t - 1)*(t + 1)
Find l, given that -12*l**2 - 4 + 14*l + 2*l**3 + 5*l**2 - 3*l**2 - 2 = 0.
1, 3
What is v in 6*v**3 + 21*v**2 - 7*v**3 + 5*v**3 + 144*v + 27*v**2 = 0?
-6, 0
Let g(h) = -h**3 - 4*h**2 + 3*h - 7. Let a be g(-5). Factor 1 + 42*z**3 - 42*z**a + z**4 - 2*z**2.
(z - 1)**2*(z + 1)**2
Let j(k) be the first derivative of 1/4*k**4 + 1 + 2/3*k**3 + 0*k + 1/2*k**2. Determine u, given that j(u) = 0.
-1, 0
Let m(j) be the third derivative of -j**6/480 - j**5/80 + j**4/24 + 8*j**2 - 2*j. Factor m(i).
-i*(i - 1)*(i + 4)/4
Let d = -262289/210 + 1249. Let s(i) be the third derivative of 0*i**3 + 0*i + 3*i**2 + 0 + d*i**7 - 1/120*i**6 + 0*i**5 + 0*i**4. Find p, given that s(p) = 0.
0, 1
Let l(q) = 3*q**2 - 3. Let f(g) = g**2 - 1. Suppose -z = 3 - 0. Let u be (9/(-6))/(z/16). Let s(o) = u*f(o) - 3*l(o). Factor s(d).
-(d - 1)*(d + 1)
Let j be 3/2 + 12/24. Factor 2/9*a**j + 4/9*a + 2/9.
2*(a + 1)**2/9
Let n(b) be the third derivative of -b**6/30 - 4*b**5/15 - b**4/2 - b**2. Factor n(f).
-4*f*(f + 1)*(f + 3)
Let v(m) be the second derivative of -m**4/12 + 2*m**3/3 - 2*m**2 - 5*m. Factor v(r).
-(r - 2)**2
Factor 6*h - 17*h**2 - 19*h**2 + 0*h - 3 + 33*h**2.
-3*(h - 1)**2
Suppose -2*w = -9 - 1. Let u(k) be the first derivative of -3 + 4/15*k**3 - 2/5*k + 1/15*k**6 + 1/5*k**2 - 1/5*k**4 - 2/25*k**w. Determine g so that u(g) = 0.
-1, 1
Let g be (-6)/((2 - 2) + -2). Suppose -m + 5 = p, 5*p + g*m = -m + 22. Factor 2*a**p + 4*a - a + 0*a**3 - 2*a**4 - 2*a**3 - a.
-2*a*(a - 1)*(a + 1)**2
Let c(q) be the third derivative of -1/120*q**5 + 0 - 1/3*q**3 - 4*q**2 + 1/12*q**4 + 0*q - 1/360*q**6. Let p(b) be the first derivative of c(b). Factor p(a).
-(a - 1)*(a + 2)
Let v be 9/(288/(-56)) - -2. Factor 3/2*u + 9/4 + v*u**2.
(u + 3)**2/4
Suppose 10*p - 5*j = 5*p - 15, -p + 12 = 4*j. Let f(c) be the third derivative of 0 + 1/210*c**5 + p*c - 1/42*c**4 - 5*c**2 + 0*c**3. Factor f(q).
2*q*(q - 2)/7
Let j(x) be the third derivative of -5*x**2 - 1/120*x**6 + 0*x**3 - 1/30*x**5 + 0*x**4 + 0 + 0*x. Suppose j(l) = 0. Calculate l.
-2, 0
Suppose 186*x + 12 = 192*x. Find i, given that -9/7*i**x - 9/7*i - 3/7 - 3/7*i**3 = 0.
-1
Let b = 17 + -15. Factor -11*h**b - 14*h**3 - 2*h**5 - 4*h - 17/2*h**4 - 1/2.
-(h + 1)**4*(4*h + 1)/2
Let k be 7/(-21) + -3 + 4/1. Factor 0*h + 0 + k*h**2.
2*h**2/3
Let g(a) = a**3 + 5*a**2 + 4*a + 4. Let h be g(-4). Suppose l + h*l - 10 = 0. Factor 4/3 + 22/3*f + 26/3*f**l + 8/3*f**3.
2*(f + 1)*(f + 2)*(4*f + 1)/3
Factor 2 - 5/2*v**2 + 3/2*v**3 - 2*v.
(v - 2)*(v + 1)*(3*v - 2)/2
Let w(c) be the first derivative of -c**3/6 - c**2 + 5*c/2 + 3. Let w(a) = 0. What is a?
-5, 1
Let j(k) be the first derivative of -k**9/1008 + k**8/280 - k**6/60 + k**5/40 - 2*k**3/3 + 7. Let h(x) be the third derivative of j(x). Factor h(d).
-3*d*(d - 1)**3*(d + 1)
Let v(n) = -n**2 + 1. Let s(g) = 10*g**2 + 15 - 23 + g + g. Let d(p) = -2*s(p) - 18*v(p). Solve d(h) = 0 for h.
-1
Let i(p) be the third derivative of p**5/20 + 5*p**4/8 + 21*p**2. Let i(w) = 0. What is w?
-5, 0
Let x(f) = -f**3 - 6*f + 6. Let y(z) = -3*z**3 - 13*z + 13. Let l(o) = 13*x(o) - 6*y(o). Let l(a) = 0. Calculate a.
0
Let c(y) = -y**2 + 23*y + 27. Let s be c(24). Suppose -2/7*q**s - 8/7*q + 8/7*q**2 + 0 = 0. What is q?
0, 2
Let l(v) be the second derivative of 0*v**2 - 1/35*v**6 - 1/70*v**5 + 0 + 1/14*v**4 + 1/21*v**3 - 7*v. Determine i so that l(i) = 0.
-1, -1/3, 0, 1
Let m(r) be the first derivative of -r**7/2100 + r**6/300 - r**5/100 + r**4/60 + 5*r**3/3 - 3. Let a(j) be the third derivative of m(j). Factor a(i).
-2*(i - 1)**3/5
Let h be (51/9 - 4) + 4/(-60). Factor h*k + 1/5*k**3 - k**2 - 4/5.
(k - 2)**2*(k - 1)/5
Determine x, given that 99*x - 20*x**2 + 10*x**5 - 36*x**4 - 99*x - 66*x**3 = 0.
-1, -2/5, 0, 5
Let a(i) be the third derivative of -i**8/7560 + i**7/1890 - i**5/270 + i**4/108 - i**3/2 - i**2. Let g(l) be the first derivative of a(l). Factor g(m).
-2*(m - 1)**3*(m + 1)/9
Let b be 1 + 10/6 + (-6)/9. Let j(a) be the second derivative of 1/6*a**3 + 0*a**b - a + 1/12*a**4 + 0. What is h in j(h) = 0?
-1, 0
Let q(p) = -p**3 - p**2 + 1. Let b(d) = 7*d**3 + 9*d**2 - 10. Let v(f) = b(f) + 6*q(f). Factor v(z).
(z - 1)*(z + 2)**2
Let o(q) = 26*q**4 - 46*q**3 + 6*q**2 + 46*q + 16. Let s(w) = -5*w**4 + 9*w**3 - w**2 - 9*w - 3. Let h(v) = 3*o(v) + 16*s(v). What is p in h(p) = 0?
-1, 0, 1, 3
Let c(b) be the first derivative of -b**6/3 + 2*b**5/5 + b**4 - 4*b**3/3 - b**2 + 2*b + 10. Find x, given that c(x) = 0.
-1, 1
Let r = 47 + -42. Let f(k) be the second derivative of 2/15*k**6 + 0*k**4 - 1/21*k**7 - 1/10*k**r + 0*k**3 + 0 - 3*k + 0*k**2. Factor f(z).
-2*z**3*(z - 1)**2
Let d(g) = -g + 8. Let w be d(4). Let z(y) be the first derivative of -1/3*y**2 - 2/3*y**w - 10/9*y**3 + 0*y + 3. Find h, given that z(h) = 0.
-1, -1/4, 0
Let c(q) be the first derivative of -2/21*q**3 + 0*q - 5 + 1/7*q**2. Factor c(n).
-2*n*(n - 1)/7
Let s(x) = -x**5 - 9*x**4 - 10*x**3 - 6*x**2 - 9*x + 3. Let h(n) = -n**5 - 8*n**4 - 10*n**3 - 7*n**2 - 8*n + 2. Let t(f) = -4*h(f) + 3*s(f). Solve t(c) = 0.
-1
Let l = 46 + -91/2. Solve -1/2*f + 0 + 1/2*f**4 + 1/2*f**3 - l*f**2 = 0 for f.
-1, 0, 1
Suppose 7*x**2 + x**4 + 17/3*x**3 - 4/3 + x = 0. Calculate x.
-4, -1, 1/3
Let o = 62 - 929/15. Let x(j) be the third derivative of 0*j - 1/3*j**3 - 1/4*j**4 - o*j**5 + 3*j**2 + 0. Factor x(s).
-2*(s + 1)*(2*s + 1)
Let f(v) be the second derivative of -v**4/24 + v**3/6 + 3*v**2/4 + 10*v. Factor f(h).
-(h - 3)*(h + 1)/2
Suppose 3*x = -5*t + 13 + 3, -4*x - 4*t = -16. Determine k so that -1/2 - 3/2*k - 1/2*k**3 - 3/2*k**x = 0.
-1
Let c(n) be the first derivative of 7 + n**4 - 4*n**3 + 4/5*n**5 - 8*n - 10*n**2. Let c(f) = 0. Calculate f.
-1, 2
Factor 0*o + 0 - 1/6*o**2.
-o**2/6
Suppose -k + 5*n + 29 = -0*n, -4*k - 4*n = -20. Factor -3*d + 7*d - 2*d**2 - k*d**3 - 21*d**3.
-2*d*(3*d - 1)*(5*d + 2)
Let s(k) be the second derivative of -2*k + 1/45*k**5 + 1/54*k**4 - 1/9*k**2 - 2/27*k**3 + 0. Factor s(j).
2*(j - 1)*(j + 1)*(2*j + 1)/9
Factor 4/3*z**2 + 0*z - 14/3*z**3 - 2*z**5 + 0 + 16/3*z**4.
-2*z**2*(z - 1)**2*(3*z - 2)/3
Let n(s) be the second derivative of s + s**2 - 1/6*s**4 + 0*s**3 + 0. Factor n(k).
-2*(k - 1)*(k + 1)
Let r + 3/2 - 1/2*r**2 = 0. Calculate r.
-1, 3
Let z be (-5)/2*5/(-250)*4. Suppose -3/5*i**2 + 2/5*i + z = 0. What is i?
-1/3, 1
Let j = -1 - -5. Let z(s) = -5*s - 1. Let l be z(-1). Solve 5*k**3 - 2*k**2 - l*k + j*k**3 - 3*k**3 = 0.
-2/3, 0, 1
Suppose 0 = 5*l - 12*l. Let j(u) be the second derivative of 2*u - 1/110*u**5 + 0*u**3 + 0 + l*u**2 - 1/66*u**4. Factor j(d).
-2*d**2*(d + 1)/11
Let d(t) = 2*t + 2. Let z(v) = v**2 - v + 1. Let i(q) = 2*d(q) - 4*z(q). Factor i(o).
-4*o*(o - 2)
Let d(s) be the second derivative of -s**7/84 + s**6/90 + s**5/30 - s**4/36 - s**3/36 + 5*s. Let d(o) = 0. Calculate o.
-1, -1/3, 0, 1
Let t(b) be the third derivative of -b**7/1512 + b**6/720 + b**5/180 + b**4/24 + 4*b**2. Let l(h) be the second derivative of t(h). What is m in l(m) = 0?
-2/5, 1
Factor 0 + 3/2*y**3 + 3/2*y**2 + 1/2*y**4 + 1/2*y.
y*(y + 1)**3/2
Let p(i) be the first derivative of 2*i + 2/3*i**3 + 2 + 1/6*i**4 + i**2. Let s(h) be the first derivative of p(h). Determine f, given that s(f) = 0.
-1
Let 64 + 43*h + h**4 + 34*h**2 + 100*h - h**2 - 31*h - 14*h**3 = 0. Calculate h.
-1, 8
Let f(i) be the third derivative of i**8/2240 + i**7/420 + i**6/240 + i**5/60 - 10*i**2. Let w(u) be the third derivative of f(u). Factor w(c).
3*(c + 1)*(3*c + 1)
Let g(n) be the second derivative of n**5/300 - n**2 + n. Let b(k) be the first derivative of g(k). Find i such that b(i) = 0.
0
Let k = -1 - -10. Suppose 0 = -b - 2*b + k. Suppose -3*c**5 + 2*c**b - c**5 + 1 + 7*c**4 + c + c - 8*c**2 = 0. What is c?
-1, -1/4, 1
Suppose 4*c - 281 = 247. Let i be 2/(-5)*(-55)/c. Suppose i*v**2 + 0*v + 0 = 0. Calculate v.
0
Factor 4/3*g + 2/3*g**2 - 2.
2*(g - 1)*(g + 3)/3
Let z = 30 - 30. Let v be (21/(-9) - -3) + z. Determine b, given that v - b + 1/3*b**2 = 0.
1, 2
Let w(k) be the third derivative of -1/36*k**6 + 1/9*k**4 + 0*k + 4/45*k