9 - 2/9*r**5 - 2/9*r + d*r**2 - 2/9*r**4 + 4/9*r**3 = 0. What is r?
-1, 1
Let q(z) = -z - 1. Let s(l) = -4*l**3 + 16*l**2 - 22*l - 6. Let m(u) = 6*q(u) - s(u). Factor m(i).
4*i*(i - 2)**2
Let a = -135 + 137. Let y = 1 - 1. Factor 1/3*f**4 + 0 + y*f - 1/3*f**a + 0*f**3.
f**2*(f - 1)*(f + 1)/3
Let f(g) = -5*g**5 - 3*g**4 - 9*g**3 - 2*g**2. Let a(c) = 44*c**5 + 28*c**4 + 80*c**3 + 18*c**2. Let j(d) = -6*a(d) - 52*f(d). Find b such that j(b) = 0.
-1, 0
Suppose 24 = -2*b - 6*b. Let x be ((-1)/b)/((-4)/(-6)). Determine v so that -x*v**2 - 9/2 + 3*v = 0.
3
Let l be (-7 - -3) + (-25)/(-5). Let o(j) be the first derivative of 1/4*j**2 - 1/8*j**4 + l - 1/6*j**3 + 1/2*j. What is y in o(y) = 0?
-1, 1
Let q = -12 + 19. Suppose 4*u - 17 = -4*f + u, 0 = 4*f - 5*u + q. What is o in 2/5*o**5 - 4/5*o**3 - 4/5*o**4 + 16/5*o**f - 14/5*o + 4/5 = 0?
-2, 1
Let z = 515/2 - 257. Factor 0*j**3 + 0*j**2 + 0 + 1/2*j**4 + 0*j - z*j**5.
-j**4*(j - 1)/2
Let a(t) be the third derivative of -t**2 + 13/84*t**4 + 0*t + 3/140*t**6 + 4/35*t**5 + 2/21*t**3 + 0. Suppose a(r) = 0. Calculate r.
-2, -1/3
Let s(m) = 7*m**4 + 32*m**3 + 17*m**2 - 8*m - 13. Let q(b) = -4*b**4 - 16*b**3 - 8*b**2 + 4*b + 6. Let k(d) = -13*q(d) - 6*s(d). Find n such that k(n) = 0.
-1, 0, 2/5
Let o(a) be the second derivative of 0*a**3 - 3*a + 0*a**2 - 1/60*a**4 + 0. Determine x so that o(x) = 0.
0
Factor -1/8*x**2 - 1/8*x**3 + 1/8*x + 1/8.
-(x - 1)*(x + 1)**2/8
Let u(l) be the second derivative of -l**4/12 - l**3 + 7*l**2/2 + 48*l. Factor u(m).
-(m - 1)*(m + 7)
Let p(g) be the third derivative of -1/210*g**7 + g**2 + 0 + 0*g + 0*g**4 + 0*g**6 - 1/6*g**3 + 1/30*g**5. What is o in p(o) = 0?
-1, 1
Let x = 189 + -189. Factor -2/3*d**3 + 4/9*d**2 + 2/9*d**4 + 0*d + x.
2*d**2*(d - 2)*(d - 1)/9
Let g be -9 + 5 + (-13)/(-5) + 3. Find s such that 0 + 2/5*s**5 - 8/5*s**4 + 12/5*s**3 + 2/5*s - g*s**2 = 0.
0, 1
Let f = 69 + -69. Factor f*k + 2/7*k**3 + 0 + 2/7*k**2.
2*k**2*(k + 1)/7
Suppose 6 + 2 = 4*o. Factor -6*k**2 + 6*k**3 + k**o + 2 - k - 2*k**2.
(k - 1)*(2*k + 1)*(3*k - 2)
Let f(u) be the third derivative of u**8/224 + u**7/70 - u**6/40 - u**5/10 + u**4/16 + u**3/2 + 12*u**2. Determine q, given that f(q) = 0.
-2, -1, 1
Let p(l) = 63*l**3 + 105*l**2 - 27*l + 15. Let v(k) = -9*k**3 - 15*k**2 + 4*k - 2. Let t(m) = -2*p(m) - 15*v(m). Let t(x) = 0. What is x?
-2, 0, 1/3
Let g(c) = -c + 4. Let x be g(0). Factor -10*m - 20*m**3 - 2*m**5 + 23 + 20*m**2 + x*m**4 - 21 + 6*m**4.
-2*(m - 1)**5
Let r(h) be the second derivative of -98*h**7/3 - 1862*h**6/15 - 364*h**5/5 + 272*h**4/3 + 64*h**3/3 - 32*h**2 - 7*h. Find y, given that r(y) = 0.
-2, -1, -2/7, 2/7
Let j(p) be the first derivative of -p**7/14 + 3*p**5/20 + 7*p + 4. Let i(n) be the first derivative of j(n). Factor i(g).
-3*g**3*(g - 1)*(g + 1)
Let x = 2/99 - -184/693. Suppose x*w**2 + 0 - 4/7*w = 0. What is w?
0, 2
Suppose 4*t - 8 = 4*v - 0*v, -4*t - 4*v = -16. Determine r, given that 145/3*r**2 - 235/3*r**t + 4/3 + 175/3*r**4 - 40/3*r - 49/3*r**5 = 0.
2/7, 1
Let b(i) be the first derivative of i**4/12 + i**3/3 + i**2/3 + 24. Determine c, given that b(c) = 0.
-2, -1, 0
Let c = 9 - 4. Let z(l) be the first derivative of 0*l**4 + 0*l**2 + 1/15*l**c + 0*l + 0*l**3 - 2. Factor z(b).
b**4/3
Let r(n) = n**2 - 3*n + 13. Let t(p) = 1. Let d = 16 + -14. Suppose -2*b = 4*w - 3*b + 83, 0 = -3*w - b - 71. Let y(k) = d*r(k) + w*t(k). Factor y(j).
2*(j - 2)*(j - 1)
Suppose 7 + 3*a**2 + 4 + 6*a + 11 - 31 = 0. Calculate a.
-3, 1
Let b(d) be the first derivative of -7*d**6/10 - 9*d**5/5 - 3*d**4/4 + d**3 + 3*d + 3. Let t(z) be the first derivative of b(z). Factor t(j).
-3*j*(j + 1)**2*(7*j - 2)
Let r be 2*1/(4/10). Suppose -r*v + 20 = -l + 2*l, -5*v + 5*l = 10. Suppose 0 + 9/4*c**2 - 1/4*c - 27/4*c**v + 27/4*c**4 = 0. Calculate c.
0, 1/3
Let a = 23/5 + -59/15. Let x = -166/3 - -56. Let 0*l**2 - x*l + a*l**3 + 0 = 0. Calculate l.
-1, 0, 1
Let v(t) = -5*t**4 + 33*t**3 + 28*t**2 - 24*t - 41. Let l(g) = g**4 - 8*g**3 - 7*g**2 + 6*g + 10. Let h(j) = -9*l(j) - 2*v(j). Let h(w) = 0. Calculate w.
-4, -2, -1, 1
Let r(k) = -k**3 + k**2. Let n be r(-1). Suppose -n = i - 6. Factor 2*v**2 - v**i - 4*v**4 + 3*v**4.
-2*v**2*(v - 1)*(v + 1)
Factor -4 + 4 + 1 - 3*c + 3*c**2 - 4*c**3 + 3*c**3.
-(c - 1)**3
Let j(z) be the second derivative of 0 - 2/15*z**3 - 1/5*z**2 - 1/30*z**4 + 3*z. Factor j(y).
-2*(y + 1)**2/5
Let n(p) be the third derivative of p**5/360 + 7*p**4/36 + 49*p**3/9 + 2*p**2 - 11*p. Let n(j) = 0. Calculate j.
-14
Let b = -21 - -23. Suppose -7 - 1 = -2*s - 2*n, b*s - 3*n = -2. Solve 1/3*m**s + 0*m - 2/3*m**3 + 1/3*m**4 + 0 = 0 for m.
0, 1
Factor 0 + 18*p**2 + 3/2*p**5 + 21*p**3 + 19/2*p**4 + 4*p.
p*(p + 2)**3*(3*p + 1)/2
Suppose -4*n = 4*d - 20, -n + 0*d - 2*d + 8 = 0. Let o be 2 + -2 - (-4)/1. Factor 0*i**4 + 6*i**4 + n*i**2 - 4*i**3 - 4*i**o.
2*i**2*(i - 1)**2
Let i(q) be the second derivative of 0 - 1/2*q**2 + 1/24*q**4 - 1/12*q**3 + 3*q. Solve i(h) = 0.
-1, 2
Suppose 2*f = -3*a, f + 0*a + 1 = -2*a. Suppose -3*j = -3*s + f, -4*j - 4*s + 36 = 8. Factor -3*b**2 - 2*b**2 + 3*b**2 - 2*b**2 - 2*b**4 + 6*b**j.
-2*b**2*(b - 2)*(b - 1)
Let l(z) be the second derivative of 2*z**5/25 - 7*z**4/30 + 2*z**3/15 + z**2/5 - 3*z - 4. Determine a, given that l(a) = 0.
-1/4, 1
Suppose 5*q + 3*b - 20 = 0, -4*q + 16 = -0*b - 3*b. Factor -2 - 2*d**4 + 0 + 3 - 4*d + 1 + q*d**3.
-2*(d - 1)**3*(d + 1)
Let k(a) = -a**2 - 17*a - 20. Let h be k(-16). Let p = -2 - h. Factor -2/7*c**4 + 0*c**3 + 0 + 0*c + 2/7*c**p.
-2*c**2*(c - 1)*(c + 1)/7
Suppose -5*o + 2*o - 5*n = -9, -5*o - n = -15. Find q such that q**2 + 0*q**2 + q - q**2 - q**o = 0.
-1, 0, 1
Let x(p) be the second derivative of p**7/12 + 2*p**6/3 - 9*p**5/2 + 115*p**4/12 - 115*p**3/12 + 9*p**2/2 + 16*p - 1. Solve x(v) = 0 for v.
-9, 2/7, 1
Let o = 7 - 4. Suppose o*m - 12 = -m. Factor -2*j - 2*j**2 - 2*j**3 - j**2 + j**m.
-j*(j + 1)*(j + 2)
Determine i, given that -3/8*i**2 - 3/4*i + 0 = 0.
-2, 0
Let u(l) be the first derivative of -l**5/80 - l**4/24 - l**3/24 + l + 3. Let z(q) be the first derivative of u(q). Factor z(w).
-w*(w + 1)**2/4
Determine g so that 1 + 96*g**3 - 48*g**4 + 1 + 1 - 6*g - 45*g**2 = 0.
-1/4, 1/4, 1
Let f(w) = -4*w + 1. Let y be f(-1). Suppose -2*g + 5*m = -g + 2, -y*m = g - 8. Factor -3*t - t**2 + 1 + g*t.
-(t - 1)*(t + 1)
Determine b, given that 6/7 + 9/7*b**2 - 3/7*b**3 - 3/7*b**4 + 15/7*b = 0.
-1, 2
Suppose -3*k = -k - 14. Find z, given that -k*z**2 + 3*z**2 + 2 + 2*z + 0*z**2 = 0.
-1/2, 1
Let q(u) = -u**3 + 3*u**2 + 4*u + 2. Let l be q(4). Let -4/3 - 10/3*d + 10/3*d**3 + 4/3*d**l = 0. What is d?
-1, -2/5, 1
Suppose -4 + 23*g**4 + 79*g**2 - 53*g**3 + 17*g**5 - 24*g - 38*g**4 + 0 = 0. Calculate g.
-2, -2/17, 1
Let p = -3/17 - -35/102. Factor 0 + p*x**2 + 1/6*x.
x*(x + 1)/6
Let t(o) be the second derivative of -o**4/42 - o**3/6 - 3*o**2/14 + 5*o. Factor t(k).
-(k + 3)*(2*k + 1)/7
Let 1/2*b**2 - b**3 + 0*b + 0 + 1/2*b**4 = 0. What is b?
0, 1
Let m be ((-2 + 2)/(-4))/(-2). Let x(c) be the third derivative of 1/24*c**4 + 0*c + m*c**3 + c**2 + 0 - 1/120*c**5. What is w in x(w) = 0?
0, 2
Let k be (-3 + 2)/((-1)/3). Let n be 22/(2/12*3). Factor -18*l**3 + 8*l**2 + 6*l**4 + n*l**4 - 22*l**k.
2*l**2*(5*l - 2)**2
Let u(f) be the third derivative of 1/210*f**7 + f**2 + 1/60*f**6 + 0*f + 1/96*f**4 + 0 + 0*f**3 + 1/48*f**5. Factor u(z).
z*(z + 1)*(2*z + 1)**2/4
Let j be -2 + 0 - (0 + 3). Let x = -5 - j. Solve 0*h**4 - h**4 - h**2 + 2*h**2 + x*h**4 = 0 for h.
-1, 0, 1
Let n(f) be the first derivative of -f**6/6 - 3*f**5/5 - f**4/2 - 6. Factor n(x).
-x**3*(x + 1)*(x + 2)
Suppose -5*p + 9 = 3*v, -16 = 3*p - 3*v - 7. Let g(j) be the first derivative of j**4 - 1 + 0*j + 2/3*j**3 + p*j**2. Determine t, given that g(t) = 0.
-1/2, 0
Let f(d) = d**2. Let n(g) = -48*g**2 + 60*g - 20. Let z(q) = 3*f(q) + n(q). Factor z(k).
-5*(3*k - 2)**2
Let k(p) be the third derivative of 2*p**7/35 - p**6/3 + 3*p**5/5 - p**4/3 + 2*p**2. What is c in k(c) = 0?
0, 1/3, 1, 2
Let r(q) be the third derivative of q**7/210 - q**6/120 - q**5/60 + q**4/24 + 12*q**2. Factor r(k).
k*(k - 1)**2*(k + 1)
Let g = 1 - -2. Let s be 2/g*2*3. Factor -5 + b**3 - 6*b**3 + 4*b + 3 + 2*b**s + b**3.
2*(b - 1)**3*(b + 1)
Let r be ((-5)/3 - -2)/(3/12). Factor -1/3*g**4 + 4/3*g**3 + 0 - r*g**2 + 