
-t**3*(5*t + 2)
Let n be 4/6 - 3/9. Let h(l) = l**3 - 7*l**2 - 9*l + 12. Let w be h(8). Factor 0*g + 0 + n*g**2 + 1/3*g**w - 2/3*g**3.
g**2*(g - 1)**2/3
Let w(q) be the first derivative of 15*q**4/4 - 25*q**3/3 - 5*q**2 - 12. Let w(j) = 0. Calculate j.
-1/3, 0, 2
What is w in -2/11*w**4 - 10/11*w**3 + 0 - 8/11*w**2 + 0*w = 0?
-4, -1, 0
Factor q**3 + 3*q**2 + 2*q - 2*q**2 - 3*q - 2 + 1.
(q - 1)*(q + 1)**2
Factor -24/7*s + 3/7*s**4 - 9/7*s**2 + 6/7*s**3 - 12/7.
3*(s - 2)*(s + 1)**2*(s + 2)/7
Let a(b) = b**2 - 1. Let i(o) = 6*o**3 - 9*o**2 + 4*o - 1. Let h(g) = 4*a(g) - 2*i(g). Factor h(r).
-2*(r - 1)**2*(6*r + 1)
Suppose -2*n + 4*h - 20 = 0, 3*n + 8*h - 20 = 4*h. Let l(k) be the third derivative of 0*k + 1/210*k**5 + 0*k**4 - k**2 + 0 + n*k**3. Factor l(b).
2*b**2/7
Let q be 62/60 - 6/45. Let u(v) be the second derivative of 0 - 2*v - v**4 + 0*v**2 + q*v**5 + 4/9*v**3 - 3/10*v**6. Let u(w) = 0. Calculate w.
0, 2/3
Suppose -8 = 4*q - 4*u, 7*q - 6*q - 5*u + 18 = 0. Determine n so that -1/3*n**q + 0*n + 1/3*n**4 + 0*n**3 + 0 = 0.
-1, 0, 1
Let a = 1/38 + 17/76. Factor 0*v + 0 + 0*v**2 - a*v**3.
-v**3/4
Find u, given that 34/13*u**2 - 14/13*u**3 + 12/13 + 2/13*u**4 - 34/13*u = 0.
1, 2, 3
Suppose 27 - 7 = 5*u. Let c(v) be the third derivative of 1/120*v**5 - v**2 - 1/24*v**u + 0*v + 1/12*v**3 + 0. Find p, given that c(p) = 0.
1
Let m(p) be the first derivative of -2*p**5/15 - 8*p**4/3 - 128*p**3/9 + 66. Determine f so that m(f) = 0.
-8, 0
Let p(h) be the first derivative of -h**3 + 12*h + 6. Factor p(d).
-3*(d - 2)*(d + 2)
Suppose -2*l - 2 + 8 = 0. What is c in -c**4 + 0*c + 4*c**4 - l*c**3 - 5*c**3 - 2*c + 7*c**2 = 0?
0, 2/3, 1
Let y(h) be the third derivative of -h**6/24 + h**5/6 + 5*h**4/3 + 13*h**2. Let y(z) = 0. What is z?
-2, 0, 4
Let u = 60 + -56. Let v(f) be the third derivative of 2/3*f**3 - 4*f**2 + 1/60*f**5 - 1/6*f**u + 0*f + 0. Factor v(p).
(p - 2)**2
Let w be (10/8)/(630/144). Suppose 0 + 0*o**2 + 1/7*o**4 + w*o**3 + 0*o = 0. What is o?
-2, 0
Let s(v) be the third derivative of 3*v**8/112 + v**7/7 - 4*v**6/15 - 13*v**5/30 + 23*v**4/24 - 2*v**3/3 - 12*v**2. Let s(n) = 0. What is n?
-4, -1, 1/3, 1
Let f(z) be the third derivative of z**7/1050 + z**6/300 - z**4/60 - z**3/30 + 15*z**2. Suppose f(j) = 0. What is j?
-1, 1
Let u(b) be the third derivative of b**6/720 - b**4/48 - b**3/18 - 16*b**2. Suppose u(l) = 0. What is l?
-1, 2
Let d(f) be the third derivative of -f**5/300 - f**4/120 - 3*f**2. Solve d(l) = 0 for l.
-1, 0
Let z be 2/8 + 28/16. Suppose -h + 6*x - 16 = z*x, 0 = 3*x - 12. Factor -1/3*c - 1/3*c**2 + h.
-c*(c + 1)/3
Solve -g**4 - 1 - 1/2*g**5 + g**3 - 1/2*g + 2*g**2 = 0.
-2, -1, 1
Let k(g) be the first derivative of 8*g**5/45 - 2*g**4/9 + g**3/9 - g**2/2 - 3. Let r(q) be the second derivative of k(q). Factor r(z).
2*(4*z - 1)**2/3
Determine z so that 1/6*z**2 - 1/3 + 1/6*z = 0.
-2, 1
Let o = -8 - -8. Suppose 2*f - 6*f + 8 = o. What is a in -1/2*a**f + 0*a + 1/2 = 0?
-1, 1
Let j(r) be the first derivative of -r**7/105 - r**6/15 - r**5/5 - r**4/3 - r**3/3 + r**2/2 - 3. Let a(c) be the second derivative of j(c). Factor a(g).
-2*(g + 1)**4
Let x**2 + 0 + 1/3*x**4 - 1/3*x - x**3 = 0. Calculate x.
0, 1
Let 0 + 4/19*q**3 + 2/19*q**4 + 2/19*q**2 + 0*q = 0. What is q?
-1, 0
Factor 3/2*l**3 + 1/4*l - l**4 + 0 - l**2 + 1/4*l**5.
l*(l - 1)**4/4
Factor 3*q**3 + 25*q**4 - 3*q**2 - 22*q**4 - 3*q**5 + 0*q**5.
-3*q**2*(q - 1)**2*(q + 1)
Let d(q) be the third derivative of q**5/60 - q**4/24 - q**3/3 + 10*q**2. Factor d(n).
(n - 2)*(n + 1)
Factor 0*n**2 - 12/5*n**3 + 0 + 0*n + 3/5*n**5 + 9/5*n**4.
3*n**3*(n - 1)*(n + 4)/5
Let n be (-25)/(-360) + (-6)/(-16). Find f such that 2/9*f**2 + n + 2/3*f = 0.
-2, -1
Let b = -29 - -31. Find h such that 4/3*h - 2/3*h**b + 0 = 0.
0, 2
Let d(y) = -10*y**3 + 2*y - 1. Let a be d(1). Let b be -3*(2 + 21/a). Factor 12*z**2 + b - 13*z**2 - z + z**3 + 0.
(z - 1)**2*(z + 1)
Let x(f) be the third derivative of f**5/420 - f**4/42 + 2*f**3/21 - 43*f**2. Let x(l) = 0. What is l?
2
Let m(r) = 9*r**5 + 12*r**4 - 9*r**3 + 9*r**2 + 21*r. Let a(w) = -2*w**5 - 3*w**4 + 2*w**3 - 2*w**2 - 5*w. Let k(d) = -21*a(d) - 5*m(d). What is s in k(s) = 0?
-1, 0, 1
Determine t, given that 54*t**2 + 4 - 52*t**2 - 4 - t = 0.
0, 1/2
Factor y**2 + 5*y**2 + 0*y**2 - 2*y**2 + 8*y.
4*y*(y + 2)
Suppose -5*g + g = -8. Let x be 2/(-1 - 1)*(2 + -2). Solve -2/7*o**3 + 0*o**g + x*o + 0 = 0 for o.
0
Let o(j) be the second derivative of -3*j + 9/20*j**5 - 2/5*j**6 + 1/4*j**4 + 0*j**2 + 0*j**3 + 0. Factor o(u).
-3*u**2*(u - 1)*(4*u + 1)
Let b(l) be the third derivative of l**8/112 + l**7/35 - l**6/20 - 2*l**5/5 - 7*l**4/8 - l**3 - l**2. Let b(k) = 0. What is k?
-1, 2
Let u = -5 + 8. Suppose 5*n - q - 6 = 9, -n = -u*q - 17. Suppose 3*s**2 - 2 - 1 + 0*s**n = 0. Calculate s.
-1, 1
Let 0 + 8/9*x + 2/9*x**2 = 0. Calculate x.
-4, 0
Let y(v) be the third derivative of -3*v**5/20 + 13*v**4/8 + 5*v**3 - 19*v**2. Suppose y(z) = 0. Calculate z.
-2/3, 5
Let d(t) be the third derivative of -t**6/300 - t**5/150 + t**4/60 + t**3/15 + 10*t**2. Suppose d(l) = 0. Calculate l.
-1, 1
Let a = 58 - 56. Factor 0 - 2/7*y**a + 2/7*y.
-2*y*(y - 1)/7
Let f be (42/(-196))/((-2)/4). Let h(d) be the first derivative of 4/21*d**3 + 2/7*d + 3 + f*d**2. Factor h(w).
2*(w + 1)*(2*w + 1)/7
Let l(k) be the third derivative of -k**7/1680 + k**6/720 - k**4/24 + 2*k**2. Let r(s) be the second derivative of l(s). Factor r(y).
-y*(3*y - 2)/2
Let l(g) be the first derivative of -2/15*g**3 + 2/5*g**2 + 2 - 2/5*g. Factor l(n).
-2*(n - 1)**2/5
Let l(z) be the first derivative of 15*z**3 + z**4 - 1 - 14*z**3 - 4*z**4. Factor l(r).
-3*r**2*(4*r - 1)
Let k be (-6)/(-2)*6/9. Suppose -4*j = -k*z - 10, 0*j = 4*z + j - 16. Factor z*c**2 + 4*c**2 - 3*c**2 - 5*c**2.
-c**2
Let u(c) be the second derivative of 0 + 0*c**4 + 3/7*c**2 + 3/140*c**5 - 2*c - 3/14*c**3. Factor u(t).
3*(t - 1)**2*(t + 2)/7
Let w(i) be the first derivative of 4*i**3/21 + 20*i**2/7 + 100*i/7 - 3. Factor w(s).
4*(s + 5)**2/7
Let a(o) be the second derivative of o**7/63 - 4*o**6/45 + 2*o**5/15 + o**4/9 - 5*o**3/9 + 2*o**2/3 - 6*o + 1. Factor a(g).
2*(g - 2)*(g - 1)**3*(g + 1)/3
Suppose 3 = 5*d - 2. Let j be 2 + d - 2/6. Factor 8/3*a**2 + 4*a**3 + 2/3*a**5 + j*a**4 + 0 + 2/3*a.
2*a*(a + 1)**4/3
Suppose -3*u + 81 = 5*y, 0*y = -5*y - 2*u + 79. Let 2 - 13*g**3 - 7*g**4 - g - 2*g**3 - y*g**2 - 4*g**3 = 0. What is g?
-1, 2/7
Let k(a) = -4*a**2 - 2*a - 1. Let m be k(-1). Let t = m - -8. Let -40*v**3 - 196*v**4 - 6*v**2 + 4 + 123*v**2 + t*v**3 - 40*v = 0. What is v?
-1, 1/4, 2/7
Let n(j) be the third derivative of 3*j**5/70 - j**4/42 - 9*j**2. Factor n(u).
2*u*(9*u - 2)/7
Determine v so that v**2 - 7*v + 0*v**2 - 49 - 2*v**2 - 7*v = 0.
-7
Let r(g) be the third derivative of g**8/84 + 8*g**7/105 + 2*g**6/15 - 10*g**2. Let r(f) = 0. Calculate f.
-2, 0
Solve 12*d**4 + 32*d**2 + 3 + 18*d + 28*d**3 + 0 + 7*d**5 - 5*d**5 + 1 = 0 for d.
-2, -1
Let y(f) be the third derivative of -f**6/360 + f**5/18 - 25*f**4/72 - 51*f**2. Factor y(h).
-h*(h - 5)**2/3
Let n(u) be the second derivative of -1/12*u**4 - 1/2*u**2 + 1/3*u**3 - 2*u + 0. Factor n(y).
-(y - 1)**2
Suppose 4*d = -d + 5, 2 = -m + 4*d. Suppose 3*l**3 + 10*l + 12*l**m + 12*l + 0*l**3 + 6 - 7*l = 0. Calculate l.
-2, -1
Factor -25 + 3*p**2 + p**2 - 4*p**3 + 6*p - 6*p**4 + 27 - 2*p**5 + 0*p**2.
-2*(p - 1)*(p + 1)**4
Suppose -5*g = -4 - 6. Factor -1/3*r**5 + 0*r + 0*r**g + 0 + 0*r**3 - 1/3*r**4.
-r**4*(r + 1)/3
Let q be 38882/(-90) + (-4)/(-18). Let z = -429 - q. Find w, given that 4/5*w**2 - 4/5 - 14/5*w + z*w**3 = 0.
-1, -2/7, 1
Let j be (-2)/(-12)*8/2. Suppose 0 + 0*z + j*z**2 = 0. What is z?
0
Factor 40/7*u**2 + 2/7 + 18/7*u.
2*(4*u + 1)*(5*u + 1)/7
Let c(z) = -2*z**5 + 2*z**3. Let n(x) be the first derivative of 2*x**6/3 - x**5/5 - x**4 + x**3/3 - 4. Let b(w) = -5*c(w) - 2*n(w). Factor b(p).
2*p**2*(p - 1)*(p + 1)**2
Let a be 36/45 + 48/15. Suppose -w = l - 1 - 0, -4*w = -a*l - 20. Suppose 0*k + 2/3*k**w - 2/3*k**5 - 2/3*k**2 + 0 + 2/3*k**4 = 0. Calculate k.
-1, 0, 1
Let t(w) be the third derivative of 0*w + 0*w**3 - 1/420*w**5 - 1/168*w**4 + 5*w**2 + 0. Factor t(c).
-c*(c + 1)/7
Suppose -10*c - 24*c = -22*c. Let -1/3*y + c - 2/3*y**2 = 0. What is y?
-1/2, 0
Let o(v) be the third derivative of v