3/2
Let x = 22 - 18. Let o(b) be the second derivative of -1/6*b**x + 0*b**2 - 2*b + 0 - 1/3*b**3. Factor o(w).
-2*w*(w + 1)
Let d(x) be the first derivative of 0*x**3 + 1/80*x**5 + 0*x + 2 + 1/32*x**4 - x**2. Let f(i) be the second derivative of d(i). Suppose f(c) = 0. What is c?
-1, 0
Find u, given that -1/5*u**2 + 0 - 1/5*u = 0.
-1, 0
Let t(u) be the first derivative of u**4/6 + 2*u**3/9 - 2*u**2/3 - 7. Determine a so that t(a) = 0.
-2, 0, 1
Let k = 192 + -57. Factor -k*w**2 - 11 + 147*w**4 + 4 + 14*w**3 - 84*w - 5 + 70*w**3.
3*(w - 1)*(w + 1)*(7*w + 2)**2
Suppose 3*m + o = -14 + 9, 2*o = 2*m - 10. Suppose 0*h - 2/9*h**4 + 4/9*h**3 - 2/9*h**2 + m = 0. What is h?
0, 1
Suppose -2*u = -3*u. Let r = 310/7 - 44. Factor u*x - 2/7*x**3 - r*x**2 + 0.
-2*x**2*(x + 1)/7
Let h(w) be the first derivative of w**6/9 - w**4/3 + w**2/3 + 1. Factor h(x).
2*x*(x - 1)**2*(x + 1)**2/3
Let t(a) be the second derivative of a**7/2520 + a**6/360 + a**4/4 + 2*a. Let c(o) be the third derivative of t(o). Factor c(j).
j*(j + 2)
Let k = -5 + 7. Factor -k + 0*w**3 - 6 + 6*w**2 + 2*w**3.
2*(w - 1)*(w + 2)**2
Let z = 21241/45 - 472. Let x(g) be the third derivative of -1/36*g**4 + 2/315*g**7 - g**2 + 0 + 1/504*g**8 - z*g**5 + 0*g**6 + 0*g**3 + 0*g. Factor x(b).
2*b*(b - 1)*(b + 1)**3/3
Let x(i) be the first derivative of -i**4/10 - 8*i**3/15 + 4. Factor x(r).
-2*r**2*(r + 4)/5
Factor 3/5*b + 1/5 - 1/5*b**5 - 3/5*b**4 + 2/5*b**2 - 2/5*b**3.
-(b - 1)*(b + 1)**4/5
Let z(o) be the second derivative of o**5/35 - o**4/42 - 2*o**3/21 + o**2/7 + 11*o. Factor z(x).
2*(x - 1)*(x + 1)*(2*x - 1)/7
Let r(i) = -i**2 - 7*i - 4. Let j be r(-6). Factor -4*d**j + 3*d**3 - 2*d**2 - 3*d**3 + 3*d**3.
3*d**2*(d - 2)
Let r(j) be the first derivative of 0*j**5 - 4 - 1/3*j**4 + 0*j**3 + 1/9*j**6 + 1/3*j**2 + 0*j. Factor r(p).
2*p*(p - 1)**2*(p + 1)**2/3
Let t(b) be the third derivative of b**8/40320 + b**7/10080 + b**5/60 - 5*b**2. Let h(k) be the third derivative of t(k). Factor h(w).
w*(w + 1)/2
Suppose -4*o = -5*o + 2. Suppose u + 2*z + 3 = -0, -o*u + 15 = -3*z. Find v such that -v - 4*v**2 - 4*v + 0*v**3 - 2*v**u + 3*v = 0.
-1, 0
Solve 15*i**3 - 48*i**4 + 51*i**4 + 21*i**2 + i + 8*i = 0 for i.
-3, -1, 0
Let t = 9 - 7. Let p(g) be the first derivative of 1 + 1/3*g**t + 0*g + 2/9*g**3. Determine a, given that p(a) = 0.
-1, 0
Factor z**5 + 3/7*z**3 - 12/7*z**4 + 2/7*z**2 + 0 + 0*z.
z**2*(z - 1)**2*(7*z + 2)/7
Solve -4/9*g**3 + 20/9*g - 4/9*g**4 + 4/3*g**2 + 8/9 = 0 for g.
-1, 2
Let -1/4*d**2 + 0*d + 3/4*d**3 + d**4 + 0 = 0. Calculate d.
-1, 0, 1/4
Factor 5/3*n**3 + 0*n + 5/3*n**2 + 0.
5*n**2*(n + 1)/3
Let l(p) = p**3 + 5*p**2 + 2. Suppose -5*s - 17 = 2*y, 0*s - y = 3*s + 11. Let k be l(s). What is m in m**3 - 2*m**3 + k*m - m = 0?
-1, 0, 1
Let j(f) be the third derivative of 1/84*f**8 + 0*f**3 + 3/40*f**6 + 1/60*f**5 + 0 + 0*f - 1/24*f**4 + 11/210*f**7 - 3*f**2. Factor j(m).
m*(m + 1)**3*(4*m - 1)
Determine s so that -2/7*s - 2/7*s**4 + 0 + 2/7*s**2 + 2/7*s**3 = 0.
-1, 0, 1
Let r(u) be the third derivative of u**8/10080 - u**7/2520 + u**5/30 + 2*u**2. Let j(f) be the third derivative of r(f). Factor j(h).
2*h*(h - 1)
Let v(j) be the first derivative of 3*j**5/40 - 3*j**4/16 + j**3/8 + 9. Factor v(a).
3*a**2*(a - 1)**2/8
Let o(u) = 6*u**2 - 6*u - 3. Let c(a) = -11*a**2 + 12*a + 5. Let w(p) = -3*c(p) - 5*o(p). Factor w(r).
3*r*(r - 2)
Factor 5*t + 44*t**2 + 12*t**4 + 4*t**2 + 15*t**3 - 33*t**4 + 7*t.
-3*t*(t - 2)*(t + 1)*(7*t + 2)
Determine y so that 45*y**2 + 9*y**3 + 12*y + 4*y**4 - 4*y**4 - 3*y**3 - 12 - 15*y**4 = 0.
-1, 2/5, 2
Let -32/5 - 2/5*z**2 + 16/5*z = 0. Calculate z.
4
Let v = 15 + -12. Let -4*h + 2*h**3 - 2*h**v - 2*h**3 - 6*h**2 = 0. What is h?
-2, -1, 0
Suppose 2*u = 4*o - 6*o - 1540, 4*u + 3072 = -2*o. Let f = -5350/7 - u. Factor -8/7*y + f*y**2 + 2/7 + 2/7*y**4 - 8/7*y**3.
2*(y - 1)**4/7
Factor 0*g - 3*g - 6 - 4 - 5*g + 2*g**2.
2*(g - 5)*(g + 1)
Let q = -77 + 233/3. Factor -1/3*w**5 - q*w - 7/3*w**2 - 3*w**3 + 0 - 5/3*w**4.
-w*(w + 1)**3*(w + 2)/3
Suppose 2*m + m - 6 = 0. Suppose 11*g + 3*g**m + g**3 - 9 - 7*g**2 - 3*g**2 + 4*g = 0. What is g?
1, 3
Suppose 45*a - 31*a**2 + 2*a**2 - 6*a**2 - 10 = 0. What is a?
2/7, 1
Let r(u) = 4*u**2 - 9*u - 13. Let j(h) = -h - 1. Let i(n) = j(n) - r(n). Factor i(k).
-4*(k - 3)*(k + 1)
Let g(s) be the third derivative of 2*s**2 + 1/35*s**7 - 1/10*s**5 + 0 + 0*s**6 + 0*s - 1/112*s**8 + 1/8*s**4 + 0*s**3. Factor g(y).
-3*y*(y - 1)**3*(y + 1)
Suppose -7*w + 28 = -0. Determine l so that -l**4 + l**4 - 2*l**4 - 6*l**w + 4*l**5 + 4*l**3 = 0.
0, 1
Let j = -406 - -829/2. Let l = j - 8. Suppose -5/2*w - 1 + 5/2*w**3 + 3/2*w**4 - l*w**2 = 0. Calculate w.
-1, -2/3, 1
Factor -2*k + 3/2*k**3 + 0 + 0*k**2 + 1/2*k**4.
k*(k - 1)*(k + 2)**2/2
Let t(j) be the third derivative of 0*j**3 + 1/60*j**4 - 2*j**2 + 1/150*j**5 - 1/525*j**7 + 0*j + 0 - 1/300*j**6. Let t(a) = 0. What is a?
-1, 0, 1
Let t be (-77)/(-84) + 1/(-4). Let x(j) be the first derivative of 1 + t*j**3 + 1/8*j**4 + j + 5/4*j**2. Factor x(u).
(u + 1)**2*(u + 2)/2
Let n(l) be the third derivative of -l**5/300 + l**4/120 - 9*l**2. Factor n(q).
-q*(q - 1)/5
Let j(q) be the first derivative of q + 6. Let x(l) = 2*l**2 + 3*l + 9. Let r(p) = 22*j(p) - 2*x(p). Let r(n) = 0. Calculate n.
-2, 1/2
Let q(a) = -2*a**2 - 38*a - 60. Let k(p) = p**2 - p. Let d(h) = -3*k(h) + q(h). Find b such that d(b) = 0.
-4, -3
Suppose -3*a = 3*a - 24. Let z(q) be the second derivative of 1/30*q**a + q + 1/5*q**2 + 0 - 2/15*q**3. Factor z(w).
2*(w - 1)**2/5
Let k(x) be the first derivative of x**6/33 - 8*x**5/55 + 3*x**4/11 - 8*x**3/33 + x**2/11 + 9. Factor k(z).
2*z*(z - 1)**4/11
Let s = 32 - 32. Let d = -23/3 + 8. Solve 0*y**4 + d*y**3 + 0 - 1/3*y**5 + 0*y + s*y**2 = 0.
-1, 0, 1
Let x(j) be the third derivative of 0 + 0*j**4 - 1/390*j**5 + 0*j - 1/780*j**6 + 1/1365*j**7 + 1/2184*j**8 + 10*j**2 + 0*j**3. Suppose x(w) = 0. Calculate w.
-1, 0, 1
Let d(f) be the first derivative of f**3/3 - 7*f**2/2 + 1. Factor d(y).
y*(y - 7)
Let q be (-6)/4*(-70)/15. Suppose -1 = -4*s + q. Determine m, given that -23/4*m**3 + 5/4*m**4 - m - 2 + 15/2*m**s = 0.
-2/5, 1, 2
Let v(h) = 12*h**2 + 21*h - 24. Let x(n) = 3*n**2 + 5*n - 6. Let f(g) = 2*v(g) - 9*x(g). Factor f(y).
-3*(y - 1)*(y + 2)
Factor 1/4 - 3/2*z**2 + 5/4*z.
-(z - 1)*(6*z + 1)/4
Let z(j) be the second derivative of -j**7/420 + j**6/240 + j**5/120 - j**4/48 - 3*j**2/2 + j. Let p(d) be the first derivative of z(d). Factor p(c).
-c*(c - 1)**2*(c + 1)/2
Let d(f) be the second derivative of 0*f**3 + 0*f**5 - f**2 - 1/72*f**4 + 0 + 1/360*f**6 + f. Let v(y) be the first derivative of d(y). Factor v(h).
h*(h - 1)*(h + 1)/3
Factor 0*d + 75/2*d**5 + 60*d**4 + 0 + 3*d**2 - 57/2*d**3.
3*d**2*(d + 2)*(5*d - 1)**2/2
Suppose -600*y + 601*y = 4. Factor -1/7*r**3 + 1/7*r**5 + 1/7*r**2 + 0 - 1/7*r**y + 0*r.
r**2*(r - 1)**2*(r + 1)/7
Factor 0 + 2/11*s**3 - 2/11*s**2 - 4/11*s.
2*s*(s - 2)*(s + 1)/11
Let l be 19/(-2) + 5/10. Let a(g) = 8*g**2 - 3*g - 5. Let c(u) = -33*u**2 + 12*u + 21. Let q(j) = l*a(j) - 2*c(j). Factor q(m).
-3*(m - 1)*(2*m + 1)
Let u(b) be the third derivative of b**5/140 + b**4/28 + 15*b**2. Factor u(v).
3*v*(v + 2)/7
Let g(l) be the first derivative of -l**3/3 + l**2/2 + 8. Solve g(y) = 0.
0, 1
Find m such that 87*m - 5*m**3 - 83*m - 11*m**3 + 12*m**2 = 0.
-1/4, 0, 1
Let a(n) be the third derivative of -n**8/2352 - n**7/1470 + n**6/140 + n**5/30 + 11*n**4/168 + n**3/14 + 19*n**2. Factor a(g).
-(g - 3)*(g + 1)**4/7
Let g(k) be the first derivative of k**4/8 - k**3/2 + k**2/2 - 25. Solve g(o) = 0 for o.
0, 1, 2
Suppose -4*l + 5 + 3 = 0. Suppose l*n + 5 = -t, 0 = 3*t + 3*n - 0*n. Factor -3*p + 2*p**5 - p**t + 4*p - 2*p**3.
p*(p - 1)**2*(p + 1)**2
Find w, given that -3/2*w + 9/8 + 3/8*w**2 = 0.
1, 3
Let w(l) be the third derivative of -3*l**2 + 0*l + 1/21*l**3 - 1/210*l**5 + 0 + 0*l**4. Find d such that w(d) = 0.
-1, 1
Let t(r) be the second derivative of 3*r**5/80 - r**4/4 + 3*r**3/8 - 6*r. Factor t(o).
3*o*(o - 3)*(o - 1)/4
Let b(k) = k**4 + k**2 - k + 1. Let j(l) be the first derivative of -4*l**5/5 + l**4/2 - 2*l**3/3 + l**2/2 - 3*l - 4. Let h(s) = 3*b(s) + j(s). Factor h(o).
-o*(o - 2)*(o - 1)*(o + 1)
Let h(q) be the first derivative of 9*q**2 - q + 4 - 2*q - 9*q**3 - 2 + 3*q**4. F