4.
3*n*(n + 1)**2*(3*n + 1)/4
Factor -1/4*j**4 + 0*j**3 + 0*j - 1/4 + 1/2*j**2.
-(j - 1)**2*(j + 1)**2/4
Let s = 14 + -12. Factor -f**3 + 2 - f + 3*f**2 - f + f**s - 3*f.
-(f - 2)*(f - 1)**2
Let l be 16/10*15/6. Solve 3 + 3 - 2*r**2 + 4*r**l - 5 - 3*r**4 = 0.
-1, 1
Suppose -3*z = 7 - 22. Factor 4/5*s**4 + 1/5*s**z + 0 + 2/5*s**2 + s**3 + 0*s.
s**2*(s + 1)**2*(s + 2)/5
Suppose -v + 1 = p - 5, -4*v + 9 = -p. Let u be 4 + (4 + 0 - v). Find t, given that 3*t**3 - 9*t**u + 3*t**5 - 2*t**4 - t**4 = 0.
-1, 0, 1/2
Let i(x) be the second derivative of -1/24*x**4 + 0 + 0*x**2 + 0*x**5 - 1/168*x**7 + 1/24*x**3 - 7*x + 1/60*x**6. Factor i(r).
-r*(r - 1)**3*(r + 1)/4
Let u be (45 + -44)*(-15)/(-2). Find i such that -9/2 - u*i - 3/2*i**2 + 3/2*i**3 = 0.
-1, 3
Let n(j) be the first derivative of -7*j**6/135 - 19*j**5/90 - 5*j**4/18 - j**3/27 + 2*j**2/9 + 6*j + 2. Let w(i) be the first derivative of n(i). Factor w(l).
-2*(l + 1)**3*(7*l - 2)/9
Let f(k) be the second derivative of 3/20*k**5 - 2*k + 0 + 0*k**2 - 1/2*k**3 + 0*k**4. Suppose f(m) = 0. Calculate m.
-1, 0, 1
Factor -3/2*w**2 - 3/4*w**5 + 9/4*w**3 + 0*w**4 + 0 + 0*w.
-3*w**2*(w - 1)**2*(w + 2)/4
Let c(l) = -l - 1. Let v(x) = 8. Let h(o) = -c(o) - v(o). Let n be h(9). Factor 2*s**3 - 2/3*s**4 - n*s**2 + 2/3*s + 0.
-2*s*(s - 1)**3/3
Let k(x) be the first derivative of -3*x**4/4 + 3*x**3 + 6*x**2 - 4. Determine h so that k(h) = 0.
-1, 0, 4
Let w be ((-75)/21 + 15/(-35))/(-2). Solve 2/9*x - 2/9*x**3 + 0 + 2/9*x**w - 2/9*x**4 = 0 for x.
-1, 0, 1
Let n(d) be the first derivative of d**6/33 - 8*d**5/55 + 3*d**4/11 - 8*d**3/33 + d**2/11 - 11. Factor n(c).
2*c*(c - 1)**4/11
Let c(i) = 5*i - 8. Let q be c(-4). Let y be ((-14)/q)/((-6)/(-8)). Factor -4/3 - y*p**2 + 2*p.
-2*(p - 2)*(p - 1)/3
Let p(t) be the second derivative of -t**5/50 - t**4/15 - t**3/15 + 14*t. Factor p(n).
-2*n*(n + 1)**2/5
Let c = -8/7 - -38/21. Let 2/3*z + 4/3*z**2 - 4/3*z**4 + 0*z**3 + 0 - c*z**5 = 0. Calculate z.
-1, 0, 1
Factor 0 - 12/7*f**3 - 12/7*f + 2/7*f**4 + 22/7*f**2.
2*f*(f - 3)*(f - 2)*(f - 1)/7
Factor 4*m**2 - 3*m - 9*m + 2 + 6.
4*(m - 2)*(m - 1)
Let v(g) = 2*g**2 - 3*g - 4. Let y be v(3). Let m = 8 - y. Factor 2 + 4*p**2 - 1 + m*p - 2.
(p + 1)*(4*p - 1)
Let u(s) = s**2 - s + 1. Let d(r) = -3*r**4 - 15*r**3 - 5*r**2 + 23*r + 4. Let z(x) = d(x) - 4*u(x). Factor z(j).
-3*j*(j - 1)*(j + 3)**2
Factor -8*d**2 + 3*d**3 + 2*d**2 + 4*d - 4*d.
3*d**2*(d - 2)
Let w = -22 - -25. Let -3/2*b**w + 0 + 3/4*b**4 + 3/4*b**2 + 0*b = 0. Calculate b.
0, 1
Let v = -1097 + 1099. Determine r so that -4/3*r**4 - 1/3*r**5 - 4/3*r**v - 2*r**3 + 0 - 1/3*r = 0.
-1, 0
Determine b so that 0*b - 7 + 8 - b**2 + 0*b = 0.
-1, 1
Let x = 117/580 + 7/145. Determine q, given that -1/4*q**2 + x + 0*q = 0.
-1, 1
Let b(z) = 5*z. Let v be b(1). Suppose -v*j + 4*j = 0. Find p, given that 0*p + j + 2/5*p**2 = 0.
0
Suppose o - 15 = -4*o. Let v(g) = 4*g**2 - 4*g - 1. Let m(s) = s. Let b(j) = o*m(j) + 3*v(j). Factor b(z).
3*(z - 1)*(4*z + 1)
Let w(d) be the second derivative of d**7/14 - d**6/2 + 9*d**5/10 + d**4 - 4*d**3 + 4*d. Suppose w(n) = 0. What is n?
-1, 0, 2
Let b(l) = 23*l**3 + 5*l**2 - 9. Let o(m) = -m**3 - 2 - 2 + 2*m**2 + 12*m**3. Let v(k) = -4*b(k) + 9*o(k). Solve v(c) = 0.
0, 2/7
Let s(w) be the first derivative of -w**6/3 + 8*w**5/5 - 5*w**4/2 + 4*w**3/3 + 17. Factor s(b).
-2*b**2*(b - 2)*(b - 1)**2
Let q be 4/12 + (0 - (-79)/6). What is t in 3/2*t**2 + q + 9*t = 0?
-3
Let s(c) be the second derivative of -c**7/105 - c**6/20 + c**4/3 - 3*c**2/2 - 2*c. Let i(k) be the first derivative of s(k). Determine v, given that i(v) = 0.
-2, 0, 1
Let b(g) be the first derivative of -g**4/16 - g**3/3 - g**2/2 - 4. Solve b(j) = 0.
-2, 0
Find h such that 0*h**2 + 0 + 0*h + 4/9*h**4 - 2/3*h**3 = 0.
0, 3/2
Let s(g) = -g**2 + 5*g - 1. Let h be s(4). Suppose 0*f - 7 = -5*f - d, h*f = 4*d + 18. Factor -5*w**2 - 1 + f*w**2 + 4*w**2.
(w - 1)*(w + 1)
Let u(z) be the second derivative of -z**6/1080 + z**5/360 + z**3/2 + z. Let b(g) be the second derivative of u(g). What is f in b(f) = 0?
0, 1
Let s(q) be the third derivative of q**7/1785 + q**6/1020 - q**5/510 - q**4/204 - q**2. Determine w, given that s(w) = 0.
-1, 0, 1
Let i = -1/32 + 49/32. Factor 0 - 9/2*b**2 - i*b**3 - 3*b.
-3*b*(b + 1)*(b + 2)/2
Let m be -1*(-188)/(-8) + -3. Let s = 27 + m. Determine j, given that -1/2*j + 0 + 1/4*j**4 - 1/4*j**2 + s*j**3 = 0.
-2, -1, 0, 1
Let i(k) be the second derivative of -k**7/315 - k**6/90 - k**5/90 + k**2 + 2*k. Let v(q) be the first derivative of i(q). Find u, given that v(u) = 0.
-1, 0
Let s(q) be the third derivative of 1/840*q**8 + 0*q**4 + 0*q**5 + 0*q - 1/300*q**6 + 0*q**3 - 4*q**2 + 0*q**7 + 0. Factor s(t).
2*t**3*(t - 1)*(t + 1)/5
Let s = 0 + 0. Suppose s = 3*b - 2*k - 4, -k - 1 = -b - 0*b. Find w, given that -2*w + 1 + 0*w - b*w**2 + 3*w**2 = 0.
1
Let n = -184 + 184. Suppose n + 2/5*o**2 + 1/5*o**3 + 0*o = 0. What is o?
-2, 0
Let g be 4/(-12) - (-64)/12. Let l = -2 + g. Factor -3/4*q**4 + 0 - 1/4*q**2 + 1/4*q**5 + 0*q + 3/4*q**l.
q**2*(q - 1)**3/4
Let s(i) be the first derivative of -1 + 0*i**3 + 1/2*i**2 - 1/24*i**4 + 0*i - 1/40*i**5 - 1/240*i**6. Let z(o) be the second derivative of s(o). Factor z(v).
-v*(v + 1)*(v + 2)/2
Let x(d) = -d**3 + 2*d**2 + 3*d - 2. Let g be x(2). Suppose -5*m + g*o + 16 = 0, -2*o = -m + 14 - 6. Let 1/2*q**2 - q + m = 0. Calculate q.
0, 2
Factor -12 - 137*r**3 - 141*r**3 + r**2 + 279*r**3 - 8*r.
(r - 3)*(r + 2)**2
Let r(u) be the second derivative of -3*u**6/160 + u**5/8 - 7*u**4/24 + u**3/3 - 2*u**2 + 2*u. Let t(q) be the first derivative of r(q). Solve t(j) = 0.
2/3, 2
Let -27*i**2 + 5*i - 20*i**4 + 27*i**2 + 15*i**2 = 0. What is i?
-1/2, 0, 1
Let y = -30 + 32. Determine g so that -3*g + 3/4*g**y + 3 = 0.
2
Let f be 4/72*-2*(-5 - 1). Let s(m) be the first derivative of 0*m**2 - 2 - 2*m + f*m**3. Let s(x) = 0. What is x?
-1, 1
Determine d, given that -12*d - 13*d**2 - 20*d**2 + 84*d + 2*d**3 + 108 + d**3 = 0.
-1, 6
Let a = 6144859/6426080 - -1/80326. Let k = a - 5/32. Factor 4/5*x**4 - k*x**2 + 0 + 2/5*x**5 - 2/5*x + 0*x**3.
2*x*(x - 1)*(x + 1)**3/5
Factor -1/4*n**3 + 0 + 5/4*n**2 - n.
-n*(n - 4)*(n - 1)/4
Let o be 201/(-536) - 54/(-16) - -1. Determine h, given that 192/11*h**2 + 150/11*h**5 - 64/11*h + 184/11*h**3 - 32/11 - 430/11*h**o = 0.
-2/5, 2/3, 1, 2
Let j(s) be the second derivative of s + 2*s**2 - 2/3*s**3 + 0 + 1/12*s**4. Factor j(a).
(a - 2)**2
Let z(s) be the third derivative of s**6/120 + s**5/15 + 5*s**4/24 + s**3/3 + 14*s**2. Factor z(k).
(k + 1)**2*(k + 2)
Factor -8 - 7*x**2 + 3*x**2 + 5*x + 7*x.
-4*(x - 2)*(x - 1)
Factor 143*w**2 + 2299 + 6341 + 131*w**2 - 94*w**2 + 2160*w + 5*w**3.
5*(w + 12)**3
Let r be 1/((-21 - -1)*-2). Let w(f) be the second derivative of 0*f**4 + 0*f**2 - r*f**6 - f + 0*f**5 + 0*f**3 + 0. Find k, given that w(k) = 0.
0
Let r be 287/(-1950) - (-10)/65. Let q(b) be the third derivative of -2/15*b**3 + 0*b + 0 - r*b**5 - 2*b**2 + 1/20*b**4. Solve q(z) = 0 for z.
1, 2
Let -1/2*u**3 - 1/4*u**4 + 0 + 0*u + 0*u**2 = 0. Calculate u.
-2, 0
Let o(n) be the first derivative of n**4/14 - 2*n**3/21 - 2*n**2/7 + 53. Factor o(b).
2*b*(b - 2)*(b + 1)/7
Let j be (-2)/24*-2 - 440/(-240). Let w(c) be the first derivative of 2*c - c**4 + j*c**2 + 0*c**3 - 2 - 2/5*c**5. Determine l so that w(l) = 0.
-1, 1
Determine f so that f**3 - 3*f - 4 + 4 + 2*f**3 = 0.
-1, 0, 1
Let y(v) be the second derivative of v**6/195 - 2*v**5/65 - v**4/78 + 4*v**3/39 - 36*v. Factor y(w).
2*w*(w - 4)*(w - 1)*(w + 1)/13
Let g be (-8)/(-14)*(-2)/(-12). Let k(z) be the third derivative of -4/105*z**5 + z**2 - 1/12*z**4 - g*z**3 - 1/140*z**6 + 0 + 0*z. Factor k(i).
-2*(i + 1)**2*(3*i + 2)/7
Let a(w) be the first derivative of -w**5/120 - w**4/24 + 2*w**2 + 4. Let k(j) be the second derivative of a(j). What is q in k(q) = 0?
-2, 0
Suppose -9*a = 7*a - 17*a. What is q in -3/2*q**3 + 0 - q**2 + a*q + 5/2*q**4 = 0?
-2/5, 0, 1
Let t(y) be the third derivative of y**8/1512 - y**7/945 - y**6/108 + y**5/270 + 2*y**4/27 + 4*y**3/27 + 15*y**2. Suppose t(s) = 0. Calculate s.
-1, 2
Let w(q) be the second derivative of 0*q**2 + 1/12*q**4 + 5*q + 1/3*q**3 + 0 - 1/20*q**5. Solve w(p) = 0 for p.
-1, 0, 2
Let o(f) be the second derivative of -f**5/60 - f**4/36 + 2*f**3/