 = 5*a - 8*a - 33. Let m(u) = a*q(u) - 4*f(u). Factor m(b).
5*b**4*(b + 1)
Let o(x) be the first derivative of -x**6/18 + 8*x**5/15 - 3*x**4/2 + 16*x**3/9 - 5*x**2/6 - 5. Factor o(i).
-i*(i - 5)*(i - 1)**3/3
Find p, given that 22/3*p + 10/3 - 4/3*p**4 - 2*p**2 - 22/3*p**3 = 0.
-5, -1, -1/2, 1
Suppose 4*o - 10 - 2 = 0. Let k be o*2/18*6. Factor -8*q + 20*q - 8*q - 2*q**2 + k*q**4 - 6*q**3 + 0*q**4 + 2*q**5.
2*q*(q - 1)**2*(q + 1)*(q + 2)
Factor -68/7*h**2 - 1096/7*h - 128/7.
-4*(h + 16)*(17*h + 2)/7
Suppose -3/2*w**2 - 3 - 19/2*w = 0. Calculate w.
-6, -1/3
Let v(m) be the second derivative of 2*m**5/25 + 11*m**4/60 + m**3/10 - 154*m. Factor v(y).
y*(y + 1)*(8*y + 3)/5
Suppose 0 = -2386*f + 2389*f - 30, -n + f - 8 = 0. Let 1/4*v**n + 64 + 8*v = 0. What is v?
-16
Let f(o) = -12*o**5 - 13*o**4 - 55*o**3 + 7*o + 7. Let y(t) = 5*t**5 + 7*t**4 + 27*t**3 - 3*t - 3. Let m(q) = -3*f(q) - 7*y(q). Factor m(s).
s**3*(s - 12)*(s + 2)
Let q be -6 + 75/105*(9 - 0). Let h(g) be the second derivative of -1/42*g**4 + 0 - q*g**2 - 5*g - 4/21*g**3. Find u such that h(u) = 0.
-3, -1
Let y(n) = -4*n - 8. Let x be y(-2). Factor -9*v**2 - 27*v**3 - 6*v - 6*v**2 - 18*v**2 + x*v**2.
-3*v*(v + 1)*(9*v + 2)
Let q(s) be the second derivative of -2*s**6/45 - 13*s**5/15 - 23*s**4/9 - 22*s**3/9 - 56*s. Solve q(z) = 0.
-11, -1, 0
Let y(d) be the second derivative of 0 + 5/12*d**4 + 0*d**2 - 18*d - 5/2*d**3. Suppose y(v) = 0. Calculate v.
0, 3
Let n(j) be the second derivative of 0 + 4/9*j**3 - 32*j - 4/9*j**2 + 1/45*j**5 - 1/6*j**4. What is y in n(y) = 0?
1/2, 2
Let x(b) be the first derivative of -b**6/195 + b**4/78 - 4*b - 13. Let n(g) be the first derivative of x(g). Factor n(s).
-2*s**2*(s - 1)*(s + 1)/13
Suppose -2 = -2*c + 2, -c = -m - 1. Let g(t) = t**3 - t**2 + t + 1. Let j(h) = -3*h**3 + 7*h**2 + 17*h - 31. Let d(w) = m*j(w) - g(w). Factor d(i).
-4*(i - 2)**2*(i + 2)
Let f(i) be the second derivative of i**5/20 + 13*i**4/6 + 110*i**3/3 + 300*i**2 + i + 40. Solve f(g) = 0.
-10, -6
Determine g so that -224/5*g + 14*g**4 - 328/5*g**3 + 96*g**2 + 32/5 = 0.
2/7, 2/5, 2
Suppose 4940*d = 4911*d + 87. Factor 0 + 2/7*a - 2/7*a**d + 1/7*a**2 - 1/7*a**4.
-a*(a - 1)*(a + 1)*(a + 2)/7
Let g(o) be the second derivative of o**6/900 + o**5/150 - o**3/2 + 18*o. Let v(h) be the second derivative of g(h). What is d in v(d) = 0?
-2, 0
Let d(n) = -5*n**3 + 5*n**2 - 4*n + 4. Let m(k) = 14*k**3 - 14*k**2 + 11*k - 11. Let h(y) = -11*d(y) - 4*m(y). Solve h(i) = 0.
0, 1
Let r(v) be the third derivative of 9*v**2 - 4/3*v**4 + 0*v + 0 + 2/15*v**5 + 64/9*v**3 - 1/180*v**6. Solve r(y) = 0.
4
Let z(p) be the first derivative of 5*p**3/12 + 145*p**2/2 + 4205*p - 167. Determine i, given that z(i) = 0.
-58
Let k(w) be the second derivative of 1/4*w**4 - 1/180*w**6 + 0 + 5*w - 1/30*w**5 - w**3 + 0*w**2. Let n(i) be the second derivative of k(i). Factor n(z).
-2*(z - 1)*(z + 3)
Let s = -43 + 47. Factor 6*l**4 + 14*l**3 + 7*l**s - 6*l**2 + 7*l**3 - l**4.
3*l**2*(l + 2)*(4*l - 1)
Let v(y) = -y**3 + 13*y**2 - 12*y - 5. Let u(a) = -a**2 + 1. Let x(p) = -5*u(p) - v(p). Suppose x(j) = 0. What is j?
0, 2, 6
Let h(l) = 11*l - 107. Let z be h(10). Determine j, given that -22/13*j**2 + 6/13*j**z + 8/13 + 16/13*j = 0.
-1/3, 2
Let k(h) be the second derivative of 0*h**2 + 0 - 1/84*h**7 + 1/20*h**6 + 0*h**3 + 11*h + 1/24*h**4 - 3/40*h**5. Suppose k(r) = 0. Calculate r.
0, 1
Let f = 30 + -24. Factor 11*a + 8*a**3 - 2*a - 11*a**3 + f.
-3*(a - 2)*(a + 1)**2
Let t be (4/2)/((-4)/(-8)). Factor -5*c**2 + 131 - 126 + t*c**3 - 5*c + c**3.
5*(c - 1)**2*(c + 1)
Let a(u) = -u**3 + 12*u**2 - 20*u. Let o(z) = 10*z**3 - 130*z**2 + 220*z. Let s(c) = 45*a(c) + 4*o(c). Factor s(t).
-5*t*(t - 2)**2
Let c(l) be the first derivative of 23 - 2*l**2 + 14*l + 2/21*l**3. Factor c(r).
2*(r - 7)**2/7
Let s(u) be the first derivative of 8*u**5/5 - 9*u**4 + 40*u**3/3 - 6*u**2 + 155. Let s(t) = 0. What is t?
0, 1/2, 1, 3
Let y(n) = 2*n - 24. Let u be y(15). Suppose 5*q = u*q. Factor 1/7*l**2 + 0*l**3 + 0 - 1/7*l**4 + q*l.
-l**2*(l - 1)*(l + 1)/7
Factor 0 - 65/3*c - 5/3*c**2.
-5*c*(c + 13)/3
Let c(t) be the second derivative of 0*t**2 + 1/4*t**4 + 0 - 22*t - 7/2*t**3. Solve c(p) = 0 for p.
0, 7
Let j(n) be the second derivative of -n**7/525 + n**6/300 - 4*n**2 - 31*n. Let r(c) be the first derivative of j(c). Determine s, given that r(s) = 0.
0, 1
Suppose 5*m = -20, -8*f + 20 = -4*f - 3*m. What is z in -84*z**3 - 4*z**f + 85*z**3 + 0*z**2 + 2*z**2 = 0?
0, 2
Let c = -147 - -149. Suppose 0*d - 10 = -c*d. Find n, given that 6/11*n**3 + 10/11*n**2 - 2/11*n**4 + 0 + 4/11*n - 2/11*n**d = 0.
-1, 0, 2
Let n = 3 + -3. Suppose n = 4*f + 3 + 1, -3*i + 7 = 2*f. Let -8 + 4*a**2 - 4*a + 4*a**i + 13 - 9 = 0. Calculate a.
-1, 1
Let k be 5/1*(176/(-110) + 2). Determine z so that -1/2*z**3 + 0*z + 0 + 1/6*z**4 + 0*z**k = 0.
0, 3
Determine p, given that 25*p + 0 - 4*p**3 - 5/2*p**2 - 1/2*p**4 = 0.
-5, 0, 2
Let s(d) be the third derivative of d**6/300 - d**5/50 - 2*d**4/5 + 16*d**3/3 - 15*d**2 - 5*d. Solve s(u) = 0.
-5, 4
Factor -23*q**4 - q - 7*q**3 - q - q - 14*q**2 - 31*q**4 + 58*q**4.
q*(q - 3)*(q + 1)*(4*q + 1)
Factor -47071*l**2 + 5 + 18*l - 18*l**3 + 10 - 3*l**4 + 47059*l**2.
-3*(l - 1)*(l + 1)**2*(l + 5)
Let c(q) = -5*q**3 + 24*q**2 - 5*q - 26. Let t(n) = 5*n**3 - 25*n**2 + 5*n + 25. Let b(d) = 5*c(d) + 4*t(d). Determine u, given that b(u) = 0.
-1, 2, 3
Suppose 32*n**3 - 1 - 4*n**5 + 479*n**2 - 287*n**2 - 20*n**4 + 1 = 0. What is n?
-4, 0, 3
Let a(n) be the first derivative of -n**4/18 - 2*n**3/27 + 89. Factor a(b).
-2*b**2*(b + 1)/9
Let p(b) = 9*b**4 - 40*b**3 + 116*b**2 - 75*b - 5. Let h(y) = -8*y**4 + 40*y**3 - 116*y**2 + 76*y + 4. Let s(f) = -5*h(f) - 4*p(f). What is d in s(d) = 0?
0, 1, 4, 5
Suppose 29*y = -76 + 163. Let 1/3*p**2 - 1/3*p**5 - 8/3*p - 1/3*p**4 + 5/3*p**y + 4/3 = 0. What is p?
-2, 1
Determine f, given that -91*f - 270 - 49*f + 5*f + 5*f**3 = 0.
-3, 6
Suppose 5*h = -2*v + 6*v - 3308, 4*h + 2*v = -2636. Let y be h/(-18)*(-6)/(-4). Factor -5 - y*j + 55*j**3 + 62*j**4 - 17*j**4 - 5 - 35*j**2.
5*(j - 1)*(j + 1)**2*(9*j + 2)
Suppose 3*z + 39 = -72. Let f be 1*2/(-18) + z/(-9). Factor 3/2*k**3 + 0*k + k**2 + 0 + 1/2*k**f.
k**2*(k + 1)*(k + 2)/2
Let m(b) be the first derivative of -b**5/15 - b**4/6 + 5*b**3/3 + 6*b**2 + 443. What is j in m(j) = 0?
-3, 0, 4
Let l = 1361/27 + -452/9. Let u = 47/108 - l. Suppose 3/4*v - u*v**2 - 1/2 = 0. What is v?
1, 2
Let t(u) be the second derivative of -u**4/114 + 10*u**3/57 + 756*u. Let t(o) = 0. What is o?
0, 10
Let d be (9/24)/(201/268). Factor -1/2*v**2 - 1/2*v + d*v**3 + 1/2.
(v - 1)**2*(v + 1)/2
Let u(w) = 2*w**3 + 10*w**2 + 8*w - 16. Let p = -65 + 60. Let c(r) = -r**3 - 7*r**2 - 5*r + 11. Let d(y) = p*u(y) - 8*c(y). Factor d(i).
-2*(i - 2)**2*(i + 1)
Let 0*u**2 - 3*u**3 + 0 + 0*u + 1/4*u**4 = 0. Calculate u.
0, 12
Suppose y = 2*u - 2, u + u = -5*y + 26. What is o in 2*o**3 - 7*o**4 + 3*o**2 + 8*o**4 - 4*o**2 - 2*o**y = 0?
0, 1
Let s(j) be the first derivative of j**4/3 + 56*j**3/9 + 26*j**2/3 + 441. Factor s(n).
4*n*(n + 1)*(n + 13)/3
Solve 544/9*c + 8/9*c**4 + 50/3 + 42*c**2 - 24*c**3 = 0 for c.
-1/2, 3, 25
Factor 3/4*t**2 + t - 1/4*t**3 + 0.
-t*(t - 4)*(t + 1)/4
Let i be 3/18*(153/(-255))/((-4)/10). Factor 0*a + 1/4*a**2 - 1/4*a**5 + i*a**3 - 1/4*a**4 + 0.
-a**2*(a - 1)*(a + 1)**2/4
Let j(h) be the second derivative of -h**5/20 + h**4/2 - 5*h**3/6 + h**2 - 4*h. Let n be j(5). Factor 2*k**2 + 4*k**3 - 2*k**4 - k**n - 3*k**3 + k**4 - k.
-k*(k - 1)**2*(k + 1)
Let w(d) be the first derivative of -2*d**6/3 - 9*d**5/5 + 9*d**4/2 + 29*d**3/3 + 3*d**2 - 5. Determine j, given that w(j) = 0.
-3, -1, -1/4, 0, 2
Let j be 59/5 + (-660)/60. Factor 32/5*n**2 + j*n + 0 + 12*n**3.
4*n*(3*n + 1)*(5*n + 1)/5
Let i(g) be the third derivative of g**6/1800 - g**4/120 + 22*g**3/3 + 47*g**2. Let j(u) be the first derivative of i(u). What is a in j(a) = 0?
-1, 1
Let s be ((-6)/4)/(12 + 615/(-50)). What is w in -4/3 - 9*w**s + 32/3*w + 23*w**4 - 5/3*w**3 - 65/3*w**2 = 0?
-1, 2/9, 1/3, 1, 2
Let d = 40 + -59. Let r = d - -19. What is p in 3/4 + r*p + 0*p**3 + 3/4*p**4 - 3/2*p**2 = 0?
-1, 1
Let b(y) be the first derivative of y**6/6 - 4*y**5/5 + y**4 + 81. Factor b(v).
v**3*(v - 2)**2
Let p(r) = -4*r**2 - 12*r + 4. Let m be p