4 - b**5 - 6*b**4 - 12*b.
-3*b*(b - 1)**2*(b + 2)**2
Determine m, given that 5/3*m - 2 + 1/3*m**2 = 0.
-6, 1
Let z be (-3 - 35/(-11)) + 346/(-2024). Let c = 87/460 + z. Find h such that 0 + c*h + 1/5*h**3 + 2/5*h**2 = 0.
-1, 0
Let q(v) = -19*v - 108. Suppose 5*i + 20 = -5*j, 5*j = -7*i + 5*i - 2. Let w be q(i). Factor 3/2*c**2 - 9/2*c - w.
3*(c - 4)*(c + 1)/2
Let z(g) be the third derivative of 5*g**8/84 - 8*g**7/35 + 2*g**6/15 + 40*g**2. Factor z(r).
4*r**3*(r - 2)*(5*r - 2)
Let w(t) be the third derivative of -t**5/15 - 4*t**4/3 - 14*t**3/3 + 32*t**2. Factor w(n).
-4*(n + 1)*(n + 7)
Suppose 3*n - 5*x + 94 = 0, 0*n + 5*x = n + 48. Let r = -20 - n. Find b such that -2/7*b - 2/7*b**4 + 2/7*b**r + 0 + 2/7*b**2 = 0.
-1, 0, 1
Let q(f) be the third derivative of f**6/270 + f**5/90 - 11*f**3/6 + 16*f**2. Let h(z) be the first derivative of q(z). Factor h(o).
4*o*(o + 1)/3
Let i(t) be the first derivative of -t**5/30 + t**4/2 - 5*t**3/3 + 7*t**2/3 + 13*t + 8. Let u(w) be the first derivative of i(w). Factor u(f).
-2*(f - 7)*(f - 1)**2/3
Suppose -h = -3*s + 4, 1 = 2*s + 5. Let a be ((-54)/45)/(3/h). Let w**4 - w**a - 3*w**2 + 3*w**4 = 0. Calculate w.
-1, 0, 1
Let m(g) = g**2 + 4*g - 6. Let a be m(-6). Factor a*q**2 - 10*q**2 - 9*q - 3*q.
-4*q*(q + 3)
Let b be 5886/10028 + 4/(-46). Factor 0*t + 0 - 2*t**2 + b*t**4 + 0*t**3.
t**2*(t - 2)*(t + 2)/2
Let b = -800 + 803. Let v(t) be the third derivative of 0 + 1/2*t**b - 5*t**2 - 1/80*t**5 + 0*t**4 + 0*t. Let v(y) = 0. What is y?
-2, 2
Factor -1835 - 1770 - 1579 - 4*a**2 - 288*a.
-4*(a + 36)**2
Let y be 11/(-11)*1/(-1). Let m(i) = 32*i + 2. Let a be m(y). Factor 8*x - 4*x**2 + 17*x**3 - a*x**3 + 13*x**3 + 0*x.
-4*x*(x - 1)*(x + 2)
Let c(u) be the second derivative of u**4/36 - 40*u**3/9 + 800*u**2/3 + 87*u - 2. Determine q, given that c(q) = 0.
40
Let f(a) = -a + 4. Let b be f(-6). Suppose -g + b = g. Factor 6*x**3 - 3*x**4 - g*x - x + 3 - x**4 + x**4.
-3*(x - 1)**3*(x + 1)
Let s(j) be the second derivative of j**7/168 + j**6/120 - 3*j**5/80 - j**4/48 + j**3/12 - 19*j. Suppose s(x) = 0. What is x?
-2, -1, 0, 1
Let i = -76 - -80. Suppose -2422*j**2 + 2426*j**2 + 2*j**3 - j**i + j**3 = 0. What is j?
-1, 0, 4
Let z be (50/(-40))/((-2)/48). Suppose -8*s = 2*s - z. Factor 4*a - 11/2*a**2 + 3/2*a**s + 2.
(a - 2)**2*(3*a + 1)/2
Let n(m) be the first derivative of 5*m**7/84 + m**6/4 + 3*m**5/8 + 5*m**4/24 + 12*m - 7. Let k(j) be the first derivative of n(j). Factor k(d).
5*d**2*(d + 1)**3/2
Let d(w) be the third derivative of w**5/210 - 55*w**4/84 - 8*w**3/3 + 354*w**2. Factor d(u).
2*(u - 56)*(u + 1)/7
Let o = -182 - -184. Suppose 3*f = -5*r + 29, 10 = o*r + 2. Let -3/8*t**f + 3/8*t - 3/8 + 3/8*t**2 = 0. What is t?
-1, 1
Suppose 0 = 5*z + 4*s - 40, 110 = -3*z + s + 117. Let u(b) be the first derivative of 2 + 4/9*b**3 + 0*b**2 + 1/12*b**z + 0*b. Solve u(n) = 0 for n.
-4, 0
Let b(f) = 3*f**4 + 28*f**3 - 4*f**2 + 4*f + 4. Let s(j) = -3*j**4 - 29*j**3 + 5*j**2 - 5*j - 5. Let d(h) = 5*b(h) + 4*s(h). Factor d(y).
3*y**3*(y + 8)
Let p = 125449/6 - 20908. What is m in 0*m + 1/2*m**2 - p*m**3 + 0 = 0?
0, 3
Let h(s) = 118*s**2 - 142*s**2 + 124*s**2 + 16 + 116*s. Let x(a) = 20*a**2 + 23*a + 3. Let u(i) = 5*h(i) - 24*x(i). Determine m so that u(m) = 0.
-1, -2/5
Suppose 4*h - 6 = -2*v, -2*v - 4*h = -5*v + 19. Let t(r) be the third derivative of 0*r + 0 - 5*r**2 + 1/6*r**3 + 0*r**4 - 1/60*r**v. What is g in t(g) = 0?
-1, 1
Let k(c) = -c**3 + 9*c**2 + 5*c + 20. Let q be k(10). Let z = q + 33. Factor -5*w**3 - 8*w + w**z + 24*w.
-4*w*(w - 2)*(w + 2)
Determine w so that 15/2*w**3 + 0 + 30*w + 78*w**2 = 0.
-10, -2/5, 0
Let b = 1292 - 1287. Factor -2/3*j**2 + 0 + 2*j**3 - 2*j**4 + 0*j + 2/3*j**b.
2*j**2*(j - 1)**3/3
Suppose -122*x = -117*x - 75. Determine o, given that 16*o**3 - 20*o - x*o**5 + 10*o**5 + 9*o**3 = 0.
-2, -1, 0, 1, 2
Let s(o) be the third derivative of -o**6/840 + o**5/420 + o**4/21 - 2*o**3/7 - 79*o**2 + 1. Factor s(b).
-(b - 2)**2*(b + 3)/7
Suppose -24*a + 52 = -44. Let x(c) be the third derivative of 0*c + 1/48*c**6 + 1/60*c**7 + 0*c**3 - 1/60*c**5 - c**2 + 0*c**a + 0. Factor x(v).
v**2*(v + 1)*(7*v - 2)/2
Let s(a) be the second derivative of -1/30*a**5 + 0 + 1/2*a**2 + 0*a**3 + 1/6*a**4 - 5*a. Let v(u) be the first derivative of s(u). What is t in v(t) = 0?
0, 2
Let a(j) be the third derivative of -j**5/690 - 49*j**4/276 + 200*j**2. Suppose a(p) = 0. What is p?
-49, 0
Let q(n) = -2*n**3 + 52*n**2 - 2*n - 11. Let k(a) = -a**3 + 18*a**2 - a - 4. Let r(p) = -11*k(p) + 4*q(p). Let r(b) = 0. What is b?
-3, -1/3, 0
Let u(l) = -16*l + 5. Let a(t) = -8*t + 3. Let m(k) = -7*a(k) + 3*u(k). Let o be m(1). Factor -1/3*x**4 + 0 + 1/3*x**3 + 0*x**o + 0*x.
-x**3*(x - 1)/3
Let q(v) be the first derivative of -5*v**6/6 - 2*v**5 + 15*v**4/4 + 7. Determine k, given that q(k) = 0.
-3, 0, 1
Let a(g) be the second derivative of g**7/1155 - g**6/220 + g**5/330 - 7*g**3/3 + 29*g. Let k(y) be the second derivative of a(y). Factor k(t).
2*t*(t - 2)*(4*t - 1)/11
Let l = 173 + -169. Let y(w) be the second derivative of -1/18*w**3 + 0 - l*w - 1/3*w**2 + 1/12*w**4. Factor y(b).
(b - 1)*(3*b + 2)/3
Let 0 - 4/3*d**5 - 124/3*d**2 - 16*d - 12*d**4 - 36*d**3 = 0. What is d?
-4, -3, -1, 0
Let y(q) = q**3 + 12*q**2 + 24*q - 7. Let x be y(-3). Solve -8/9*h - 2/9*h**x - 2/3 = 0.
-3, -1
Let k(s) be the third derivative of -s**6/240 - s**5/5 - 23*s**4/48 + 319*s**2 - s. Factor k(j).
-j*(j + 1)*(j + 23)/2
Let a be (-8)/32 + (-466)/(-8). Suppose 5*v - 3*v - a = 0. Factor 5*t**2 + 2*t + 31*t**3 - v*t**3 + 0*t.
t*(t + 2)*(2*t + 1)
Let r be (12 - 84/(-70)) + -13. Let r*m**3 + 0 + 1/5*m**2 + 0*m = 0. What is m?
-1, 0
Suppose t = -54 + 59. Let d(z) be the first derivative of 3 - 1/3*z + 1/18*z**6 + 1/6*z**2 - 1/15*z**t + 2/9*z**3 - 1/6*z**4. Factor d(v).
(v - 1)**3*(v + 1)**2/3
Let 0 + 2/3*v**4 + 0*v + 0*v**3 + 0*v**2 = 0. Calculate v.
0
Let a(l) = -20*l - 4. Suppose 0 = -2*n + 1 + 7. Let d(i) = i**2 - 20*i - 3. Let c(m) = n*d(m) - 3*a(m). Determine t, given that c(t) = 0.
0, 5
Let r(z) = 2*z**3 + 4*z - 2. Let q be r(1). Let a(p) be the first derivative of 0*p + 1/26*p**q - 2/65*p**5 + 0*p**2 - 3 + 4/39*p**3. Let a(b) = 0. Calculate b.
-1, 0, 2
Solve 32/5*s + 2*s**3 - 34/5*s**2 - 8/5 = 0.
2/5, 1, 2
Let n = -302 + 1511/5. Let p(j) be the first derivative of 2 + 0*j**4 - n*j**2 + 4/15*j**3 + 0*j - 4/25*j**5 + 1/15*j**6. Factor p(f).
2*f*(f - 1)**3*(f + 1)/5
Let h(d) be the first derivative of -5*d**3/3 - 15*d**2 - 40*d - 76. Factor h(p).
-5*(p + 2)*(p + 4)
Let k(s) = s**2 - 1. Let i(z) = -4*z**2 + z - 1. Let m(a) = 3*i(a) + 3*k(a). Let w(b) = 1 + b**2 + 7*b**2 + 4 - 2*b. Let f(v) = 5*m(v) + 6*w(v). Factor f(h).
3*h*(h + 1)
Let g be 2/((-1)/5*-2). Suppose -1 - 3 = -2*y + 4*w, -w - 10 = -g*y. Let 7*l - 10*l - 7*l**2 - 27*l**3 - 11*l**y = 0. Calculate l.
-1/3, 0
What is n in -44*n**2 + 94/3*n - 16/3 + 46/3*n**3 + 8/3*n**4 = 0?
-8, 1/4, 1
Let w be (-6)/51 - (-57)/340. Let z(u) be the first derivative of 0*u**2 + 3 + w*u**5 - 1/8*u**4 + 1/12*u**3 + 0*u. What is v in z(v) = 0?
0, 1
Suppose 2*w - 23*w + 63 = 0. Let z(r) be the second derivative of -1/240*r**6 + 0*r**2 + 0*r**4 + 0*r**w + 1/80*r**5 - 1/336*r**7 + 0 - 3*r. Factor z(b).
-b**3*(b - 1)*(b + 2)/8
Factor 2/5*b**3 + 32/5 - 18/5*b**2 + 12/5*b.
2*(b - 8)*(b - 2)*(b + 1)/5
Let m be 13/(455/30)*1. Let s = 67/406 + 7/58. Factor 4/7 - s*a + 2/7*a**3 + 2/7*a**4 - m*a**2.
2*(a - 1)**2*(a + 1)*(a + 2)/7
Let v = -1239 - -1241. Let q(k) be the second derivative of 0*k**v + 3*k - 3/10*k**5 + 0 + 4/3*k**3 - 1/15*k**6 + 0*k**4. Factor q(c).
-2*c*(c - 1)*(c + 2)**2
Let o be 1040/468 + 1 + (-44)/36. Factor 4/7*v - 4/7*v**3 + 16/7 - 16/7*v**o.
-4*(v - 1)*(v + 1)*(v + 4)/7
Let d(o) be the first derivative of o**5 - 185*o**4/2 + 2155*o**3 + 7030*o**2 + 7220*o + 32. Factor d(j).
5*(j - 38)**2*(j + 1)**2
Let o(q) = -q**2 + 6*q - 14. Let j be o(7). Let x be (2 - 27/j) + -3. Solve x*f - 2/7*f**2 + 4/7 = 0.
-1, 2
Let p(x) be the third derivative of x**5/30 - 5*x**4/2 + 75*x**3 - 85*x**2. Factor p(b).
2*(b - 15)**2
Let n(h) be the first derivative of h**8/9240 - h**6/330 - 2*h**5/165 - h**4/44 + 22*h**3/3 - 1. Let b(u) be the third derivative of n(u). Factor b(a).
2*(a - 3)*(a + 1)**3/11
Let u be (-120)/15*(1 + -2). Suppose 0 = -