
Let g = 387871/15 - 25868. Let k = g - -53/5. Suppose -k*i + 2/3*i**2 + 0 = 0. What is i?
0, 1
What is q in -38/7*q**2 - 66/7*q**3 - 8/7*q**5 + 0 - 6/7*q - 6*q**4 = 0?
-3, -1, -1/4, 0
Let 8/13 + 6/13*i - 2/13*i**2 = 0. What is i?
-1, 4
Let g be (11 - 2)/1 - 4. Factor 4*t**3 + g*t**3 - 8*t**3 - 2*t**3 + 2*t**2.
-t**2*(t - 2)
Factor 95/3*h**2 + 2*h + 0 + 31/3*h**3.
h*(h + 3)*(31*h + 2)/3
Let n(w) be the second derivative of w**10/6048 - w**8/672 + w**6/144 - w**4/2 - 18*w. Let p(j) be the third derivative of n(j). Solve p(s) = 0.
-1, 0, 1
Let h = -8839 + 8841. Factor -6/7 - 2/7*x**h + 8/7*x.
-2*(x - 3)*(x - 1)/7
Let c(t) be the second derivative of 0 - 5/9*t**4 + 4/9*t**3 - 1/30*t**6 - 30*t + 7/30*t**5 + 0*t**2. Factor c(d).
-d*(d - 2)**2*(3*d - 2)/3
Let b(d) be the second derivative of d**4/6 + d**3/3 - 6*d**2 - 66*d. Factor b(s).
2*(s - 2)*(s + 3)
Factor 3/2*t**3 - 57/2*t + 15 + 12*t**2.
3*(t - 1)**2*(t + 10)/2
Let y be 46/10 - (-78)/195. Let x(s) be the second derivative of 4*s + 1/2*s**4 + 3/10*s**y + 0*s**2 + 0 + 1/3*s**3 + 1/15*s**6. Factor x(v).
2*v*(v + 1)**3
Let y = -2/11965 - -7181/11965. Factor -6/5 + 6/5*q**3 - y*q**2 - 3*q.
3*(q - 2)*(q + 1)*(2*q + 1)/5
Let d(r) be the third derivative of -20*r**2 - 5/24*r**4 + 1/6*r**5 + 0*r + 1/24*r**6 + 0 - 5/3*r**3. Factor d(u).
5*(u - 1)*(u + 1)*(u + 2)
Let p(c) be the second derivative of c**6/20 - 3*c**5/4 + 19*c**4/8 - 3*c**3 + 37*c**2/2 + 4*c. Let s(b) be the first derivative of p(b). What is g in s(g) = 0?
1/2, 1, 6
Let x = 66 + -48. Factor 4 + 0 + 15*b - 2 + 1 - x*b**2.
-3*(b - 1)*(6*b + 1)
Let n = 5905/3 - 1967. Factor 2*o**3 + n*o**2 + 4/3*o**4 + 1/3*o**5 + 1/3*o + 0.
o*(o + 1)**4/3
Let k(l) be the third derivative of l**8/1176 + 3*l**7/245 + 13*l**6/210 + 3*l**5/35 - 9*l**4/28 - 9*l**3/7 + 269*l**2. Factor k(f).
2*(f - 1)*(f + 1)*(f + 3)**3/7
Factor -o**2 - o + 11*o + 4*o**2 + 39*o + 11*o.
3*o*(o + 20)
Let r(h) be the third derivative of 1/4*h**4 + 11*h**2 + 3/70*h**7 + 7/30*h**5 + 1/168*h**8 + 0*h + 0 + 1/6*h**3 + 2/15*h**6. Determine i so that r(i) = 0.
-1, -1/2
Suppose -l + 34 = 30. Solve -z**2 + 9*z - 5*z - 3*z**2 - 4*z**3 + 8*z**4 - l*z**2 = 0 for z.
-1, 0, 1/2, 1
Let q(l) be the second derivative of -7*l**5/20 - 13*l**4/6 - 13*l**3/6 + 3*l**2 - 2*l + 136. What is z in q(z) = 0?
-3, -1, 2/7
Let c(b) be the third derivative of -b**5/15 + 245*b**4/24 - 61*b**3/6 + 107*b**2 + b. Factor c(m).
-(m - 61)*(4*m - 1)
Let u(s) be the second derivative of -3*s**5/100 - s**4/5 + s**3/2 - 2*s + 31. Solve u(f) = 0 for f.
-5, 0, 1
Let f(g) = -23*g - 2093. Let q be f(-91). What is t in 0*t**2 - 1/4*t + q + 1/4*t**3 = 0?
-1, 0, 1
Let a(g) be the first derivative of g**4/24 - g**3/2 + 5*g**2/4 - 14*g + 11. Let t(z) be the first derivative of a(z). Factor t(s).
(s - 5)*(s - 1)/2
Determine v, given that -63*v**3 - 3*v**5 - 7*v**4 - 14*v**2 - 24*v - 64*v**2 - 17*v**4 + 12*v**2 = 0.
-4, -2, -1, 0
Let s(q) be the first derivative of q**5/60 + q**4/12 - 4*q**2 + 11. Let h(n) be the second derivative of s(n). Factor h(v).
v*(v + 2)
Let z = -266 + 278. Suppose -20*y = -z*y - 16. Factor 0 + 0*p - 1/3*p**y + 1/3*p**3.
p**2*(p - 1)/3
Let x = -1400 - -1405. Let q(f) be the second derivative of 6*f + 0*f**3 + 0*f**2 - 1/15*f**4 + 0 - 1/50*f**x + 1/75*f**6. Solve q(u) = 0.
-1, 0, 2
Suppose -5*o + 99 = 4*o. Factor 14*p + 6*p**5 + o*p - 128*p**2 + 7*p + 160*p**4 + 48*p**3 + 44*p**5.
2*p*(p + 2)**2*(5*p - 2)**2
Let m = -5018/5 + 1004. Factor -m*t**4 + 0*t**2 + 0 + 2/5*t**3 + 0*t.
-2*t**3*(t - 1)/5
Let l(y) be the first derivative of -y**6/40 + 3*y**5/40 - y**4/16 + 14*y + 7. Let h(p) be the first derivative of l(p). Find t, given that h(t) = 0.
0, 1
Let t(i) be the first derivative of 0*i + 5/3*i**3 + 20*i**2 + 11. Factor t(u).
5*u*(u + 8)
Find y such that -12*y + y + 60 - 5*y**2 - 7*y - 2*y = 0.
-6, 2
Suppose 0 = -18*y + 44*y. Find m, given that y*m - 1/2*m**2 + 0 = 0.
0
Let m be (-3 + (-28)/(-16))/((-14)/56). Let q(l) be the third derivative of 0 + 11/120*l**6 - 4*l**2 + 13/60*l**m + 0*l + 0*l**3 + 1/12*l**4. Factor q(i).
i*(i + 1)*(11*i + 2)
Let c(p) be the first derivative of p**6/24 - 17*p**5/12 + 105*p**4/8 + 135*p**3/2 - p**2 + 7*p + 49. Let k(h) be the second derivative of c(h). Factor k(z).
5*(z - 9)**2*(z + 1)
Let o(k) = k**5 - 6*k**4 - 7*k**3 - 4*k**2 + 2*k - 2. Let c(f) = f**5 + f**3 + f - 1. Let g(d) = -10*c(d) + 5*o(d). Let g(z) = 0. Calculate z.
-4, -1, 0
Let w be (-28)/3*(0 + 3). Let k be w/(-20)*(-30)/(-35). What is i in 0 + 2/5*i**4 - k*i**3 - 2*i**2 - 4/5*i + 2/5*i**5 = 0?
-1, 0, 2
Let p = 2231 - 17847/8. Determine o so that p*o**3 - 2 + 7/8*o**2 + o = 0.
-4, 1
Let k(x) be the third derivative of x**8/84 + 4*x**7/35 + 11*x**6/30 + 2*x**5/5 + 83*x**2. Factor k(p).
4*p**2*(p + 1)*(p + 2)*(p + 3)
Factor 13*h + 141*h**2 + 25*h**3 - 98*h - 96*h**2 + 14 + 1.
5*(h - 1)*(h + 3)*(5*h - 1)
Let x(s) be the second derivative of s**7/315 + s**6/90 - s**2 - 10*s. Let k(v) be the first derivative of x(v). Factor k(q).
2*q**3*(q + 2)/3
Suppose 3*g - 3 = 33. Find r such that -4*r**3 - 6*r + g*r**2 - 8*r + 6*r = 0.
0, 1, 2
Factor 8788 + 1014*v + 1/2*v**3 + 39*v**2.
(v + 26)**3/2
Suppose 5*t + 4*d - 75 = d, 2*t + 4*d - 44 = 0. Suppose 2*b + 9 + 11 = 5*w, 3*w - t = 0. Factor b + 4/3*x - 2/3*x**2.
-2*x*(x - 2)/3
Suppose -5 = 5*g + 5*x, 4*x - 1204 = 2*g - 1232. Solve 0 - 3/2*k**2 - 3/2*k**3 + 3/2*k + 3/2*k**g = 0 for k.
-1, 0, 1
Let w(m) be the second derivative of -2*m**6/15 + 18*m**5/5 - 17*m**4/3 + 2*m - 2. Factor w(d).
-4*d**2*(d - 17)*(d - 1)
Let p = 1/207 - 151/2691. Let i = 5/13 + p. What is r in 0*r - 1/3 + i*r**2 = 0?
-1, 1
Suppose 0 = -w + 1 + 4, 4*k + 4 = 4*w. Let 5 - k - v + 1 - v**2 = 0. What is v?
-2, 1
Solve -3/2*r**2 + 3/8*r**5 + 0 + 15/8*r - 9/4*r**3 + 3/2*r**4 = 0 for r.
-5, -1, 0, 1
Suppose -5*r - 2*y + 14 = 0, 0 = -5*r + 9*r + 3*y - 7. Let -3*j**4 - 43*j**3 - 15*j**r + 30*j**2 + 138*j**3 - 17*j**4 = 0. Calculate j.
-2/7, 0, 3
Let l(u) = 3*u**2 - 9*u + 6. Let p(g) = 3*g**2 - 9*g + 6. Let o(d) = -6*l(d) + 5*p(d). Factor o(x).
-3*(x - 2)*(x - 1)
Suppose -5*s - 177 = 3*l - 38, 12 = -4*l. Let h = s - -30. Factor -2*z**2 + 3*z**3 - z - z**3 + 2*z**h + 0*z - z.
2*z*(z - 1)*(z + 1)**2
Suppose -4 = 3*l - 10. Factor 8 + 19*v - 2*v**l + 27*v - 40*v.
-2*(v - 4)*(v + 1)
Let w(o) be the second derivative of -o**4/132 + 19*o**3/33 - 361*o**2/22 + 4*o + 8. Factor w(h).
-(h - 19)**2/11
Let g = -9941/2 - -4971. Let r be 1/36 + 2/9. Factor -g - r*q**2 + 3/4*q.
-(q - 2)*(q - 1)/4
Suppose -107*r + 16*r + 89 = -93. Solve -15/2*h + 5/2*h**r + 0 = 0.
0, 3
Let k be (2 + 3)/(60/36). Factor 3/4*y**2 + 9/4 + k*y.
3*(y + 1)*(y + 3)/4
Let s(y) be the first derivative of y**7/4200 - 13*y**6/1800 + 2*y**5/25 - 3*y**4/10 + 13*y**3/3 - 4. Let o(m) be the third derivative of s(m). Factor o(q).
(q - 6)**2*(q - 1)/5
Let s(t) = t - 7. Let z be s(11). Suppose -z*a - i + 0*i = -24, -4*a + i + 16 = 0. Find k such that -5*k**4 - 2*k**a - 3*k**4 + 4*k**4 = 0.
-2, 0
Let u(g) = -2*g - 10. Let k be u(-10). What is h in 17*h**4 + 9*h**4 - 27*h**3 - 4*h**5 + 8*h**2 - k*h**4 + 7*h**3 = 0?
0, 1, 2
Factor -22*b**3 + 2*b**4 + 84*b**2 + 32*b - 160*b - 2000 + 2064.
2*(b - 4)**2*(b - 2)*(b - 1)
Let n be (-4248)/(-234) + -18 + 4/(-26). Let m(l) be the second derivative of 2/3*l**3 + l + 0*l**2 + 5/6*l**4 + 1/15*l**6 + n + 2/5*l**5. Factor m(u).
2*u*(u + 1)**2*(u + 2)
Suppose 2100*l - 2109*l + 45 = 0. Solve -4/9*s**2 + 2/9*s**3 + 0 + 4/9*s**4 + 0*s - 2/9*s**l = 0.
-1, 0, 1, 2
Let w be 30/(-297) + 48/88. Let j(u) be the first derivative of 0*u**2 - 3 + 0*u - 1/9*u**6 - 5/6*u**4 + w*u**3 + 8/15*u**5. Factor j(f).
-2*f**2*(f - 2)*(f - 1)**2/3
Let t(p) = -5*p**3 - 5*p**2 - 3*p - 4. Let o be t(-4). Let q = o + -167. Factor -121*l**2 + 14*l + 108*l**5 + 17*l**2 - 351*l**4 + q*l**4 + 2*l + 252*l**3.
2*l*(2*l - 1)*(3*l - 2)**3
Let w(z) = 2*z**3 - 7*z**2 + 10*z + 4. Let p be w(6). Suppose 2*h = 5*v + 144, -v + 2*v = -4*h + p. Let 58 - h - 2*i**2 + 2*i + 4*i = 0. What is i?
1, 2
Let m(f) be the third derivative of f**5/20 - 13*f**4/8 + 20*f**3 - 555*f**2. Factor m(v).
3*(v - 8)*(v - 5)
Let i(y) be the second derivative of 0 + 1/4*y**5 + 10*y**3 + 55/12*y**4 - 1/2*y**6 + 10*y**2 - 5/42*y**7 + 17*y. Factor i(b).
-5*(b - 2)*(b + 1)**3*(b + 2)
Factor 179 - 356 +