i + 20*i**2 + 3*i - 4*i**t.
-4*(i - 2)**2*(i - 1)
Let o = -553/232 - -80/29. Find j, given that -3/4 + 3/8*j + o*j**2 = 0.
-2, 1
Factor 0 + 0*t + 1/3*t**5 + 280*t**3 - 300*t**2 + 59/3*t**4.
t**2*(t - 1)*(t + 30)**2/3
Let m(l) be the first derivative of -l**9/5292 + l**7/1470 + 13*l**3/3 + 12. Let g(d) be the third derivative of m(d). Let g(u) = 0. Calculate u.
-1, 0, 1
Let w = -30739 + 154091/5. Solve 33/5*p - 84/5*p**5 + 162/5*p**2 - 18/5 + w*p**4 - 489/5*p**3 = 0 for p.
-2/7, 1/2, 1, 3
Let s = -2253 - -2257. Factor 0*b**2 - 1/2*b**s + 0*b + 0 - 1/2*b**3.
-b**3*(b + 1)/2
Suppose 3*j - 11 - 10 = 0. Suppose -19 = -3*s - 2*g, -j*s = -2*s - 3*g. Solve -n**3 + 2*n**3 - 3*n**s - n**4 - 4 + 5 + 2*n = 0 for n.
-1, 1
Let w(l) be the first derivative of -9*l**5/20 + 11*l**4/8 - l**3 + 3*l**2 + 5. Let b(v) be the second derivative of w(v). Let b(r) = 0. Calculate r.
2/9, 1
Let 1044 + 125*j - 3744 - 3*j**2 + 55*j = 0. Calculate j.
30
Let a = -192 - -192. Let z(n) be the third derivative of a*n**4 + 0 + 1/945*n**7 - 1/270*n**5 + 0*n + 3*n**2 + 0*n**3 + 0*n**6. Factor z(r).
2*r**2*(r - 1)*(r + 1)/9
Let g(y) be the first derivative of 4*y**5/5 + 102*y**4 + 4624*y**3 + 78608*y**2 + 36. Factor g(h).
4*h*(h + 34)**3
Suppose 4*y + 3*w = -495, 5*y = -5*w - 381 - 234. Let f be (-100)/y - (-1)/(27/(-6)). Factor 2/7*x**5 - 4/7*x**2 - f*x**3 + 2/7*x**4 + 2/7*x + 2/7.
2*(x - 1)**2*(x + 1)**3/7
Suppose -5*z + y + 9 = 0, -3*z + 2*y = -0*z - 4. Let 63*o + 105*o + 1 + 196*o**z + 11 + 24 = 0. Calculate o.
-3/7
Let i be -5*-1*2/2. Suppose 0 = -h + i*h - 8. Factor -2 + 5 + 3*n**h + 9*n + 3.
3*(n + 1)*(n + 2)
Suppose -16*g + 32 = -8*g. Let f(m) be the first derivative of 5/2*m**2 + 15/4*m**g + 0*m + m**5 + 3 + 5*m**3. Find o, given that f(o) = 0.
-1, 0
Suppose 0 = 227*x - 310*x + 166. Factor 0*u - 1/2 + 1/2*u**x.
(u - 1)*(u + 1)/2
Let b(l) = -9*l**3 - 15*l**2 - 53*l + 28. Let y(r) = -5*r**3 - 10*r**2 - 27*r + 14. Let f(v) = -4*b(v) + 7*y(v). Determine i so that f(i) = 0.
1, 2, 7
Suppose 8*u - 5*u = -75. Let m = 27 + u. Let -m*f**2 - 5 - 4*f + 5*f**2 - 4 + 10*f = 0. What is f?
-3, 1
Let x(j) be the second derivative of 0 - j**3 + 1/15*j**6 - 7*j + 3/10*j**5 - 2*j**2 + 1/6*j**4. Factor x(a).
2*(a - 1)*(a + 1)**2*(a + 2)
Let p be (24/176)/((-6)/(-5)*20/32). Solve -6/11*b**2 + p*b + 4/11 = 0.
-2/3, 1
Let t(x) be the second derivative of 1/22*x**4 + 4/33*x**3 + 1/11*x**2 + 0 + 16*x. Suppose t(o) = 0. Calculate o.
-1, -1/3
Suppose 3*m - 3*r = -3, -2*m - 2*r + 0 + 14 = 0. Let l(w) be the first derivative of -8/5*w**m + 32/5*w + w**4 - 8/5*w**2 - 4/25*w**5 - 1. Factor l(t).
-4*(t - 2)**3*(t + 1)/5
Let m(a) = -a**3 - a**2 - 3*a - 68. Let d be m(0). Let p = d + 70. Factor -3/2*f**3 - 1/2*f**4 - 3/2*f**p - 1/2*f + 0.
-f*(f + 1)**3/2
Factor -3/2*y**2 + 60*y - 600.
-3*(y - 20)**2/2
Let r be 760/(-570)*(2 + 36/(-16)). Determine w, given that 1/3*w**5 + 0 + 8*w**2 + r*w**3 + 16/3*w - 2*w**4 = 0.
-1, 0, 4
Factor 6936/11*g + 128/11*g**3 + 1632/11*g**2 + 9826/11.
2*(4*g + 17)**3/11
Suppose 14 = 2*n - 2. Let h be n/32 - 14/(-8). Determine u, given that -u**4 + h*u**5 + u**5 - 2*u**4 = 0.
0, 1
Let y be (3/2 + 3)/6. Let k = -1235 - -4943/4. Factor 0 - k*t**4 + 3/4*t**2 + y*t**3 - 3/4*t.
-3*t*(t - 1)**2*(t + 1)/4
Let b(t) be the first derivative of -12 + 0*t - 5/2*t**2 + 5*t**3 + 5/4*t**4 - 3*t**5. Let b(p) = 0. What is p?
-1, 0, 1/3, 1
Suppose 6*v + 46 = 4*v. Let y be (-8)/12 - v/12. Let -y*i - 3/4 - 1/2*i**2 = 0. Calculate i.
-3/2, -1
Factor -3*c - 3/2*c**4 - 2*c**3 + 13/2*c**2 + 0.
-c*(c - 1)*(c + 3)*(3*c - 2)/2
Solve -4*v**2 + 6443*v - 6459*v - 9 - 5 + 2*v**2 = 0.
-7, -1
Let f(u) be the third derivative of 15*u**2 - 7/30*u**6 - 11/6*u**4 + 0*u + 0 + 16/15*u**5 + 4/3*u**3. Find p such that f(p) = 0.
2/7, 1
Let n = 74 - 72. Let -16*r**5 + 12*r**3 - 8*r**2 + 0*r**n + 3*r**3 + r**4 + 7*r**4 + r = 0. What is r?
-1, 0, 1/4, 1
Let b be 4531/345 - 2/15. Factor 11 - 19 - 5*o**2 + 14 - b*o.
-(o + 3)*(5*o - 2)
Factor 4/9*c**3 + 40/9 + 16/3*c**2 + 28/3*c.
4*(c + 1)**2*(c + 10)/9
Let y = -12005 - -12007. Factor 0 + 4/3*n**4 + 0*n + 4/3*n**3 + 0*n**y.
4*n**3*(n + 1)/3
Let v(k) be the third derivative of -k**6/8 - k**5/12 + 5*k**4/6 + 18*k**2. Determine b, given that v(b) = 0.
-4/3, 0, 1
Let m(o) = 100*o**3 + 73*o**2 - 22*o - 7. Let f(h) = 100*h**3 + 77*h**2 - 23*h - 8. Let x(w) = -3*f(w) + 2*m(w). Factor x(u).
-5*(u + 1)*(4*u + 1)*(5*u - 2)
Suppose 202*o**4 + 4*o - 18*o**2 + 48*o**5 - o - 130*o**4 + 3*o**3 = 0. Calculate o.
-1, 0, 1/4
Let b(s) = 5*s**4 + 35*s**3 + 48*s**2 - 2. Let c(j) = -135*j**4 - 945*j**3 - 1295*j**2 + 55. Let a(d) = 55*b(d) + 2*c(d). Factor a(n).
5*n**2*(n + 2)*(n + 5)
What is q in 2*q**3 - 24 + 12*q**2 - 1443*q + 730*q + 723*q = 0?
-4, -3, 1
Suppose -2*n + 10 = 5*q, -6*n - 15 = 4*q - 9*n. Let x(j) be the third derivative of 2/15*j**5 + q*j + 1/30*j**6 + 5*j**2 - 1/6*j**4 + 0 - 4/3*j**3. Factor x(i).
4*(i - 1)*(i + 1)*(i + 2)
Let b = -863 - -865. Let f(g) be the first derivative of 8/3*g**3 - g**4 + 1 - 2*g**b + 0*g. Solve f(y) = 0 for y.
0, 1
Let n(w) be the first derivative of 2/3*w**2 + 1/6*w**4 + 0*w - 2/3*w**3 + 3. Factor n(s).
2*s*(s - 2)*(s - 1)/3
Let b(o) be the second derivative of 5*o**7/42 - 16*o**6/3 + 337*o**5/4 - 3335*o**4/6 + 5590*o**3/3 - 3380*o**2 - 3*o - 32. Determine t, given that b(t) = 0.
2, 13
Let l(k) be the first derivative of 4*k**3/3 - 22*k**2 + 72*k + 4. Suppose l(r) = 0. What is r?
2, 9
Let b(a) be the second derivative of 1/6*a**6 + 8*a + 0*a**2 + 1/3*a**3 + 1/42*a**7 + 7/12*a**4 + 9/20*a**5 + 0. Factor b(v).
v*(v + 1)**3*(v + 2)
Let y(q) = -11*q**3 - 19*q**2 + 4*q + 12. Let f(n) = 6*n**3 + 10*n**2 - 2*n - 6. Suppose 4*l + 12 = -4. Let d(r) = l*y(r) - 7*f(r). Suppose d(o) = 0. What is o?
-3, -1, 1
Suppose 16 = -250*k + 258*k. Suppose 0*o + 2/9*o**3 + 0 - 4/9*o**k = 0. What is o?
0, 2
Let z(q) be the first derivative of -2*q**6/21 - 4*q**5/7 - 9*q**4/7 - 4*q**3/3 - 4*q**2/7 - 74. Factor z(w).
-4*w*(w + 1)**3*(w + 2)/7
Suppose 0 = 3*n - 3*j - 3, -5*n - 2*j - 9 = 7. Let c = n + 2. Factor 2 + c + 8 - 4*r**2 - 2 + 4*r.
-4*(r - 2)*(r + 1)
Let o = -23 - -26. Let a(t) be the third derivative of 0*t**4 + 0*t - 1/40*t**5 - 3*t**2 + 0*t**o + 0 + 1/240*t**6. Factor a(g).
g**2*(g - 3)/2
Let x(k) be the second derivative of -k**4/3 + 10*k**3 + 32*k**2 + 6*k + 4. Factor x(v).
-4*(v - 16)*(v + 1)
Suppose -f + 3*f + 111 = 3*g, 2*f = -5*g - 135. Let h = 140 + f. Determine a, given that -52*a**3 + 177*a**3 - 15*a**2 - h*a - 10*a**2 - 20 = 0.
-2/5, 1
Let s be ((-1)/((-3)/(-6)*12))/(10/(-40)). Solve s*v**2 + 0 - 16/3*v = 0 for v.
0, 8
Let g(j) be the second derivative of j**6/450 - j**5/600 + 5*j**3/3 + j. Let d(w) be the second derivative of g(w). Solve d(f) = 0.
0, 1/4
Let f(y) = 10*y**2 - 10*y + 5. Let m(z) = z**3 + 10*z**2 - 11*z + 4. Suppose -4*k + 27 = -k + 3*b, -3*k = -5*b + 13. Let q(g) = k*f(g) - 5*m(g). Factor q(c).
-5*c*(c - 1)*(c + 3)
Let p = -1655 + 1657. Factor 242/3*d**4 + 8/3*d**p + 0*d + 0 + 88/3*d**3.
2*d**2*(11*d + 2)**2/3
Let w = 369/2 - 184. Let t(c) be the first derivative of -1/10*c**5 + 1/2*c - 1/4*c**4 + 0*c**3 + 1 + w*c**2. Solve t(u) = 0.
-1, 1
Let m(o) be the first derivative of 4*o**3 - 94*o**2 + 120*o - 720. Solve m(h) = 0.
2/3, 15
Suppose -5*i = -4*s - 3*i + 8, 5*s + i = 10. Factor 3 - 6*m + m**4 - 3 + s*m + 3*m**3.
m*(m - 1)*(m + 2)**2
Let b = 7 + -25/4. Let z be 5/2*8/10. Determine y, given that -b*y - y**z + 1/4 = 0.
-1, 1/4
Let q(k) = -71*k - 636. Let y be q(-9). Factor 10/13*n**2 + 2/13*n**y + 6/13*n - 18/13.
2*(n - 1)*(n + 3)**2/13
Let g = 67811/5 + -13562. Solve -8/5*y + 0 - g*y**2 = 0.
-8, 0
Let i = -139 + 142. Let g(k) be the first derivative of -11/8*k**2 - 2 + 1/2*k + 4/3*k**i - 7/16*k**4. Factor g(u).
-(u - 1)**2*(7*u - 2)/4
Let y(i) be the first derivative of i**4 - 32*i**3 + 288*i**2 + 199. Factor y(m).
4*m*(m - 12)**2
Let b(t) be the second derivative of 43*t + 0 - 1/10*t**6 + 1/10*t**5 + 1/2*t**2 + 1/42*t**7 - 1/2*t**3 + 1/6*t**4. Factor b(g).
(g - 1)**4*(g + 1)
Let x(t) be the first derivative of t**3/15 + 57*t**2/10 + 228. Let x(w) = 0. Calculate w.
-57, 0
Let o(t) = 4*t**2 + 5*t - 12. Let b(r) = 2*r**2 + 32*r - 4. Let j be b(-16). Let p(x) = -4*x**2 - 4*x + 12. Let a(d) = j*o(d) - 3*p(d). Factor a(v).
-4*(v - 1)*(v + 3)
Let