 1)*(u + 2)/5
Let i(b) be the third derivative of 29*b**2 + 1/12*b**5 - 5/3*b**4 + 0*b + 0 + 40/3*b**3. Determine h, given that i(h) = 0.
4
Find w, given that -188*w - 4*w**3 + 133 - 202*w**2 - 1 + 262*w**2 + 0*w**3 = 0.
1, 3, 11
Let g be 8 + 50/5 + -18. Factor 1/3*q**3 - 2/3*q**2 + g*q + 0.
q**2*(q - 2)/3
Factor -27/7*k**4 - 15/7*k**2 - 48/7*k**3 + 6/7*k + 0.
-3*k*(k + 1)**2*(9*k - 2)/7
Let y(h) be the second derivative of h**4/16 + 3*h**3/2 + 33*h**2/8 - 293*h. Find r, given that y(r) = 0.
-11, -1
Let m(r) = -r**2 + 60*r + 193. Let t be m(-3). What is v in -1/3 + 1/6*v - 1/6*v**t - 1/6*v**3 + 1/2*v**2 = 0?
-2, -1, 1
Let t(n) = 9*n + 336. Let r be t(-37). Let a(z) be the first derivative of 16*z**2 + z**4 - 20/3*z**r - 1 - 16*z. Factor a(o).
4*(o - 2)**2*(o - 1)
Let a(d) = -255*d**2 - 185*d - 155. Let n(u) = 23*u**2 + 17*u + 14. Let l(p) = 4*a(p) + 45*n(p). Factor l(h).
5*(h + 1)*(3*h + 2)
Let m(u) be the second derivative of u**7/56 + 3*u**6/20 - 3*u**5/4 - 75*u**4/8 - 125*u**3/8 + 264*u. Find k, given that m(k) = 0.
-5, -1, 0, 5
Determine w so that 4882*w - 231*w**3 + 4888*w - 147*w**4 - 9782*w - 96*w**2 = 0.
-1, -2/7, 0
Let z = 827/1700 - -5/68. Let o = -3/50 + z. Factor b**4 + 0*b**3 - b**2 - o*b**5 + 1/2*b + 0.
-b*(b - 1)**3*(b + 1)/2
Determine n so that 352/9*n - 4/9*n**2 - 7744/9 = 0.
44
Let f(h) = -h**2 + 8*h - 7. Let q(w) = 3*w - 6. Let z be q(4). Let k be f(z). Let 5*a**2 + 0*a**2 + a**2 + 2*a**3 - 3*a - k*a**3 = 0. Calculate a.
0, 1
Suppose -4*b + 5*r + 143 = 100, -2*r = -4*b + 22. Factor 4/7 + 6/7*i + 2/7*i**b.
2*(i + 1)*(i + 2)/7
Let n(g) be the second derivative of 0*g**2 - 2/9*g**3 + 20*g + 0 - 1/135*g**6 + 1/63*g**7 - 19/54*g**4 - 17/90*g**5. Suppose n(z) = 0. Calculate z.
-1, -2/3, 0, 3
Let q(y) = -69*y**3 - 2*y**2 - 3*y - 2. Let z be q(-1). Let s = 409/6 - z. What is b in 0 - s*b - 1/6*b**2 = 0?
-1, 0
Let y = 26982 - 80945/3. Factor 2/3*x**3 + y - 4/3*x**4 + x**2 - 7/6*x + 1/2*x**5.
(x - 1)**3*(x + 1)*(3*x - 2)/6
Let d(q) be the third derivative of q**5/20 - 3*q**4 - 25*q**3/2 + 9*q**2 + 12*q. Let d(k) = 0. What is k?
-1, 25
Let k = -6020/3 - -2045. Let i = k + -343/9. What is a in 2 + i*a**2 + 4/3*a = 0?
-3
Let s(n) be the third derivative of n**6/120 + n**5/15 + 5*n**4/24 + n**3/3 - 18*n**2 + 1. Let s(b) = 0. What is b?
-2, -1
Let o be 248/60 + (520/(-39))/(-20). Factor -3/5*p**3 + 3*p**2 - o*p + 12/5.
-3*(p - 2)**2*(p - 1)/5
Find u such that 0 - 12/7*u**4 + 0*u + 64/7*u**2 - 2/7*u**5 + 0*u**3 = 0.
-4, 0, 2
Let g = 8001 + -7981. Find i, given that -70*i**2 + 0 - g*i**4 - 30*i - 5/2*i**5 - 115/2*i**3 = 0.
-3, -2, -1, 0
Let b be (-7)/(-3) + (-5)/15. Find g, given that -3*g**b + 40*g + 8*g**2 + 96 - 16 = 0.
-4
Let u(i) be the first derivative of i**6/324 + 7*i**5/540 + i**4/54 + 16*i**3/3 + 28. Let n(q) be the third derivative of u(q). Let n(y) = 0. What is y?
-1, -2/5
Let w be (10/(-6))/((-320)/128). Find r, given that -w + 4/9*r + 2/9*r**2 = 0.
-3, 1
Let v(c) be the first derivative of -2*c**5/45 + c**4/9 + 128*c**3/27 + 160*c**2/9 - 782. Factor v(j).
-2*j*(j - 10)*(j + 4)**2/9
Suppose 108/5*g - 18/5*g**2 - 216/5 + 1/5*g**3 = 0. What is g?
6
Suppose 0 = 258*f - 264*f. Let i(p) be the first derivative of 2/27*p**3 + 1/27*p**6 + f*p**2 - 2/45*p**5 - 6 + 0*p - 1/18*p**4. Factor i(s).
2*s**2*(s - 1)**2*(s + 1)/9
Let m be (-3 + 2121/657)*(-14)/(-5). Let o = 2/73 + m. Let 7/6*d**2 + 1/6*d**3 + 0*d - 1/2*d**4 - 1/6*d**5 - o = 0. What is d?
-2, -1, 1
Let o(n) be the third derivative of -n**5/10 - 3*n**4/8 + 101*n**2 + 2*n. Solve o(z) = 0.
-3/2, 0
Let p = -604 + 607. Let g(o) be the first derivative of 0*o**2 - 4 + 2/3*o**p - 8*o. Factor g(q).
2*(q - 2)*(q + 2)
Let x = -14 - -31. Factor x*f + 7*f + 4*f**2 + 2*f - 6*f - 24.
4*(f - 1)*(f + 6)
Let d(p) be the second derivative of -p**4/48 - p**3/4 - 5*p**2/8 + 4*p + 7. Let d(k) = 0. Calculate k.
-5, -1
Let w(z) = 6*z - 27. Let y be w(5). Let u(m) be the first derivative of -63/5*m**5 + 3 + 3/2*m**2 + 23*m**y - 3/4*m**4 - 6*m. Determine a so that u(a) = 0.
-1, -1/3, 2/7, 1
Let t be (-137)/3014 - 49/(-110). Solve 4/5*v**2 - 2/5*v**3 + 0 + t*v - 4/5*v**4 = 0 for v.
-1, -1/2, 0, 1
Let d(t) be the second derivative of 0 - 9/10*t**5 - 4/3*t**4 - 28*t + 0*t**2 + 8/15*t**6 + 5/21*t**7 + 4/3*t**3. Determine s, given that d(s) = 0.
-2, -1, 0, 2/5, 1
Let w(q) = -3*q**2 - 53*q. Let x(c) = -8*c**2 - 158*c. Suppose -3*s + v + 4 = 5, 4*s - 4*v - 12 = 0. Let g(u) = s*x(u) + 7*w(u). Factor g(p).
-5*p*(p + 11)
Let g(w) be the first derivative of -2*w**3/27 + w**2/9 + 4*w/3 + 108. Factor g(f).
-2*(f - 3)*(f + 2)/9
Let v(x) be the first derivative of x**5 + 5*x**4/2 - 5*x**3 - 10*x**2 + 20*x - 136. Suppose v(q) = 0. Calculate q.
-2, 1
Let g(m) be the first derivative of 2*m**5/15 - 4*m**3/3 + 8*m**2/3 - 2*m - 130. Suppose g(c) = 0. Calculate c.
-3, 1
Let i(a) be the second derivative of 3/10*a**5 - 6*a + 0 - 11/18*a**4 + 1/126*a**7 - 1/2*a**2 - 7/90*a**6 + 13/18*a**3. Find j, given that i(j) = 0.
1, 3
Let f(j) be the first derivative of -2*j**5/5 - j**4/42 + 2*j**3/21 + 5*j + 26. Let w(h) be the first derivative of f(h). Factor w(i).
-2*i*(4*i - 1)*(7*i + 2)/7
Suppose 30 = 4*c - 5*c. Let z be -6 + 6 + (-3)/c*4. Find g, given that 2/5*g**2 + 2/5*g**3 - z - 2/5*g = 0.
-1, 1
Suppose 3*q - 3*q**3 + 8/5 - 2*q**2 + 2/5*q**4 = 0. Calculate q.
-1, -1/2, 1, 8
Let z = 8387/2 + -4192. Solve z*d + 1/2*d**2 - 3/2*d**3 - 1/2 = 0.
-1, 1/3, 1
Suppose -30*a + 17 - 3*a**2 + 0*a**2 - 2*a**2 + 63 = 0. What is a?
-8, 2
Let j(m) be the third derivative of m**7/2100 - m**6/1200 - m**5/300 + m**2 - 12. Factor j(n).
n**2*(n - 2)*(n + 1)/10
Find s, given that 66*s + 43*s**2 + 90 - 7*s**3 + 5*s**3 - 69*s**2 = 0.
-15, -1, 3
Let h(m) be the third derivative of m**6/1080 - m**5/72 + m**4/18 + 5*m**3/6 - m**2. Let w(x) be the first derivative of h(x). Let w(n) = 0. Calculate n.
1, 4
Let c(j) be the second derivative of -j**4/4 + 7*j**3/2 + 12*j**2 - 91*j. What is l in c(l) = 0?
-1, 8
Let r = -17315/3 + 34639/6. Factor 0 + r*w**3 + 3*w**4 + 0*w + 0*w**2 + 3/2*w**5.
3*w**3*(w + 1)**2/2
Suppose 0 = -12*o + 142 + 194. Factor 9*p**2 + 8*p**4 - 13*p**2 - 32*p**4 - o*p**3.
-4*p**2*(p + 1)*(6*p + 1)
Let u(y) = 2*y - 37. Let b be u(20). Factor -v**4 - v**4 - v**3 + v**3 - 2*v**b.
-2*v**3*(v + 1)
Factor 3/5*r**5 + 6/5*r**2 + 9/5*r - 12/5*r**3 - 6/5 + 0*r**4.
3*(r - 1)**3*(r + 1)*(r + 2)/5
Suppose 11 = -4*v + 11. Factor -65*t + v*t**2 + 50*t - 5*t**2.
-5*t*(t + 3)
Let y(i) be the second derivative of i**6/60 + 3*i**5/20 - i**4/24 - i**3/2 + i + 48. Factor y(b).
b*(b - 1)*(b + 1)*(b + 6)/2
Let q(y) = -y + 4. Let b be q(4). Let f(o) be the third derivative of 0 - 1/10*o**5 + 0*o - 2*o**2 + 3/40*o**6 - 1/8*o**4 + b*o**3. Factor f(p).
3*p*(p - 1)*(3*p + 1)
Let u(k) be the second derivative of k**6/40 + 11*k**5/20 + 35*k**4/8 + 25*k**3/2 + 5*k**2/2 - 32*k. Let n(i) be the first derivative of u(i). Factor n(o).
3*(o + 1)*(o + 5)**2
Let h = -8/4257 + 51140/29799. Find z such that -22/7*z + h + 6/7*z**2 = 0.
2/3, 3
Let z = 9 - 1. Let p(c) = 2*c - 12. Let g be p(z). What is x in -25*x + 33*x - 8*x**3 - 4*x**3 - g*x**2 = 0?
-1, 0, 2/3
Let j(k) be the third derivative of k**9/5040 + k**8/1120 + 19*k**4/12 + 43*k**2. Let s(r) be the second derivative of j(r). Factor s(z).
3*z**3*(z + 2)
Let i(c) be the second derivative of -c**4/42 - 4*c**3/21 + 5*c**2/7 + 76*c. Solve i(b) = 0 for b.
-5, 1
Let s(j) be the first derivative of -j**5/50 - j**4/30 + 2*j**3/15 - 23*j + 35. Let o(l) be the first derivative of s(l). Factor o(t).
-2*t*(t - 1)*(t + 2)/5
Let v(k) be the first derivative of k**4 - 12*k**3 - 59. Solve v(x) = 0.
0, 9
Let a(y) be the first derivative of -3*y**4/4 - 6*y**3 + 96*y + 264. Suppose a(d) = 0. What is d?
-4, 2
Let m = -49853/5 + 9973. Factor 0 + 12/5*b**3 + 4/5*b - m*b**2 - 4/5*b**4.
-4*b*(b - 1)**3/5
Let c(k) be the first derivative of -k**2/2 + 11*k - 1. Let i be c(8). Factor 2/3*b**2 - 2/3*b**i + 1/3*b**5 - 1/3*b**4 - 1/3 + 1/3*b.
(b - 1)**3*(b + 1)**2/3
Let k be 14 + 2180/(-110) + 6. Factor -4/11*f + 2/11*f**2 + k.
2*(f - 1)**2/11
Let g = 35/3 + -34/3. Let u(j) be the second derivative of g*j**2 - 8*j - 1/18*j**3 + 0 - 1/36*j**4. Find d, given that u(d) = 0.
-2, 1
Let d(t) = -2*t**3 - 2*t**2 - 4*t. Let i(n) = n**3 + n**2 + 2*n. Let u(v)