*y - 32)/3
Let b(n) be the first derivative of -6 + 43*n**3 - 93/2*n**2 - 27/5*n**5 - 27/4*n**4 + 18*n. Suppose b(t) = 0. What is t?
-3, 1/3, 2/3, 1
Let n(d) be the third derivative of -1/5*d**3 + 0*d + 1/100*d**5 + 13*d**2 + 0 - 1/40*d**4. Factor n(h).
3*(h - 2)*(h + 1)/5
Let i = -35 + 18. Let v = 20 + i. Factor -w**2 - 8*w**3 + 2*w**v - 2*w**4 + w**2 - 4*w**2.
-2*w**2*(w + 1)*(w + 2)
Let w be -11 + 3 + 2 + 88/11. Let d = -118 + 251/2. Factor 3*k + d*k**w + 9/2*k**3 - 3/2*k**4 - 3/2*k**5 + 0.
-3*k*(k - 2)*(k + 1)**3/2
Let h(g) = g + 57. Let d be h(-55). Find k, given that -4/5*k + 8/5*k**3 + 4/5*k**d - 2/5*k**4 - 4/5*k**5 - 2/5 = 0.
-1, -1/2, 1
Suppose -3*n + 3 - 5 + 2 = 0. Find g such that -3*g + 6*g**2 + n - 15/4*g**3 + 3/4*g**4 = 0.
0, 1, 2
Factor -12*m - 16*m - 1 + 4*m**2 + 31*m.
(m + 1)*(4*m - 1)
Let y be (-55)/(-20) - (-3)/(-4). Suppose -165 + 161 = -y*l. Solve 2/3*k + 0 - 2/3*k**l - 2/3*k**3 + 2/3*k**4 = 0 for k.
-1, 0, 1
Let k(w) be the second derivative of w**8/112 - 2*w**7/35 + w**6/10 + 6*w**2 + 3*w. Let y(t) be the first derivative of k(t). Let y(x) = 0. Calculate x.
0, 2
Let p(k) = 3*k + 12. Let f(g) = -3*g - 13. Let t(b) = -4*f(b) - 5*p(b). Let c be t(-4). Factor -1/2*m**c + m**3 + 0*m**2 + 0 + 0*m.
-m**3*(m - 2)/2
What is z in -z**4 + 2463774 - 2463774 - 2*z - 4*z**3 - 5*z**2 = 0?
-2, -1, 0
Let q(o) be the second derivative of -103/140*o**5 + 3/7*o**4 + 33/70*o**6 + 0 - 2/21*o**7 - 2/21*o**3 - o + 0*o**2. What is x in q(x) = 0?
0, 1/4, 2/7, 1, 2
Let a(p) be the first derivative of 5*p**3/3 - 635*p**2/2 + 630*p + 266. Factor a(g).
5*(g - 126)*(g - 1)
Factor -6750*d**2 + 48 + 81 + 6747*d**2 - 126*d.
-3*(d - 1)*(d + 43)
Let s(j) be the third derivative of -j**7/840 + j**6/16 - 157*j**5/240 - 85*j**4/8 - 289*j**3/6 + 209*j**2. Factor s(h).
-(h - 17)**2*(h + 2)**2/4
Let k = 71 - 68. Determine s so that -2/9*s**4 + 0*s + 4/9*s**2 + 0*s**k - 2/9 = 0.
-1, 1
Let q(h) = -5*h**3 - 7*h**2 + 12. Let r(i) = -11*i**3 - 14*i**2 - i + 25. Let k(w) = 13*q(w) - 6*r(w). Let a(x) = -1. Let j(o) = 6*a(o) + k(o). Factor j(v).
v*(v - 6)*(v - 1)
Determine k, given that 444/7*k + 2/7*k**2 + 24642/7 = 0.
-111
Suppose 64 = -3*t + q, -3*t + 17 = -5*q + 85. Let k = 25 + t. Factor 3/4*v**2 + 0*v + 0 + 3/4*v**k + 3/2*v**3.
3*v**2*(v + 1)**2/4
Let l(j) = -2*j**2 - 5*j - 1. Let t(a) = -a - 1. Let z = 19 + -15. Suppose -4*u + 0*u = -z. Let i(p) = u*t(p) - l(p). Factor i(x).
2*x*(x + 2)
Let q = 12032 + -60158/5. Factor 0*p**3 + q*p**2 + 0*p - 2/5*p**4 + 0.
-2*p**2*(p - 1)*(p + 1)/5
Factor 2/13*k + 16/13*k**2 - 2/13*k**3 - 16/13.
-2*(k - 8)*(k - 1)*(k + 1)/13
Factor 0 + 2/5*z**4 + 0*z**2 - 6/5*z**3 + 8/5*z.
2*z*(z - 2)**2*(z + 1)/5
Find k, given that 2/5*k**3 - 12/5*k**2 - 14/5*k + 0 = 0.
-1, 0, 7
Let l(n) be the third derivative of -n**6/780 - 19*n**5/65 - 361*n**4/13 - 54872*n**3/39 + 621*n**2. Factor l(a).
-2*(a + 38)**3/13
Let q = 13529/4 + -3382. Factor -1/4*u**2 - q + 1/2*u.
-(u - 1)**2/4
Suppose 8*f - 15 = 3*f. Suppose -f*u + 12 = u. Factor -k**u - 3*k**5 + 2*k**3 - 3*k + 5*k**3.
-3*k*(k - 1)**2*(k + 1)**2
Let n(u) be the first derivative of -u**4/34 - 56*u**3/51 - 196*u**2/17 - 238. Determine f, given that n(f) = 0.
-14, 0
Let t(i) be the third derivative of -5*i**8/336 - 11*i**7/42 - i**6/3 + 5*i**5/3 - 3*i**2 - 29. Let t(w) = 0. What is w?
-10, -2, 0, 1
Suppose 0 = 3*z - 5*m + 43, -2*z + 4 = 4*m - 4. Let f(a) = 9*a**2 + 9*a. Let o(c) = -c**2 - c - 1. Let p(g) = z*o(g) - f(g). Suppose p(y) = 0. What is y?
-2, 1
Determine k so that 69/5*k + 3/5*k**4 - 36/5 - 9/5*k**3 - 27/5*k**2 = 0.
-3, 1, 4
Let y(x) be the second derivative of -x**5/60 - 17*x**4/36 - 18*x - 2. Factor y(b).
-b**2*(b + 17)/3
Let g(o) be the second derivative of -o**7/63 - o**6/9 - 3*o**5/10 - 7*o**4/18 - 2*o**3/9 + o + 99. Determine s, given that g(s) = 0.
-2, -1, 0
Let c be (-2)/(-2) + (-560)/575. Let n = 209/805 + c. Suppose 0 - n*d**5 + 2/7*d**4 - 2/7*d**2 + 0*d + 2/7*d**3 = 0. What is d?
-1, 0, 1
Let v(b) be the second derivative of b**5/5 - 17*b**4/3 - 12*b**3 + 209*b + 2. Determine k, given that v(k) = 0.
-1, 0, 18
Let k(l) be the first derivative of -l**6/36 + 11*l**5/30 + 19*l**4/8 - 227*l**3/18 + 61*l**2/3 - 14*l - 277. Find o, given that k(o) = 0.
-6, 1, 14
Let i(g) = 33*g + 301. Let y be i(-9). Let x(v) be the second derivative of 0*v**y + 0*v**2 + 1/140*v**5 - 2/21*v**3 - 7*v + 0. Factor x(h).
h*(h - 2)*(h + 2)/7
Let b be (-1 + 6)*2/10*2. Factor -6/13*r**4 + 4/13*r**b + 2/13 + 6/13*r - 2/13*r**5 - 4/13*r**3.
-2*(r - 1)*(r + 1)**4/13
Suppose -3*c = 2*d - 523, 4*c + c - 533 = -2*d. Let b = -252 + d. Find p such that 1/2*p + 0 - b*p**2 + 3/2*p**3 = 0.
0, 1/3, 1
Let y(j) be the second derivative of 1/60*j**4 + 0*j**2 + 1/15*j**3 - 1/100*j**5 + 0 + 19*j. Let y(o) = 0. What is o?
-1, 0, 2
Determine h so that 112/3*h + 14*h**2 - 6*h**4 - 32 - 38/3*h**3 - 2/3*h**5 = 0.
-4, -3, 1
Factor 12 - 4*s**4 + 0*s**4 - 5*s**2 - s**5 + 5*s**4 - s**3 + 10*s**3 - 16*s.
-(s - 3)*(s - 1)**2*(s + 2)**2
Find q such that -14/5*q**2 + 0 + 4/5*q**3 + 2/5*q**4 + 8/5*q = 0.
-4, 0, 1
Let t = -1829 + 1832. Let s = -4/33 + 49/132. Factor -1/4*f**t - 1/2 + 1/2*f**2 + s*f.
-(f - 2)*(f - 1)*(f + 1)/4
Suppose -k + 72 = 8*k. Find i, given that k - 3*i**2 - 19*i - 14 + 10*i = 0.
-2, -1
Let w(q) = -2*q**2 + 54*q - 6. Let c be w(24). Let a = c - 964/7. Suppose 4/7*u**2 - a + 2/7*u = 0. What is u?
-1, 1/2
Let w(g) be the first derivative of -g**6/24 + g**5/3 + 4*g**2 + 18. Let v(j) be the second derivative of w(j). Factor v(r).
-5*r**2*(r - 4)
Suppose 5*v - 44 = 21. Let x be 6/15 + v/5. What is q in -2*q**4 - 9*q**2 + 2*q - 4*q**4 - q**2 + 14*q**x = 0?
0, 1/3, 1
Let j(c) be the first derivative of c**6/24 - 5*c**5/12 - 7*c**2 - 3. Let n(y) be the second derivative of j(y). Solve n(r) = 0 for r.
0, 5
Let v(p) be the second derivative of p**4/15 - 3*p**3/5 - p**2 + 118*p. Factor v(x).
2*(x - 5)*(2*x + 1)/5
Let j(k) be the first derivative of -k**6/3 + 7*k**4/2 + 4*k**3 + 250. Find z, given that j(z) = 0.
-2, -1, 0, 3
Let d = -45530 + 45532. What is u in 34/11*u**d - 6/11*u**3 - 42/11*u - 18/11 = 0?
-1/3, 3
Let n(y) = -5*y**4 + 25*y**3 + 347*y**2 - 1643*y - 1962. Let l(f) = 10*f**4 - 50*f**3 - 695*f**2 + 3285*f + 3925. Let u(w) = 2*l(w) + 5*n(w). Factor u(a).
-5*(a - 7)**2*(a + 1)*(a + 8)
Let c(u) = 3*u**3 + u + 1. Let p(t) = 3*t**4 + 6*t**3 + 9*t**2 - 14*t - 14. Let f(o) = -2*c(o) - p(o). Factor f(m).
-3*(m - 1)*(m + 1)*(m + 2)**2
Suppose 0 = -3*d - 4*m - 14, 2*d + 3*m - 931 + 942 = 0. Determine l, given that -14/3*l**5 + 4 - 4*l**3 - 64/3*l**d + 52/3*l**4 + 26/3*l = 0.
-1, -2/7, 1, 3
Factor 0*n - 1/5*n**2 + 9/5.
-(n - 3)*(n + 3)/5
Let h(w) be the third derivative of w**7/1050 - w**6/75 + 123*w**2. Find q such that h(q) = 0.
0, 8
Let -23*r**2 + 10*r**2 - 29*r + 68*r**3 - 8 - 7 - 67*r**3 = 0. Calculate r.
-1, 15
Let v be (-6)/(10 - 22 - -10). Solve 0*z + 2/3*z**2 + 0 - 4/3*z**v + 2/3*z**4 = 0.
0, 1
Factor -65*z**2 - 214*z - 3*z**3 - 49*z**2 + 133*z + 24*z**2 + 174*z.
-3*z*(z - 1)*(z + 31)
Let u = 5 + 1. Let l be (-24)/(3 - (-10)/(-2)). Let 13 - 1 + u + 2*k**2 - l*k = 0. What is k?
3
Let o = -6 + 19/3. Let b be 5 + (-28)/(-2)*(-60)/180. Factor 0*u**3 + 0 - 1/6*u**5 + 1/6*u - b*u**4 + o*u**2.
-u*(u - 1)*(u + 1)**3/6
Let b(y) = -2*y**2 - 5*y - 9. Let d(m) = 10*m**2 + 24*m + 46. Suppose 24 = -0*x + 8*x. Let r(a) = x*d(a) + 16*b(a). Determine z so that r(z) = 0.
-3, -1
Suppose -113 = -4*j + 2*p - 39, 0 = -5*j - 3*p + 109. Suppose -3*h**3 - 2*h**2 - j*h**4 + 19*h**3 - 19*h**4 + 33*h**4 + 8 - 16*h = 0. Calculate h.
-1, 2/3, 1, 2
Let q = 1235 + -1232. Let 1/2*k**2 + 1/2*k - 1/2*k**4 + 0 - 1/2*k**q = 0. Calculate k.
-1, 0, 1
Determine m so that 9/2 + 3/4*m**3 + 0*m**2 - 21/4*m = 0.
-3, 1, 2
Let k(z) be the first derivative of 5*z**6/12 - z**5/4 - 165*z**4/16 - 70*z**3/3 - 25*z**2/2 - 218. Solve k(t) = 0.
-2, -1/2, 0, 5
Let v(s) be the first derivative of -2*s**3/15 + 4*s**2/15 - 46. Factor v(j).
-2*j*(3*j - 4)/15
Suppose 1/2 - 2*k + 3*k**2 + 1/2*k**4 - 2*k**3 = 0. Calculate k.
1
Let w = -31 + 33. Solve -3*g - 14*g + 0*g**3 - 3*g - 5*g**3 + 20*g**w = 0 for g.
0, 2
Suppose -34/15*r**2 + 4/15 - 2*r = 0. What is r?
-1, 2/17
Let q(s) be the second derivative of -s**9/5040 + s**8/1120 - s**6/120 + s**5/40 + 7*s**4/4 + 14*s. Let l(a)