1, 2
Let n(g) be the second derivative of 2/39*g**4 + 0 - 10*g + 0*g**2 + 3/65*g**5 - 8/39*g**3 - 1/273*g**7 - 1/195*g**6. Solve n(v) = 0 for v.
-2, 0, 1, 2
Suppose 119 - 298*y - 23*y - 2730*y**3 + 2727*y**3 + 165*y**2 + 40 = 0. What is y?
1, 53
Let s(f) be the second derivative of f**5/20 - 5*f**2 + 4*f. Let z(b) be the first derivative of s(b). Let z(r) = 0. What is r?
0
Determine d, given that 30 + 10*d**3 - 51*d - 4*d + d**3 + 4*d**3 - 5*d**4 + 15*d**2 = 0.
-2, 1, 3
Let b(x) be the first derivative of 4/15*x**3 + 0*x + 0*x**2 - 1/10*x**4 - 4/25*x**5 + 1/15*x**6 - 7. Solve b(j) = 0 for j.
-1, 0, 1, 2
Let m(j) be the first derivative of j**4/16 + 31*j**3/6 + 121*j**2/8 + 15*j - 615. Suppose m(h) = 0. What is h?
-60, -1
Let o(m) be the first derivative of 1/7*m**4 + 0*m**2 - 2/35*m**5 - 2/21*m**3 + 0*m + 6. Determine t so that o(t) = 0.
0, 1
Suppose -1/6*x**3 + 0*x + 0 + 23/6*x**2 = 0. Calculate x.
0, 23
Let l = 2137 - 6407/3. Let d(k) be the second derivative of 0*k**2 - 8/15*k**6 + 7*k - 1/5*k**5 + 2/3*k**3 + l*k**4 + 0. Let d(i) = 0. Calculate i.
-1, -1/4, 0, 1
Let s(u) be the first derivative of -u**4/4 + 3*u**3 + 23*u + 1. Let o(f) be the first derivative of s(f). Suppose o(t) = 0. Calculate t.
0, 6
Suppose -2*b - b - d = -20, 0 = -d + 5. Suppose 5*y - b = 4*y. Factor -7*u**2 + y*u - 5*u**2 - 3*u**2 + 5*u**2.
-5*u*(2*u - 1)
Let 79/2*d + 9/2*d**2 - 9 = 0. What is d?
-9, 2/9
Let r(n) be the first derivative of 3*n**4/8 + 11*n**3/2 + 15*n**2/2 - 3. Factor r(i).
3*i*(i + 1)*(i + 10)/2
Solve -104*w - 4*w**2 - 29 + 76 - 47 = 0 for w.
-26, 0
Let b(a) be the first derivative of 2*a**3/15 + 2*a**2/5 + 2*a/5 + 14. Factor b(f).
2*(f + 1)**2/5
Let g = 145/98 - -1/49. Suppose -57*q + 2 = -56*q. Factor -3/4*d**3 + 0 - 3/4*d - g*d**q.
-3*d*(d + 1)**2/4
Let y = 9465 - 28345/3. Determine c so that -y - 2/3*c**2 + 20/3*c = 0.
5
Let w(y) be the first derivative of 9*y**8/112 - 3*y**7/7 + 7*y**6/10 - 2*y**5/5 + 3*y**2 + 2. Let o(l) be the second derivative of w(l). Factor o(p).
3*p**2*(p - 2)*(3*p - 2)**2
Let j = 45423/16643 - 3/1513. Suppose -32/11*c + 68/11*c**3 + 2/11*c**2 - 8/11 - j*c**4 = 0. Calculate c.
-2/5, -1/3, 1, 2
Suppose 286 - 374 + 14*j + 3*j**2 - j**2 = 0. Calculate j.
-11, 4
Let b = -2334/539 - -132/49. Let k = -32/33 - b. Let -14/9*q**4 + 0 - k*q**2 + 8/3*q**3 - 4/9*q = 0. What is q?
-2/7, 0, 1
Let r(s) = -6*s**2 - 42*s + 7. Let c(h) = 4*h**2 + 28*h - 5. Let a(w) = -7*c(w) - 5*r(w). Let a(x) = 0. Calculate x.
-7, 0
Let p(n) be the second derivative of -1/9*n**2 + 1/18*n**4 + 1/90*n**5 - 1/27*n**3 + 0 + 3*n - 2/135*n**6. Suppose p(x) = 0. Calculate x.
-1, -1/2, 1
Find x such that 4/7*x**2 - 4/7*x + 0 = 0.
0, 1
Suppose -5*m = 2*z + 8, m - 4*z - 15 - 1 = 0. Let q(l) be the second derivative of -1/102*l**4 - 5*l + 0*l**2 + 0*l**3 + m. Let q(v) = 0. Calculate v.
0
Let p(w) = 18*w**2 - w. Let y(x) = 10*x**2. Let m(g) = 6*p(g) - 11*y(g). Let m(v) = 0. Calculate v.
-3, 0
Let b(v) = v**2 - 25*v + 26. Let u be b(24). Let w be 8/2 + -1 + 2. Solve -4*q**3 + 0 + u + 5*q**3 - 3*q**3 - w*q**2 - q = 0.
-2, -1, 1/2
Let s(a) be the third derivative of -1/2*a**5 + 0*a + 0*a**3 + 29/24*a**6 + 0*a**4 + 0 - 3/14*a**7 + 43*a**2. Solve s(w) = 0 for w.
0, 2/9, 3
Let w(q) be the first derivative of -q**4/20 - q**3/5 + 14*q - 5. Let r(h) be the first derivative of w(h). Factor r(k).
-3*k*(k + 2)/5
Let q(y) = -11*y**2 - 2. Let a(k) = 59*k**2 + 11. Let d(c) = -2*a(c) - 11*q(c). Factor d(v).
3*v**2
Let s(a) be the third derivative of -a**5/180 + a**4/36 - 11*a**2 + 3. Determine z, given that s(z) = 0.
0, 2
Solve -845 - 4*o**4 - 445*o**2 + 2090*o - 145*o**2 - 530*o - o**4 - 120*o**3 = 0.
-13, 1
Factor 0 - 8/13*r + 2/13*r**4 - 8/13*r**2 + 2/13*r**3.
2*r*(r - 2)*(r + 1)*(r + 2)/13
Let v = -83 - -84. Let w(p) be the first derivative of 1/2*p**6 + 0*p + 6/5*p**5 - 2*p**3 - 3/2*p**2 + 0*p**4 + v. Factor w(s).
3*s*(s - 1)*(s + 1)**3
Let o(b) = -b**3 + 3*b**2 + 17*b + 6. Let g be o(6). Let u(k) be the second derivative of 1/6*k**3 - 1/20*k**5 + 0 + g*k**2 + 0*k**4 - 4*k. Factor u(f).
-f*(f - 1)*(f + 1)
Let z(t) be the first derivative of t**5/15 - 5*t**4/12 - 31*t**3/9 - 43*t**2/6 - 6*t - 97. Suppose z(a) = 0. Calculate a.
-2, -1, 9
Let o = 519/322 + -18/161. Let n(a) be the first derivative of 0*a - 9/5*a**5 - 4 + 3*a**3 - 3*a**2 + o*a**4. Suppose n(f) = 0. Calculate f.
-1, 0, 2/3, 1
Find f such that -57*f**2 - 346*f**3 + 126*f**2 + 305*f**4 - 44*f + 112*f**2 + 4 + 60*f**5 - 160*f**5 = 0.
1/4, 2/5, 1
Let o(i) be the first derivative of i**5/5 + 13*i**4/12 - 28*i**3/9 + 2*i**2 - 202. Factor o(c).
c*(c - 1)*(c + 6)*(3*c - 2)/3
Let l(y) be the second derivative of -y**5/16 - 61*y**4/16 + 37*y**3/12 - 515*y. Factor l(v).
-v*(v + 37)*(5*v - 2)/4
Let f(m) be the first derivative of 2*m + 0*m**4 + 2/5*m**5 - 4/3*m**3 + 5 + 0*m**2. Solve f(x) = 0.
-1, 1
Let v = -12625/2 - -6028. Let o = v - -285. Factor 1/2*b + 0 + o*b**2.
b*(b + 1)/2
Let m(p) be the third derivative of -p**5/90 - 17*p**4/18 - 11*p**3/3 + p**2 - 6*p. Solve m(s) = 0 for s.
-33, -1
Let z(f) be the first derivative of 13 + 0*f - 16/9*f**3 + 1/4*f**4 - 2*f**2. Factor z(a).
a*(a - 6)*(3*a + 2)/3
Let s(a) be the second derivative of a**5/20 + a**4/2 + 3*a**3/2 + 2*a**2 + 16*a. Factor s(g).
(g + 1)**2*(g + 4)
Let p = 23/154 - -3/22. Let h = -7/2 + 57/14. Find k such that -p*k - h + 4/7*k**2 + 2/7*k**3 = 0.
-2, -1, 1
Let u(w) = -w**2 + 3*w + 4. Let j(q) be the first derivative of 8*q**3/3 - 14*q**2 - 36*q - 10. Let g(m) = 6*j(m) + 52*u(m). Factor g(h).
-4*(h + 1)*(h + 2)
Let b = 285 - 281. Let k(y) be the first derivative of -3/5*y**5 - 1/12*y**6 - y**2 - 2*y**3 - 13/8*y**4 - b + 0*y. Let k(n) = 0. Calculate n.
-2, -1, 0
Let w(o) = -7*o**2 + 37*o - 6. Let z be w(5). Let k(a) be the second derivative of -a + 1/3*a**3 + 0 + 2*a**2 - 1/6*a**z. Factor k(b).
-2*(b - 2)*(b + 1)
Suppose 10*x + 175 = 17*x. Let l be ((-120)/x)/(-6) + (-22)/40. Factor -l*y**3 - 1/8*y**2 + 0*y + 0.
-y**2*(2*y + 1)/8
Let x(s) = -2*s**2 + 30*s - 66. Let g(t) = t**3 + 5*t**2 + 7*t + 14. Let i be g(-4). Let b(v) = 3*v**2 - 59*v + 133. Let c(l) = i*b(l) + 5*x(l). Factor c(u).
-4*(u - 4)**2
Let p(n) = -16*n**4 + 12*n**3 + 60*n**2 - 4*n - 4. Let z(u) = -u**5 - 16*u**4 + 13*u**3 + 61*u**2 - 3*u - 3. Let r(j) = 3*p(j) - 4*z(j). Factor r(f).
4*f**2*(f - 2)*(f + 2)*(f + 4)
Suppose 3*d - 2*m + 2 = 0, 2*d - 5*d + 18 = 3*m. Find t, given that 1/6*t**3 + 0 + 0*t + 1/3*t**d - 1/6*t**4 = 0.
-1, 0, 2
Let v(y) be the third derivative of y**6/150 + 2*y**5/75 - 2*y**4/3 + 16*y**3/5 - 48*y**2 - 4*y. Suppose v(g) = 0. What is g?
-6, 2
Suppose 2*u = -2, -4*j - 6 + 3 = 3*u. Find d such that j*d + 1/5 - 1/5*d**2 = 0.
-1, 1
Let n be (9/(-132))/((-48)/256)*(-2)/(-2). Let -6/11*w**2 + 0 + n*w + 2/11*w**3 = 0. What is w?
0, 1, 2
Let n(d) = d**2 + 7*d - 6. Let l be n(-8). Suppose 2*o**l + 6*o + 8*o + 8 + 2*o - 6*o = 0. What is o?
-4, -1
Let m(i) be the first derivative of 5*i**6/6 - 85*i**4/4 - 60*i**3 - 50*i**2 + 78. Suppose m(u) = 0. Calculate u.
-2, -1, 0, 5
Let s = -38 + 38. Let b be 4 + s - (-14 + 16). Factor 30 - 5*u**b - 20 - u - u - 3*u.
-5*(u - 1)*(u + 2)
Factor -q**5 + 4*q - q + 27*q**4 - 1 - 28*q**4 + q**3 + q**3 - 4*q + 2*q**2.
-(q - 1)**2*(q + 1)**3
Solve -3*q**4 + 4*q - 8*q**2 - 3*q**5 + 11*q**4 + 82498*q**3 - 82499*q**3 = 0 for q.
-1, 0, 2/3, 1, 2
Let m(v) be the second derivative of -v**6 - 2*v + 11/6*v**4 - 19/20*v**5 - 3/14*v**7 + 4*v**2 + 3 + 14/3*v**3. Find k, given that m(k) = 0.
-2, -1, -2/3, 1
Let c be (-1)/3 + (-3)/(-9). Let m(b) = -b**2 - 5*b + 46. Let i be m(4). What is j in 5 + c*j + 0*j**2 + i*j + 5*j**2 + 0*j = 0?
-1
Let w(s) be the third derivative of 5*s**8/336 - s**7/14 - 5*s**6/24 + 5*s**5/4 + 5*s**4/6 - 10*s**3 + 4*s**2 - 20*s. Let w(f) = 0. Calculate f.
-2, -1, 1, 2, 3
Let w(z) be the first derivative of 3*z**3/5 + 111*z**2/5 - 15*z - 48. Factor w(s).
3*(s + 25)*(3*s - 1)/5
Suppose 5*k**4 + 8719*k**2 + 3*k**5 - 5*k**3 + 2*k**5 + 0*k**4 - 8724*k**2 = 0. What is k?
-1, 0, 1
Let v(k) = -k**4 + 41*k**3 + 98*k**2 - 147*k + 9. Let p(a) = a**4 - 21*a**3 - 48*a**2 + 72*a - 4. Let q(h) = -9*p(h) - 4*v(h). Factor q(s).
-5*s*(s - 6)*(s - 1)*(s + 2)
Let u(l) be the third derivative of -l**8/1848 - l**7/385 + l**6/330 + l**5/55 - l**4/132 - l**3/11 + 114*l*