/60 + s**4/12 - s**3/2 - 2*s**2. Let c(i) be the first derivative of a(i). Factor c(k).
-2*(k - 1)*(k + 1)**2
Determine y, given that 0*y**2 + 4*y**3 - 4*y**2 - 7*y**2 - y**2 = 0.
0, 3
Let h(b) be the first derivative of 4*b**5/15 + 5*b**4/12 - b**3/3 - 5*b**2/6 - b/3 - 7. Factor h(c).
(c - 1)*(c + 1)**2*(4*c + 1)/3
Let q = 4 - 0. Let y be 17/q + (-4)/16. Let 5*j**2 - j**2 + j**3 + j - y*j**3 - 2 = 0. What is j?
-2/3, 1
Let k(b) be the second derivative of -8*b**7/7 - 28*b**6/5 - 219*b**5/20 - 43*b**4/4 - 11*b**3/2 - 3*b**2/2 - 11*b. Determine h so that k(h) = 0.
-1, -1/4
Suppose f - 4*i = 22, -4*f - 24 + 7 = 5*i. Factor -2 - 2*u**2 + 9*u**3 - 11*u**3 + f*u + 4.
-2*(u - 1)*(u + 1)**2
Let -h**4 - 1/2*h**5 + 0 + 0*h - 1/2*h**3 + 0*h**2 = 0. What is h?
-1, 0
Let h = -109513 - -3832072/35. Let n = 159/5 + h. Determine j, given that -4/7 + n*j**2 - 40/7*j**3 - 2/7*j = 0.
-1/4, 2/5, 1
Let a(u) = -3*u**4 - 7*u**3 + 3*u**2 + 3*u - 2. Let n(x) = 2*x**4 + 8*x**3 - 2*x**2 - 2*x + 3. Let c(r) = -3*a(r) - 2*n(r). Factor c(k).
5*k*(k - 1)*(k + 1)**2
Let h(m) be the second derivative of -m**6/105 + 3*m**5/35 - m**4/6 - 2*m**3/7 + 8*m**2/7 - 24*m. Solve h(o) = 0.
-1, 1, 2, 4
Let f = 7 - 11. Let z be (f + -2)*2/(-3). Determine p, given that -4/9*p**3 - 2/9*p**z + 0 + 0*p + 0*p**2 = 0.
-2, 0
Let b(n) be the second derivative of n**6/10 - 3*n**5/5 + 5*n**4/4 - n**3 + 3*n. Find r, given that b(r) = 0.
0, 1, 2
Suppose 0 = 2*l + 2*l + 5*c - 37, 3*c = -2*l + 21. What is f in -4*f**l - 7*f + 13*f + 9*f**2 + 7*f**3 = 0?
-2, -1, 0
Let r(p) be the first derivative of 2/9*p**3 - 4/3*p - 2 + 1/3*p**2. Factor r(j).
2*(j - 1)*(j + 2)/3
Let i(p) be the second derivative of -p**5/150 - p**4/45 + p**3/45 + 2*p**2/15 + 35*p. Solve i(o) = 0.
-2, -1, 1
Let p(l) = -l + 2. Let k be p(5). Let m = 4 + k. Let c(b) = b**2. Let f(u) = u**2 + 4*u. Let r(n) = m*f(n) - 3*c(n). Factor r(o).
-2*o*(o - 2)
Let z(k) be the first derivative of -2/3*k**5 - 1/3*k**6 - 7/18*k**4 - 2/27*k**3 + 1 + 0*k + 0*k**2. Determine v, given that z(v) = 0.
-1, -1/3, 0
Let o be -2 - -4 - (1 + -1). Let t be (-5)/10 - (-19)/o. Factor -2 + 2*f - 6*f**2 - t*f**3 - 8*f + 7*f**3.
-2*(f + 1)**3
Let u(l) = -l**3 + 8*l**2 + 9*l + 3. Let c be u(9). Factor 18/5*x**2 + 4/5*x + 14/5*x**c + 0.
2*x*(x + 1)*(7*x + 2)/5
Let f(c) be the second derivative of c**2 + c - 1/6*c**4 - 1/3*c**3 + 0 + 1/10*c**5. Find z such that f(z) = 0.
-1, 1
Let y(n) be the first derivative of -n**3/6 + n**2/2 - n/2 - 1. Factor y(r).
-(r - 1)**2/2
Let a(q) = 13*q**5 + 25*q**4 + 13*q**3 - 11*q**2 - 19*q + 7. Let w(y) = -9*y**5 - 17*y**4 - 9*y**3 + 7*y**2 + 13*y - 5. Let j(z) = 5*a(z) + 7*w(z). Factor j(k).
2*k*(k - 1)*(k + 1)**2*(k + 2)
Let z(h) be the first derivative of h - 1/6*h**3 + 1/20*h**5 - 1/12*h**4 + 2 + 1/2*h**2. Let r(c) be the first derivative of z(c). Factor r(q).
(q - 1)**2*(q + 1)
Let s(i) be the first derivative of i**4/4 + i**3 - 9*i**2/2 + 5*i + 16. Factor s(v).
(v - 1)**2*(v + 5)
Let q = -329 + 331. Solve 1/2*o - 7/4*o**3 - 5/4*o**q + 0 = 0 for o.
-1, 0, 2/7
Let s = -10 - -14. Let w(g) = -27*g**3 - 21*g**2 - 9*g - 15. Let x(l) = -7*l**3 - 5*l**2 - 2*l - 4. Let d(h) = s*w(h) - 15*x(h). Factor d(i).
-3*i*(i + 1)*(i + 2)
Determine b, given that -4*b**2 - 8 - 16*b**2 + 2*b**2 - 40*b = 0.
-2, -2/9
Let z = -52457/84 - -4428/7. Let a = 25/3 - z. Determine h, given that 1/4 + a*h**4 + 0*h**3 - 1/2*h**2 + 0*h = 0.
-1, 1
Determine w, given that 14*w**3 - 18*w**2 - 3*w + 11*w - 4*w = 0.
0, 2/7, 1
Suppose -t = 2*t - 6, 4*a + t - 22 = 0. Factor -19*g - 2*g - 6 + a*g - 21*g**2 - 11*g.
-3*(g + 1)*(7*g + 2)
Let h = 128/3 + -42. Let -h*p + 4/3*p**2 - 2/3 + 4/3*p**3 - 2/3*p**5 - 2/3*p**4 = 0. Calculate p.
-1, 1
Factor -16*a**3 + 5*a + 30*a**2 + 2*a**4 - 32 - 5*a + 16*a.
2*(a - 4)**2*(a - 1)*(a + 1)
Let z(v) be the second derivative of -v**4/6 + v**3/3 - 7*v. Solve z(d) = 0.
0, 1
Suppose -1 = g - 3. Let v(i) be the third derivative of 1/24*i**3 + 0*i + 0 - 1/240*i**5 + 0*i**4 - 2*i**g. Factor v(k).
-(k - 1)*(k + 1)/4
Let y = 13 + -11. Let d(g) = 3*g**4 - 8*g**3 + 2*g**2 - 2*g - 2. Let c(k) = -12*k**4 + 33*k**3 - 9*k**2 + 9*k + 9. Let t(a) = y*c(a) + 9*d(a). Factor t(s).
3*s**3*(s - 2)
Factor -u - 2*u + u + 6*u**2 + 0*u**2 + 2*u**3 - 6*u**4.
-2*u*(u - 1)*(u + 1)*(3*u - 1)
Let v(w) = -3 + 7*w - w**2 + 6*w + 2 + 3. Let j be v(13). Factor 2/5*a**3 + 6/5*a - 6/5*a**j - 2/5.
2*(a - 1)**3/5
Let s(n) = -3*n - 1. Let v be s(-1). Let z(c) be the first derivative of -c + 1/3*c**3 + 1/4*c**v - 1/8*c**4 - 2. Find l such that z(l) = 0.
-1, 1, 2
Let a(o) = 8*o**2 - 5. Let z(n) = -4*n**2 + 3. Let g(m) = -3*a(m) - 5*z(m). Factor g(f).
-4*f**2
Let b = -25/34 - -21/17. Let o(h) be the second derivative of -1/20*h**5 - b*h**2 - 1/4*h**4 + 0 - 1/2*h**3 - h. Suppose o(r) = 0. Calculate r.
-1
Let a be ((-5)/(-1))/(1 + 0). Suppose a*s = b + 16, s = b - s + 4. Solve -2*t + t**5 - 2 + t**4 + 0*t**5 - 3*t**b + 4*t**2 + 4*t**3 - 3*t**5 = 0 for t.
-1, 1
Let p = 13/324 - 1/81. Let d(x) be the second derivative of -p*x**4 + 1/9*x**3 + 0 - x - 1/6*x**2. What is w in d(w) = 0?
1
Suppose 0*u + u = 5. Let s(z) be the third derivative of 1/21*z**4 + 1/210*z**u + 2*z**2 + 0*z + 0 + 4/21*z**3. Determine y so that s(y) = 0.
-2
Let h(v) = -3*v - 3. Let c be h(-1). Determine p, given that 0*p - 4/5*p**3 + c*p**2 + 0 - 6/5*p**4 + 2*p**5 = 0.
-2/5, 0, 1
Let i be 0*2/(24/(-6)). Suppose 2/5*p**2 - 1/5*p**4 + 0*p**3 - 1/5 + i*p = 0. Calculate p.
-1, 1
Solve 4*z**2 - 2*z**2 + 6*z + 3*z**5 - 9*z**3 + 3*z**4 - 5*z**2 + 0*z**2 = 0.
-2, -1, 0, 1
Let z be (-1 + 8/6)*12. Suppose 2*b = -2*b + 44. Suppose -7*l**5 + 7*l**4 + z*l**4 + 5*l**4 + 2*l**2 - b*l**3 = 0. Calculate l.
0, 2/7, 1
Let i(t) be the second derivative of -3*t**3 - 9/4*t**4 - 2*t - 3/2*t**2 + 0. Let i(d) = 0. Calculate d.
-1/3
Let k(l) be the second derivative of l**6/10 + 19*l**5/20 + 19*l**4/12 - 7*l**3/6 - 5*l**2 - 11*l. Determine i so that k(i) = 0.
-5, -1, 2/3
Let p(i) be the third derivative of -i**7/420 - i**6/45 - i**5/15 + i**3/2 - i**2. Let t(r) be the first derivative of p(r). Factor t(m).
-2*m*(m + 2)**2
Let r(h) = -4*h**3 - 2*h**2 + 1. Let n be r(-1). Let l(q) = q**3 + 4*q**2 + 3*q + 1. Let o be l(-2). Find i such that i**4 - i**2 + n + 2*i - 3 - 2*i**o = 0.
-1, 0, 1, 2
Let d = -266 - -1334/5. Find q such that d*q - 2*q**2 + 0 - 14/5*q**3 = 0.
-1, 0, 2/7
Determine d so that 5*d**3 - 4*d**3 - 2*d**2 + 0*d**2 = 0.
0, 2
Let x(j) be the first derivative of -10 + 2/45*j**3 + 2/15*j - 2/15*j**2. Factor x(n).
2*(n - 1)**2/15
Let a(m) = 8*m**3 - 12*m + 7. Let i(b) = b**3 + b - 1. Let r(s) = -a(s) + 3*i(s). Factor r(l).
-5*(l - 1)**2*(l + 2)
Let x(y) = -y**5 + y**4 + 6*y**3 - 16*y**2 - 2*y + 18. Let t(d) = d**4 - d**3 + d - 1. Let z(i) = -4*t(i) - 2*x(i). Find v such that z(v) = 0.
-2, -1, 2
Let m(g) = -g**2 + 5*g - 6. Let y be m(4). Let o be 3 - 0*y/(-4). Solve 4/7*r**o - 2/7*r**4 - 4/7*r + 0*r**2 + 2/7 = 0 for r.
-1, 1
Suppose 18 + 2 = 5*v. Suppose k - 24 = -2*j - 0*j, -4*j = v*k - 52. Find q such that 21*q**2 + 6*q**4 - j*q**2 + 5*q - q**4 + 1 + 10*q**3 + q**5 = 0.
-1
Let t(s) be the first derivative of -s**6/15 + 12*s**5/25 - 13*s**4/10 + 8*s**3/5 - 4*s**2/5 + 19. Factor t(d).
-2*d*(d - 2)**2*(d - 1)**2/5
Let n be 2 - -39*4/(-90). Let d(u) be the first derivative of -1 - 4/9*u**3 - 1/6*u**2 - n*u**5 - 1/18*u**6 + 0*u - 1/2*u**4. Solve d(z) = 0 for z.
-1, 0
Let q(t) = t**5 - t**3 - t**2 + 1. Let x(c) = 3*c**5 - 4*c**3 - 4*c**2 + 4. Let j(y) = 12*q(y) - 3*x(y). Find w such that j(w) = 0.
0
Let p(r) be the third derivative of -r**7/175 + 13*r**6/200 - 7*r**5/25 + 23*r**4/40 - 3*r**3/5 - 5*r**2. Solve p(u) = 0.
1/2, 1, 2, 3
Let z = 18 + -17. Let q = -1 + z. Factor q + 0*g**2 + 1/4*g**3 + 1/4*g**4 + 0*g.
g**3*(g + 1)/4
Let y(j) be the first derivative of -3 + 0*j**4 + 0*j**2 - 2/9*j + 4/27*j**3 - 2/45*j**5. Factor y(g).
-2*(g - 1)**2*(g + 1)**2/9
Suppose 5*s - 37 = -4*k, 3*s - 3*k - 27 = -7*k. Factor -2*m + m**2 + 3*m**2 + 3*m**3 - s*m**3.
-2*m*(m - 1)**2
Let t(d) be the first derivative of -5*d**4/4 + 22*d**3/9 + 5*d**2/2 + 2*d/3 - 10. Let t(a) = 0. What is a?
-1/3, -1/5, 2
Let g be 1 + 3 - (-3 + 4). Factor 5*b**2 + g*b**3 + b**2 + 0*b**3 + 3*b.
3*b*(b + 1)**2
Let m(x) be the first derivative of -x**4/12 + 5*x**3/9 - 2*x**2/3 - 25