t u(r) be the second derivative of 3/20*r**5 - i*r**4 + 0*r**2 + 1/2*r**3 - 5*r + 0. Determine b so that u(b) = 0.
0, 1
Let p(i) be the first derivative of i**4/6 + 2*i**3/9 - 2*i**2/3 + 1. Suppose p(u) = 0. Calculate u.
-2, 0, 1
Let w = -730/3 - -9514/39. Factor -2/13*r**2 - 8/13 - w*r.
-2*(r + 2)**2/13
Let b be (-2 - 0) + 1 + 6. What is w in 84*w**2 + 60*w**4 + 76*w**2 + 144*w**3 + 0*w**5 + 48*w - 16*w**2 + 9*w**b = 0?
-2, -2/3, 0
Factor 1/3*q**2 + 0 + 0*q.
q**2/3
Let k(m) be the first derivative of -13/2*m**2 - 20/3*m**3 - 9/4*m**4 + 2 - 2*m. Find s such that k(s) = 0.
-1, -2/9
Let y(h) = 7*h**3 + 5*h**2 - 4*h - 2. Let z(w) = -8*w**3 - 6*w**2 + 5*w + 3. Let v be 0*(-2)/(-6)*-1. Let s = -2 - v. Let n(x) = s*z(x) - 3*y(x). Factor n(l).
-l*(l + 1)*(5*l - 2)
Let o be (-5)/(-120)*4*(-4)/(-1). Suppose -3 = -5*d + 3*u, 1 = -3*u - 2. Factor 2/9*g**3 - o*g + d*g**2 - 4/9.
2*(g - 2)*(g + 1)**2/9
Let a(y) be the third derivative of -y**5/210 - y**4/42 + y**3/7 - 7*y**2. Factor a(h).
-2*(h - 1)*(h + 3)/7
Let b = 97/9 - 436/63. Let z = -67/21 + b. Factor 0 + z*d**2 + 0*d - 4/3*d**3 + 2/3*d**4.
2*d**2*(d - 1)**2/3
Let n be 5 - -1*(-1 - 1). Factor 3*j - j**3 + n*j**3 - 4*j - j**3.
j*(j - 1)*(j + 1)
Let j(x) be the first derivative of -x**4/6 - 8*x**3/9 - 5*x**2/3 - 4*x/3 + 13. Find c such that j(c) = 0.
-2, -1
Let z(p) = 2*p**2 - 12*p + 2. Let d(i) be the second derivative of -i**4/12 - i**3/6 - i**2/2 + 3*i. Let u(l) = -2*d(l) + z(l). Factor u(f).
2*(f - 2)*(2*f - 1)
Let r = 3 + -4. Let d = r + 3. Suppose 2/9*f**d + 0*f + 0 = 0. Calculate f.
0
Let 4/11 + 2/11*g**4 - 2/11*g**3 + 2/11*g - 6/11*g**2 = 0. Calculate g.
-1, 1, 2
Let a(k) be the third derivative of -k**6/160 + k**5/30 - 7*k**4/96 + k**3/12 - 26*k**2. Factor a(p).
-(p - 1)**2*(3*p - 2)/4
Let -4*h + 4*h + 3*h**3 - h**4 - 3*h**2 + h = 0. Calculate h.
0, 1
Suppose -4*q + 9*q = 0. Suppose 4*j = -5*h - 0*j + 35, -4*h = -5*j + 13. Factor -2/3*d**4 + q - 2/3*d - 2*d**2 - 2*d**h.
-2*d*(d + 1)**3/3
Let u(n) be the second derivative of -n**6/480 - 5*n**3/6 - 4*n. Let r(g) be the second derivative of u(g). Find w such that r(w) = 0.
0
Let i = -2 + 0. Let l be 0/(-2) - -2 - i. Factor -2*n**l - 2*n + 3*n**2 + n**5 + n - n**2.
n*(n - 1)**3*(n + 1)
Let b = 5261/1155 + -50/11. Let v(o) be the second derivative of 2/21*o**3 + 1/42*o**4 + 0 - 1/35*o**5 - b*o**6 + 0*o**2 - 4*o. Determine k so that v(k) = 0.
-2, -1, 0, 1
Let k(l) be the third derivative of 0 - 4*l**2 + 0*l**3 + 1/40*l**5 + 1/240*l**6 + 0*l - 1/140*l**7 - 1/48*l**4. Factor k(q).
-q*(q - 1)*(q + 1)*(3*q - 1)/2
Let g be (-48)/60*(-5)/18. Let 0 - 2/9*q**5 + 2/9*q**3 + 2/9*q**2 - g*q**4 + 0*q = 0. What is q?
-1, 0, 1
Suppose x - 4 = -3, -d - 2 = -4*x. Let j(w) be the first derivative of -4 + 0*w**d + 3/2*w**4 + 4/15*w**3 + 56/25*w**5 + 0*w. Factor j(t).
2*t**2*(4*t + 1)*(7*t + 2)/5
Let i be -6 - (-4)/2 - -7. Suppose 4*r = -2*y + 50, 0 = -y - 1 - 0. Factor -i*c**2 - 10*c + r*c + 0 + 0.
-3*c*(c - 1)
Factor 0 - 9/2*w - 3/2*w**2.
-3*w*(w + 3)/2
Let i(b) be the second derivative of 0*b**2 - 2/27*b**3 - 8*b + 0 - 1/189*b**7 - 1/10*b**5 + 1/27*b**6 + 7/54*b**4. Suppose i(n) = 0. What is n?
0, 1, 2
Factor -i - 6*i**2 + 7*i**3 + 2 - i**4 - i**4 + 0*i**4.
-(i - 2)*(i - 1)**2*(2*i + 1)
Factor -d - 1/4*d**3 + d**2 + 0.
-d*(d - 2)**2/4
Let f = -18/11 - -76/33. Factor -z**3 + 0 + 5/3*z**2 - f*z.
-z*(z - 1)*(3*z - 2)/3
Solve 0*a**2 + 1/5 - 1/5*a**4 + 2/5*a**3 - 2/5*a = 0 for a.
-1, 1
Let y(j) be the first derivative of 2*j**5/5 + 9*j**4/14 - 10*j**3/21 - 9*j**2/7 - 4*j/7 + 5. Solve y(g) = 0.
-1, -2/7, 1
Let s(y) be the second derivative of 0 + 1/168*y**7 + 1/40*y**6 + 1/48*y**4 + 3/80*y**5 + 0*y**2 - 3*y + 0*y**3. Factor s(c).
c**2*(c + 1)**3/4
Let n(v) be the third derivative of 0 + 0*v**3 + 1/48*v**4 + 0*v - 1/240*v**5 - 5*v**2. Factor n(i).
-i*(i - 2)/4
Let h(r) = 1. Let z(v) = -2*v - 9. Let b(d) = 6*h(d) + z(d). Let t be b(-3). Let -14*l**t + 3*l - l**2 + 2*l + 9*l**5 - 1 + 3*l**4 - l**2 = 0. What is l?
-1, 1/3, 1
Let d(q) be the first derivative of -2 + 0*q - 2/3*q**3 + 0*q**2. Factor d(n).
-2*n**2
Let u(v) = v**2 - 4*v - 2. Let g be u(5). Suppose 3 = 3*i, 0*i = g*x + 2*i - 17. What is m in -5*m**2 + 0*m - 2 - x*m + 3*m + 9*m = 0?
2/5, 1
Let l(x) be the second derivative of 5*x**4/12 - 5*x**3/6 - 5*x. Suppose l(t) = 0. Calculate t.
0, 1
Let v(a) be the third derivative of -a**10/378000 + a**9/302400 + a**8/100800 + a**5/30 - 2*a**2. Let g(y) be the third derivative of v(y). Factor g(l).
-l**2*(l - 1)*(2*l + 1)/5
Let o be (116/50)/((-6)/(-10)). Let p = o - 16/5. Find n, given that 2/3*n**2 + 0*n**3 - p*n**4 + 0 + 0*n = 0.
-1, 0, 1
Let y(c) be the second derivative of c**9/22680 + c**8/2520 + c**7/756 + c**6/540 + 5*c**4/12 + 5*c. Let i(d) be the third derivative of y(d). Factor i(x).
2*x*(x + 1)**2*(x + 2)/3
Suppose -6*p = 5*t - 3*p + 10, 5*t + 2*p = -10. Let g = t - -6. Factor -z - 49/4*z**5 - 63/2*z**g - 109/4*z**3 + 0 - 9*z**2.
-z*(z + 1)**2*(7*z + 2)**2/4
Let w(o) be the second derivative of 1/90*o**6 + 3*o - 1/20*o**5 + 1/36*o**4 + 0 - 1/3*o**2 + 1/6*o**3. Solve w(s) = 0.
-1, 1, 2
Let x(b) = b**2 - 8*b + 16. Let u be x(4). Find z such that 0*z**2 + u*z + 0 - 21/2*z**4 - 3*z**3 = 0.
-2/7, 0
Let u(f) be the first derivative of f**7/210 + f**6/120 - f**5/60 - f**4/24 - 3*f**2 - 1. Let t(j) be the second derivative of u(j). Factor t(o).
o*(o - 1)*(o + 1)**2
Let j(g) be the third derivative of -g**7/70 + g**6/20 + g**5/20 - g**4/4 - 2*g**2. Factor j(v).
-3*v*(v - 2)*(v - 1)*(v + 1)
Let a(l) be the third derivative of l**6/600 - l**4/40 + l**3/15 - 19*l**2. Suppose a(w) = 0. Calculate w.
-2, 1
Let o(d) = d**2 + 3*d - 1. Let r be o(-5). Let 4 - 3*y**2 + 4*y**3 + 6*y**2 + r*y**2 + 12*y = 0. What is y?
-1
Let n be 18/2 + 121/(-33). Factor -6*w**3 + n + 40/3*w + 4*w**2.
-2*(w - 2)*(3*w + 2)**2/3
What is q in -3 + 1/2*q + 1/2*q**2 = 0?
-3, 2
Suppose k = 4*z - 8, -5*z = -k - k - 10. Factor k + 6/11*r**2 - 4/11*r.
2*r*(3*r - 2)/11
Let y(k) be the first derivative of 5*k**4/4 - 10*k**3/3 - 75*k**2/2 + 180*k - 45. Factor y(j).
5*(j - 3)**2*(j + 4)
Let g(j) be the first derivative of j**6/30 - 3*j**4/20 - 2*j**3/15 - 17. What is o in g(o) = 0?
-1, 0, 2
Suppose -4*o + 3 = -5*o. Let b = o + 5. Suppose -b*u**2 + u + u**2 + 0*u**2 = 0. What is u?
0, 1
Suppose -5*y = -2*i - 521, 0 = -2*i - 0*y - 2*y - 556. Let u be 42/i - (-32)/39. Suppose -2/3*s**4 - u*s**3 + 4/3 + 2*s**2 + 10/3*s = 0. What is s?
-1, 2
Let j(n) be the third derivative of -n**5/60 + n**4/8 - n**3/3 - 4*n**2. Let r be j(2). Find c such that -2/7*c + r - 8/7*c**2 = 0.
-1/4, 0
Suppose 4*f + 1 + 3 = 0. Let t be f - 1 - (2 + -6). Find z such that 4*z**2 + 0*z**t + z - z**2 - 7*z = 0.
0, 2
Let f(a) = -4*a**2 + 26*a + 2. Let x(d) = 8*d**2 - 51*d - 5. Let m(p) = -5*f(p) - 2*x(p). Factor m(u).
4*u*(u - 7)
Let q(z) be the second derivative of -z**6/10 - 3*z**5/8 - 3*z**4/8 + z**3/4 + 3*z**2/4 - 3*z. Determine n so that q(n) = 0.
-1, 1/2
Let c be 6 - (5 - 3)/1. Let l(n) be the first derivative of 0*n**2 + 7/15*n**5 - 2/9*n**6 - 1/9*n**3 - 1/6*n**c + 0*n - 2. Factor l(o).
-o**2*(o - 1)**2*(4*o + 1)/3
Let p(l) be the first derivative of 5*l**8/1512 + 2*l**7/945 - 3*l**2/2 + 2. Let j(z) be the second derivative of p(z). What is w in j(w) = 0?
-2/5, 0
Let j = -1618 + 11344/7. Determine l, given that 3/7*l**5 + 0 + j*l**3 + 3/7*l + 12/7*l**4 + 12/7*l**2 = 0.
-1, 0
Suppose 21*n**3 + n**4 + 0*n**4 - 7*n**4 + 15*n + 42*n**2 = 0. What is n?
-1, -1/2, 0, 5
Let t(j) = -j**3 - 7*j**2 + j - 5. Let r(b) = 2*b**3 + 0*b**3 + 3 + 8 - 2*b + 15*b**2. Let m(o) = 6*r(o) + 13*t(o). Find v such that m(v) = 0.
-1, 1
Let v be 4/(-14) + 299/91. Suppose v*i - 4*i + 3 = 0. Factor 0*l**2 + 0 + 1/2*l**i - 1/2*l.
l*(l - 1)*(l + 1)/2
Let j(d) be the first derivative of 3*d**5/35 + 3*d**4/7 + 5*d**3/7 + 3*d**2/7 - 24. Factor j(c).
3*c*(c + 1)**2*(c + 2)/7
Let y(c) be the second derivative of -5*c + 1/60*c**5 - 1/6*c**2 - 1/18*c**3 + 1/36*c**4 + 0. Factor y(q).
(q - 1)*(q + 1)**2/3
Let f(k) be the second derivative of k**6/195 - 7*k**5/65 + 11*k**4/26 + 112*k**3/39 + 64*k**2/13 - 8*k. Factor f(b).
2*(b - 8)**2*(b + 1)**2/13
What is k in -8/3*k - 2/3*k**4 + 0 + 2*k**3 + 0*k**2 = 0?
-1, 0, 2
Let v = -125 - -129. Let t(b) be the third derivative of 1/540*