+ 7*o. Let a(y) be the first derivative of z(y). Suppose a(k) = 0. What is k?
0, 2/9, 1
Let r be 1/(14/(-4)) + (-2)/(-7). Let o(v) be the second derivative of -2*v - 1/3*v**2 - 1/10*v**5 + 5/18*v**4 - 1/9*v**3 + r. Factor o(b).
-2*(b - 1)**2*(3*b + 1)/3
Let g(m) = m**2 - m + 1. Let r(f) = -18*f**2 - 5*f + 4. Let n = 4 - 3. Let i(a) = n*r(a) - 2*g(a). Find z such that i(z) = 0.
-2/5, 1/4
Let k be (-13)/13 + (0 - -17). Solve 44/5*p**3 + k*p**2 - 8/5 + 28/5*p = 0.
-1, 2/11
Let b(r) = -12*r**2 - 3*r. Let v(a) = -a - 10 - 3*a**2 + 10. Let i(z) = -4*b(z) + 15*v(z). Factor i(k).
3*k*(k - 1)
Let i be 0/(-9) + (3 - 1). Let y(n) be the first derivative of -4*n - 49/4*n**4 - 7*n**3 - 2 + 12*n**i. Factor y(u).
-(u + 1)*(7*u - 2)**2
Suppose 0 + 16/9*d**4 - 16/9*d**3 - 64/3*d**2 + 2/9*d**5 + 32*d = 0. What is d?
-6, 0, 2
Let p = 57/244 - -1/61. Factor -p*k**2 + 1/4 - 1/4*k**3 + 1/4*k.
-(k - 1)*(k + 1)**2/4
Let o(r) = r**3 + r**2 - r. Let d(z) = 4*z**3 + z**2 - z. Let l(f) = d(f) + 2*o(f). Let l(h) = 0. What is h?
-1, 0, 1/2
Let h(a) be the first derivative of a**3 - 6*a**2 + 12*a + 7. What is v in h(v) = 0?
2
Let i(j) be the third derivative of -j**7/1155 - j**6/330 - j**5/330 - 6*j**2. Factor i(p).
-2*p**2*(p + 1)**2/11
Let r be (-1)/((-3)/(-519) - 0). Let d = 1559/9 + r. Find g such that -d*g + 0 - 2/9*g**2 = 0.
-1, 0
Factor -27*c + 243/2 + 3/2*c**2.
3*(c - 9)**2/2
Let p(v) be the third derivative of v**6/60 + v**5/10 + v**4/6 - v**2. Let p(f) = 0. Calculate f.
-2, -1, 0
Let u(z) = -z**2 - 12*z - 2. Let v be u(-8). Suppose -5*w - 4*q + v = q, 3*w + q - 16 = 0. Solve -n**4 + n - n + 3*n**w = 0.
0, 1/3
Let a = 2 - -1. Find x such that x - x**2 - x - a + 2 + 2*x = 0.
1
Let r(d) be the second derivative of d**6/45 - d**5/15 + 6*d. Solve r(w) = 0.
0, 2
Let k(n) = -n**5 + n**4 + n**2. Let j(d) = 3*d**5 - d**4 + 2*d**3 - 9*d**2. Let z(v) = -j(v) - 5*k(v). Factor z(p).
2*p**2*(p - 2)*(p - 1)*(p + 1)
Let n(v) = -6*v**5 - 36*v**4 + 57*v**3 + 57*v**2 - 6*v - 36. Let h(l) = l**5 + 5*l**4 - 8*l**3 - 8*l**2 + l + 5. Let y(s) = 15*h(s) + 2*n(s). Factor y(w).
3*(w - 1)**2*(w + 1)**3
Let g = -40/9 + 14/3. Let x = -1/139 - -287/1251. Suppose 0 - x*v**2 - g*v = 0. What is v?
-1, 0
Suppose 0 = 3*u + 2*u + 75. Let v be 2/8 - u/36. Let 0 - 2/3*r**2 + 2/3*r**4 + 2/3*r**5 - v*r**3 + 0*r = 0. Calculate r.
-1, 0, 1
Let g(r) be the third derivative of 0*r**3 + 0 + 0*r**6 - 1/60*r**5 - 2*r**2 + 0*r**4 + 1/210*r**7 + 0*r. Determine p, given that g(p) = 0.
-1, 0, 1
Let q(g) be the third derivative of -g**8/10080 + g**7/630 - g**6/90 + g**5/20 - g**2. Let o(w) be the third derivative of q(w). Factor o(k).
-2*(k - 2)**2
Suppose 3*g = -13 + 25. Let l(k) be the second derivative of -1/78*k**g + 1/39*k**3 - 1/130*k**5 + 0*k**2 - k + 0 + 1/195*k**6. Factor l(y).
2*y*(y - 1)**2*(y + 1)/13
Let w(g) be the first derivative of -1/7*g**2 + 4/21*g**3 + 3 - 2/7*g. Factor w(x).
2*(x - 1)*(2*x + 1)/7
Suppose 0 = 4*z - 5*h + 46, -3*z + 4*h - 54 = -20. Let t be ((-2)/(-1))/((-21)/z). Find o, given that -t - 2/3*o**2 - 2*o = 0.
-2, -1
Let d(k) be the second derivative of 0 + 0*k**2 + 1/4*k**4 - 4*k + 9/40*k**5 + 1/12*k**3 + 1/15*k**6. Factor d(y).
y*(y + 1)**2*(4*y + 1)/2
Let g(w) be the third derivative of -2*w**7/105 + w**6/10 - w**5/5 + w**4/6 - 6*w**2. Suppose g(k) = 0. Calculate k.
0, 1
Let c(q) be the second derivative of 27*q**5/130 - 18*q**4/13 + 48*q**3/13 - 64*q**2/13 - 19*q. Factor c(j).
2*(3*j - 4)**3/13
Determine p, given that -p**4 - 12*p**5 + 6*p**2 + 8*p + 14*p**5 - 10*p**3 - 5*p**4 = 0.
-1, 0, 1, 4
Let v(c) be the third derivative of c**7/315 + c**6/90 - c**5/90 - c**4/18 + 4*c**2. Factor v(a).
2*a*(a - 1)*(a + 1)*(a + 2)/3
Factor 18/5*j**2 + 22/5*j + 4/5.
2*(j + 1)*(9*j + 2)/5
Let g be (-2 - 3) + (6 - (-4 + 3)). Factor 1/2*a - 1/2*a**g + 0.
-a*(a - 1)/2
Factor 6 + 55/2*t**2 + 28*t - 25/2*t**3.
-(t - 3)*(5*t + 2)**2/2
Factor 12 + 1/3*f**2 + 4*f.
(f + 6)**2/3
Let v(z) = -17*z**3 - 10*z**2 + 21*z + 6. Let q(m) = 18*m**3 + 9*m**2 - 21*m - 6. Let g(w) = 4*q(w) + 3*v(w). Solve g(f) = 0 for f.
-1, -2/7, 1
Let p(b) be the third derivative of -2*b**7/315 - b**6/45 + b**4/9 + 2*b**3/9 - 15*b**2. Factor p(o).
-4*(o - 1)*(o + 1)**3/3
Let s(i) = -9 - 4*i**2 + 3*i + 5*i**2 + 2*i. Let k be s(-7). Find x, given that -4/7*x**3 + 2/7*x**k + 0 + 0*x**2 + 0*x**4 + 2/7*x = 0.
-1, 0, 1
Factor -2/19*q**5 - 20/19*q**2 + 16/19 - 2/19*q**3 + 8/19*q**4 + 8/19*q.
-2*(q - 2)**3*(q + 1)**2/19
Let f be (-6)/(-20)*-8*140/(-546). Find i such that -f*i**2 + 0*i - 10/13*i**4 + 2/13*i**5 + 16/13*i**3 + 0 = 0.
0, 1, 2
Factor -23/5*u - 11/5 - 2/5*u**2.
-(u + 11)*(2*u + 1)/5
Let f(p) be the third derivative of 0*p - 1/24*p**4 - 2*p**2 + 0 + 0*p**5 + 1/120*p**6 + 0*p**3. Let f(i) = 0. What is i?
-1, 0, 1
Let z(h) be the third derivative of 2*h**7/105 - 7*h**6/30 + 16*h**5/15 - 2*h**4 + 9*h**2. Suppose z(m) = 0. What is m?
0, 2, 3
Suppose 7 = 2*d + 1. Suppose d*c = -3 + 9. Let 0*q + 0 - 1/4*q**c = 0. Calculate q.
0
Let f(m) be the third derivative of -m**5/270 + m**4/108 + 2*m**3/27 - 4*m**2. Let f(w) = 0. What is w?
-1, 2
Let v(w) = 23*w**4 + 8*w**3 - 38*w**2 - 8*w + 23. Let l(b) = -15*b**4 - 5*b**3 + 25*b**2 + 5*b - 15. Let r(j) = -8*l(j) - 5*v(j). Solve r(k) = 0 for k.
-1, 1
Let p(o) be the third derivative of o**8/560 + 3*o**7/140 + 3*o**6/40 + o**3 - 6*o**2. Let n(j) be the first derivative of p(j). Factor n(a).
3*a**2*(a + 3)**2
Let k = 4 + -2. Determine q so that -3/5*q**k - 3/5 - 6/5*q = 0.
-1
Let c(j) be the second derivative of 2*j + 1/10*j**5 + 11/12*j**3 + 1/2*j**2 + 13/24*j**4 + 0. Factor c(z).
(z + 1)*(z + 2)*(4*z + 1)/2
Let r(y) be the second derivative of -3*y**7/14 - 11*y**6/10 - 9*y**5/4 - 9*y**4/4 - y**3 + 10*y. Solve r(o) = 0 for o.
-1, -2/3, 0
Let r = 4/65 - -53/195. Factor -r + 5/6*d**2 + 1/6*d + 1/3*d**3.
(d + 1)*(d + 2)*(2*d - 1)/6
Let b(u) = -4*u**4 + 15*u**3 - 31*u**2 + 23*u - 3. Let j(o) = -12*o**4 + 44*o**3 - 92*o**2 + 68*o - 8. Let n(m) = -16*b(m) + 5*j(m). Factor n(y).
4*(y - 2)*(y - 1)**3
Let r(w) be the second derivative of 0*w**2 + 0 + 0*w**3 - 16/5*w**5 + 9*w - 6/7*w**7 + 14/5*w**6 + 4/3*w**4. Determine o so that r(o) = 0.
0, 2/3, 1
Let t(d) = 12*d - 12. Let c(z) = z**2 - 24*z + 23. Let w(g) = -4*c(g) - 7*t(g). Factor w(p).
-4*(p - 2)*(p - 1)
Let u(r) be the second derivative of -1/18*r**3 + 0*r**2 + 1/36*r**4 + 0 + 2*r. Determine o, given that u(o) = 0.
0, 1
Let g(k) be the second derivative of -k**9/68040 + k**8/30240 + k**7/11340 - k**6/3240 - k**4/12 + 4*k. Let w(u) be the third derivative of g(u). Factor w(x).
-2*x*(x - 1)**2*(x + 1)/9
Let c(a) = 7*a + 105. Let m be c(-15). Find y, given that -1/3*y**3 + m*y + 1/3*y**2 + 0 = 0.
0, 1
Let t(b) be the third derivative of b**6/360 + b**5/60 - b**3/6 + b**2. Let r(y) be the first derivative of t(y). What is w in r(w) = 0?
-2, 0
Let u = -7 + 9. Factor d - 5 - d**3 - d**2 + 4 + 2*d**u.
-(d - 1)**2*(d + 1)
Let m be (-44)/(-70) + (-15)/35 + 0. What is z in 0 - 1/5*z**2 + 1/5*z - 1/5*z**3 + m*z**4 = 0?
-1, 0, 1
Let d(s) be the first derivative of 72*s**3 + 5 + s - 71*s**3 - 4*s. Suppose d(r) = 0. Calculate r.
-1, 1
Suppose 15*a - 37 - 8 = 0. Let d(w) be the second derivative of 1/5*w**2 - 1/30*w**4 + a*w + 1/15*w**3 - 1/50*w**5 + 0. Determine l, given that d(l) = 0.
-1, 1
Let i(g) = g**3 + g**2 - g + 1. Let a(w) = -w**3 + w**2 + 4*w - 2. Let d(q) = 2*a(q) + 4*i(q). Suppose d(m) = 0. What is m?
-2, -1, 0
Let i be 1/(-2) - (-65)/10. Let c be 127/3 - 2/i. Suppose -28/3*b + c*b**3 - 13/3*b**2 - 27*b**4 - 4/3 = 0. What is b?
-2/9, 1
Let s(i) be the third derivative of -1/60*i**4 + 0*i**3 + 0*i + 0*i**5 + 1/300*i**6 + 2*i**2 + 0. Factor s(d).
2*d*(d - 1)*(d + 1)/5
Let b = -1091/48 + 91/4. Let f(o) be the second derivative of 0 + 1/24*o**3 + b*o**4 - o + 0*o**2. Suppose f(j) = 0. What is j?
-1, 0
Suppose -15/4*i**2 + 5/4*i**4 - 5/4*i**3 + 25/4*i - 5/2 = 0. Calculate i.
-2, 1
Suppose 0 = -5*k - 6 + 26. What is j in -6*j**2 + k*j**2 + 0*j**3 - 3*j**4 + 4*j**3 + j**4 = 0?
0, 1
Let u = -35/47 + 281/188. Factor 0 - u*a**2 + 1/4*a**4 + 0*a**3 + 1/2*a.
a*(a - 1)**2*(a + 2)/4
Let f(b) be the second derivative of -b**6/360 + b**5/60 - b**4/24 - 5*b**3/6 - 6*b. Let w(v) be the second derivative of f(v). Factor w(k).
-(k - 1)**2
Factor -9/4*h + 3 - 3/4*h**2.
