t q(r) be the first derivative of -1/3*r**3 - 2 - z*r**2 + 0*r. Let q(w) = 0. What is w?
-1, 0
Let o(d) be the third derivative of -d**8/336 + 2*d**7/105 - d**6/30 - d**5/30 + 5*d**4/24 - d**3/3 + 4*d**2. Factor o(i).
-(i - 2)*(i - 1)**3*(i + 1)
Let i(r) be the first derivative of r**5/360 - r**4/36 + r**3/12 - r**2/2 + 5. Let u(m) be the second derivative of i(m). Suppose u(p) = 0. What is p?
1, 3
Suppose 3*u - 22 = u. Let f = u - 31/3. Factor 0 - 1/3*w**2 + f*w.
-w*(w - 2)/3
Let g(z) be the second derivative of 1/120*z**6 + 1/20*z**5 + 5/48*z**4 + 1/12*z**3 + 4*z + 0*z**2 + 0. Determine n, given that g(n) = 0.
-2, -1, 0
Let w(l) be the second derivative of -l**6/180 + l**5/60 - l**3/3 + 3*l. Let r(z) be the second derivative of w(z). Factor r(s).
-2*s*(s - 1)
Suppose -1 = 5*l + 4*m - 13, 0 = -3*l + 4*m + 20. Suppose -5*h - 2*s + 1 + 1 = 0, -4*s = h - l. Factor -1/6*o**3 - 1/6*o**4 + h*o + 1/6*o**5 + 1/6*o**2 + 0.
o**2*(o - 1)**2*(o + 1)/6
Let v(p) = -p**3 + 7*p**2 + 2*p + 1. Let f be v(7). Suppose 5*s - 10 = f. Factor -9*o**4 + s - 3*o**2 + 9*o**3 - 5 + 3*o**5.
3*o**2*(o - 1)**3
Let c(k) be the first derivative of 3*k**4/22 - 16*k**3/33 + 7*k**2/11 - 4*k/11 - 48. Let c(t) = 0. What is t?
2/3, 1
Let q(o) be the first derivative of -o**6/2 + o**5/5 + 9*o**4/4 + o**3 - o**2 + 33. Determine p so that q(p) = 0.
-1, 0, 1/3, 2
Let n be (-15)/25 - (296/(-180))/2. Solve n + 2/9*k**4 + 4/3*k**2 + 8/9*k**3 + 8/9*k = 0 for k.
-1
Let o be 10/55 + 4/(-22). Let -3*y**4 + 6*y**3 + 5*y**4 + y + 2*y**4 + 4*y**2 + y**5 + o*y = 0. Calculate y.
-1, 0
Suppose -2 = 5*c + 33. Let y = c + 10. Factor -6/7*b**2 + 0 - 2/7*b - 2/7*b**4 - 6/7*b**y.
-2*b*(b + 1)**3/7
Let s(k) = -k**2 + 1. Let m = 6 + -4. Let a(u) = -m*u**3 + u**3 + 2 - u - 6 + 2*u**2. Let i(h) = -a(h) - 4*s(h). Find o such that i(o) = 0.
-1, 0
Let b(v) = -v**3 + 7*v**2 + v - 6. Let f be b(7). Let p(g) be the first derivative of 4/7*g**2 - 2/7*g + 1/7*g**4 + f - 10/21*g**3. Suppose p(l) = 0. What is l?
1/2, 1
Let z = 489 - 488. Factor 9/2*r**4 - 11/2*r - 7/2*r**2 - z + 11/2*r**3.
(r - 1)*(r + 1)**2*(9*r + 2)/2
Factor -20 - 6*d - 13 - 2*d**2 + 3*d**2 + 26.
(d - 7)*(d + 1)
Let q(b) be the second derivative of b**5/100 + b**4/30 - 2*b**3/15 - 4*b**2/5 - 16*b. Factor q(l).
(l - 2)*(l + 2)**2/5
Let u = -4 - -7. Let i(f) = -f**2 - 3*f + 3. Let n(k) = -2*k**2 - 4*k + 4. Suppose 3*m = -2 - 10, 5*h - 2*m + 12 = 0. Let q(w) = h*i(w) + u*n(w). Factor q(t).
-2*t**2
Let k(v) be the second derivative of 0 + 1/12*v**3 - 3*v - 1/8*v**2 - 1/48*v**4. Factor k(c).
-(c - 1)**2/4
Let f(d) = d**4 + d**3 - d**2 + d + 1. Let c(h) = 18*h**4 - 33*h**3 + 9*h**2 + 3*h + 3. Let k(v) = c(v) - 3*f(v). Solve k(s) = 0.
0, 2/5, 2
Let j(w) be the second derivative of 0*w**2 + 4*w + 0 - 1/30*w**4 + 1/15*w**3. Let j(a) = 0. Calculate a.
0, 1
Let l(q) be the third derivative of -q**7/1995 + q**6/1140 + q**2. Factor l(g).
-2*g**3*(g - 1)/19
Let m(v) be the first derivative of 1/3*v**2 + 1/9*v**6 + 0*v**3 + 0*v + 6 - 1/3*v**4 + 0*v**5. Factor m(y).
2*y*(y - 1)**2*(y + 1)**2/3
Let x(q) be the second derivative of -q**6/30 + q**5/10 - q**3/3 + q**2/2 + 2*q. Factor x(k).
-(k - 1)**3*(k + 1)
Determine l, given that 4*l**5 + 14*l**2 - 12*l**4 + 22*l**4 + 18*l**3 - 2*l**5 + 4*l = 0.
-2, -1, 0
Let w(s) = 5*s**3 - 5*s**2 - 5*s + 5. Let t(h) = 2*h**3 - 2*h**2 - 2*h + 2. Let r be -1 + 0 + 1 - -3. Let m(n) = r*w(n) - 7*t(n). Factor m(d).
(d - 1)**2*(d + 1)
Suppose -z + 3*z - 6 = 0. Let n(g) be the second derivative of 2/3*g**z + 1/5*g**5 + g + 1/2*g**4 + 0 + 1/30*g**6 + 1/2*g**2. Factor n(f).
(f + 1)**4
Let i(o) be the first derivative of -o**5 + 15*o**4/4 - 5*o**3/3 - 15*o**2/2 + 10*o + 5. What is y in i(y) = 0?
-1, 1, 2
Let u(t) be the third derivative of -t**6/300 + 3*t**5/50 - 9*t**4/20 + 9*t**3/5 + 35*t**2. Suppose u(y) = 0. What is y?
3
Let y be (-3)/(-6)*2 + 1. Suppose -y*g - 2*g = -l - 17, 2*g - l = 7. Determine c, given that -2*c**2 - 2 + 3*c + 5*c**4 + 1 - 2*c**4 - c**g - 2*c**3 = 0.
-1, 1
Let d(f) be the third derivative of f**5/60 - 13*f**4/24 + 18*f**2. Factor d(j).
j*(j - 13)
Let z(o) = -2*o - 12. Let d be z(-8). Factor 2*k + 2*k**2 + d*k**2 + k**3 - 3*k**2.
k*(k + 1)*(k + 2)
Let a(t) be the first derivative of -t**3/3 + t**2/2 + 5*t + 2. Let q be a(0). Determine c, given that -q*c - c**4 + 5*c = 0.
0
Suppose -k - 3*k = 0. Factor -3/5*m + k*m**2 + 0 + 3/5*m**3.
3*m*(m - 1)*(m + 1)/5
Let s(f) be the first derivative of -4*f**3/3 - 6*f**2 - 8*f - 15. Let s(d) = 0. What is d?
-2, -1
Let y be -1 - 4/(4/(-1)). Let g be (-3 + 3 + y)/(-2). Determine n so that g*n - 2/9*n**4 + 0 + 4/9*n**3 - 2/9*n**2 = 0.
0, 1
Let w = -205/11 - -207/11. Find z, given that -2/11*z**3 + w*z**2 + 2/11*z - 2/11 = 0.
-1, 1
Let l(q) = q**2 + 9. Let u(p) = p**2 + 1. Let w(x) = -l(x) + 5*u(x). Factor w(y).
4*(y - 1)*(y + 1)
Let u(q) = q**5 + 5*q**4 - 5*q**3 - q**2 + 4*q + 4. Let z(g) = g**5 + 4*g**4 - 4*g**3 - g**2 + 3*g + 3. Let i(w) = 3*u(w) - 4*z(w). Solve i(o) = 0.
-1, 0, 1
Factor -u**2 - 2 - 3 - u**2 - 4*u + 3.
-2*(u + 1)**2
Factor 48/7*a**2 + 0 + 36/7*a**3 + 8/7*a**4 + 16/7*a.
4*a*(a + 2)**2*(2*a + 1)/7
Solve 6 - v + v**2 - 6*v**2 + 2*v**2 - 2*v = 0.
-2, 1
Find q such that -32 + 12*q**2 + 0 - 25*q**4 - 100*q + 18*q**2 - 8 + 65*q**3 = 0.
-1, -2/5, 2
Let a(f) = -2*f**2 + 7*f + 3. Let w(d) = -2*d**2 + 8*d + 2. Let o(t) = 2*a(t) - 3*w(t). Factor o(s).
2*s*(s - 5)
Let r(g) = -2*g**2 + 12*g - 6. Let n(u) = u - 1. Let c(o) = 10*n(o) - r(o). Factor c(s).
2*(s - 2)*(s + 1)
Let f(k) be the third derivative of -k**7/2940 + k**6/630 + k**5/420 - k**4/42 + k**3/2 + 5*k**2. Let a(r) be the first derivative of f(r). Solve a(s) = 0.
-1, 1, 2
Let v(a) = 4*a**2 - 3*a - 7. Let z(s) = 4*s**2 - 2*s - 7. Let j(t) = 5*v(t) - 6*z(t). Let w(q) = q**2 + q - 2. Let o(r) = 2*j(r) + 7*w(r). Factor o(c).
-c*(c - 1)
Let k be -3 + 2/8*14. Let h(r) be the first derivative of 8/5*r**5 - 8/3*r**3 - r**2 + k*r**4 + 0*r + 1. Find d such that h(d) = 0.
-1, -1/4, 0, 1
Let s(q) be the third derivative of -5*q**8/336 + q**6/24 + 5*q**2. Factor s(a).
-5*a**3*(a - 1)*(a + 1)
Let f(r) = -4*r**4 + 5*r**3 + 4*r**2 - 6*r. Let d(m) be the second derivative of m**6/30 + m**5/20 - m**4/12 - 10*m. Let h(w) = -d(w) - f(w). Factor h(v).
3*v*(v - 2)*(v - 1)*(v + 1)
Let y(t) = 5*t**3 + t**2 - t - 5. Let a(w) = 6*w**3 + 2*w**2 - 2*w - 6. Let j(f) = 4*a(f) - 5*y(f). Factor j(z).
-(z - 1)**3
Let m(n) be the first derivative of -2*n**3/3 + 3*n**2/2 - n - 13. What is g in m(g) = 0?
1/2, 1
Let u(g) be the first derivative of 6 + 16/9*g**2 + 1/27*g**6 + 50/27*g**3 + 14/45*g**5 + 19/18*g**4 + 8/9*g. Determine k, given that u(k) = 0.
-2, -1
Let h be (-2)/18*(2 + -8). Let f be (-4)/(-6) - 2/(-1). What is z in -f*z**3 + 0 + 8/3*z**5 + 0*z - h*z**4 + 2/3*z**2 = 0?
-1, 0, 1/4, 1
Determine c so that -30/11*c**3 - 98/11*c + 126/11*c**2 + 2/11*c**4 + 0 = 0.
0, 1, 7
Let u(o) = o**3 - 5*o**2 + 2*o + 3. Let s be u(4). Let d be s/(-10) + (-1)/2. Solve 1/2*j + j**2 + 1/2*j**3 + d = 0.
-1, 0
Let m(j) = -6*j**2 + j. Let f(b) = b**3 + 7*b**2 + 2*b + 7. Let a be f(-7). Let l(h) = 3*h**2. Let y(u) = a*l(u) - 3*m(u). Factor y(c).
-3*c*(c + 1)
Let v(k) be the third derivative of 7/30*k**5 + 0*k + 5/12*k**4 + 0 - 8*k**2 - 2/3*k**3. Suppose v(o) = 0. What is o?
-1, 2/7
Factor -4*c**3 + 0 - 4/5*c**2 + 0*c.
-4*c**2*(5*c + 1)/5
Let v(r) be the third derivative of r**6/180 - r**5/30 + r**4/12 - r**3/9 - 4*r**2. Factor v(z).
2*(z - 1)**3/3
Let q = -1 + 6/5. Factor -1/5*u - q*u**3 + 0 - 2/5*u**2.
-u*(u + 1)**2/5
Suppose -97*r + 40*r = -228. Solve 2/3*x**2 + 0 + 2/3*x - 2/3*x**r - 2/3*x**3 = 0 for x.
-1, 0, 1
Let i(v) be the third derivative of 0 + 0*v**4 - 1/24*v**3 + v**2 + 1/240*v**5 + 0*v. Factor i(f).
(f - 1)*(f + 1)/4
Let s = 8 + -4. Let v**2 - 12*v - v**5 - s*v**5 + 2*v**5 + 6*v**4 - 13*v**2 + 9*v**3 = 0. Calculate v.
-1, 0, 2
Determine i so that -2/7*i + 0 + 8/7*i**2 = 0.
0, 1/4
Let f(n) = -4*n**3 - 3*n**2. Let t = -3 + 6. Suppose 0*y - 3*y - 3 = 0. Let k(j) = -j**3 - j**2. Let v(p) = t*k(p) + y*f(p). Suppose v(h) = 0. What is h?
0
Let i(q) be the third derivative of q**9/1512 + q**8/420 + q**7/420 + q**3/2 + 5*q**2. Let h(w) be the first derivative of i(w). What is r in h(r) = 0?
-1, 0
Let s = 270/13 + -527/26. Find l, given that -3/4*l + s + 1/