 z**6/6 + 2*z**5/5 - 2*z**3/3 - z**2/2 + 20. Factor v(j).
j*(j - 1)*(j + 1)**3
Suppose 0 = -t - 6*o + 11*o - 11, 2*t = 2*o + 2. Factor -1/8*f**2 + 0*f + 1/8*f**t - 1/8*f**5 + 1/8*f**3 + 0.
-f**2*(f - 1)**2*(f + 1)/8
Let u(p) be the second derivative of p**4/54 - p**3/27 - 8*p. Suppose u(q) = 0. What is q?
0, 1
Let c(g) = -g + 1. Let a(x) = -2*x**3 + 6*x**2 + 5*x - 9. Let l(f) = -2*a(f) - 22*c(f). Determine k, given that l(k) = 0.
1
Let t(z) = -z**2 + 3*z + 4. Let g = 12 - 9. Let y be t(g). Factor 6*r - 40 + 3*r**y + 37 - 6*r**3 + 0*r.
3*(r - 1)**3*(r + 1)
Let r(u) = 5*u**5 + u**4 - 3*u**3 - 3*u**2 + 2. Let y(p) = 21*p**5 + 3*p**4 - 12*p**3 - 12*p**2 + 9. Let x(s) = 9*r(s) - 2*y(s). Factor x(b).
3*b**2*(b - 1)*(b + 1)**2
Let h(v) be the second derivative of 3*v**5/80 - 19*v**4/16 + 99*v**3/8 - 243*v**2/8 - 5*v + 1. Determine y so that h(y) = 0.
1, 9
Let g(s) be the third derivative of 0*s**3 + 0*s - 1/105*s**7 + 1/30*s**5 + 0 + 1/60*s**6 + 2*s**2 - 1/12*s**4. Factor g(z).
-2*z*(z - 1)**2*(z + 1)
Let x(o) be the third derivative of 0*o + 0 - o**2 + 1/96*o**4 + 0*o**3 + 1/240*o**5. Suppose x(b) = 0. What is b?
-1, 0
Let i(d) = -d - 5. Suppose -t + 4*t + 29 = 2*k, -4*t = 5*k + 8. Let f be i(t). Determine y, given that -4*y - 2*y**f - 3*y + 3*y = 0.
-2, 0
Let f(v) be the first derivative of v**5/90 + v**4/18 + v**3/9 + 3*v**2/2 + 1. Let q(n) be the second derivative of f(n). Find t, given that q(t) = 0.
-1
Suppose -f - 28 = -5*m - 3*f, m + 2*f - 12 = 0. Determine j so that 10*j**5 - 15/2*j + 31/2*j**2 - 5/2*j**3 + 1 - 33/2*j**m = 0.
-1, 1/4, 2/5, 1
Let i(q) be the first derivative of q**6/2 + 3*q**5/5 - 3*q**4/4 - q**3 + 6. Factor i(s).
3*s**2*(s - 1)*(s + 1)**2
Factor -2/3*h**3 - 4/3 + 0*h**2 + 2*h.
-2*(h - 1)**2*(h + 2)/3
Let l(q) be the second derivative of -q**3/6 + 4*q**2 - q. Let v be l(0). Factor -v*f**2 + 18*f + 6*f - 3 - 2 - 13.
-2*(2*f - 3)**2
Suppose -7*u + 4*u = -9. Factor 2 + 3*l**2 + 12*l**4 - 8 + 6 + 15*l**u.
3*l**2*(l + 1)*(4*l + 1)
Let i(w) be the first derivative of -3*w**7/35 - 2*w**6/25 + 4*w**5/25 + w**4/5 + w**3/15 + 2*w - 2. Let x(p) be the first derivative of i(p). Solve x(m) = 0.
-1, -1/3, 0, 1
Let u = -17 + 20. Factor 0*j**5 + 4*j**4 + 4*j - 2 + 0*j**4 - 2*j**2 + j - j**5 - 4*j**u.
-(j - 2)*(j - 1)**3*(j + 1)
Suppose -5*z + 3*m - 9 = 0, z = 5*m - 0*m - 15. Let d(q) = -q + 3. Let o be d(0). Factor 4 + 10*c**o + 7*c + 18*c**2 + z + 2*c**4 + 7*c.
2*(c + 1)**3*(c + 2)
Find z such that -686/5*z**4 + 16/5 - 152/5*z - 98/5*z**3 + 84*z**2 = 0.
-1, 2/7
Let z(m) be the second derivative of -m**6/135 - m**5/90 + 3*m. Factor z(p).
-2*p**3*(p + 1)/9
Suppose 12 = -5*i - 13, -4*i - 25 = -n. Let -1/7*z**3 + 0 + 1/7*z**2 - 1/7*z**4 + 0*z + 1/7*z**n = 0. Calculate z.
-1, 0, 1
Let r(y) be the third derivative of y**7/70 - 3*y**6/40 + 3*y**5/20 - y**4/8 + 9*y**2. Factor r(d).
3*d*(d - 1)**3
Solve 0*j - 4/7*j**2 + 4/7*j**4 + 0 + 0*j**3 = 0.
-1, 0, 1
Let i be (8/(-168))/(2/(-24)). Let d = 3/46 - -71/322. Find k such that -d*k**4 + 0 + i*k + 8/7*k**3 - 10/7*k**2 = 0.
0, 1, 2
Factor -13/5*w**2 - 9/5*w + 3/5*w**4 + 2/5*w**5 - 2/5 - w**3.
(w - 2)*(w + 1)**3*(2*w + 1)/5
Let d(u) be the first derivative of u**5/30 - u**4/3 + 4*u**3/3 + 3*u**2/2 + 2. Let b(g) be the second derivative of d(g). Determine k so that b(k) = 0.
2
Find u, given that -20*u**5 + 9*u**2 - 28*u**3 - 17*u**3 - 4*u**2 - u + 6*u + 55*u**4 = 0.
-1/4, 0, 1
Let t be 9/(1 + 20/(-8)). Let f(u) = u - 1. Let b(p) = p**3 + p**2 + 5*p - 7. Suppose -2 + 1 = -k. Let g(z) = k*b(z) + t*f(z). Factor g(w).
(w - 1)*(w + 1)**2
Factor 0*j**3 + 2/7*j**4 + 0*j + 0 - 2/7*j**2.
2*j**2*(j - 1)*(j + 1)/7
Factor 3/2 - 13/4*w + 2*w**2 - 1/4*w**3.
-(w - 6)*(w - 1)**2/4
Let k = -1/153 + 313/1071. Let a(g) = -g. Let w be a(-5). Factor -4/7*o**3 + k*o**w + 2/7*o + 0 + 0*o**4 + 0*o**2.
2*o*(o - 1)**2*(o + 1)**2/7
Let c(s) be the third derivative of s**8/84 - 2*s**7/105 - 9*s**2. Factor c(h).
4*h**4*(h - 1)
Let l = 457/4 - 114. Find w, given that l*w**5 + w**4 + 0 + 1/4*w + 3/2*w**3 + w**2 = 0.
-1, 0
Let s be (0/(-3))/(2/(-2)). Let u be -3 + (16 - s/(-3)). Determine k, given that -u*k**2 - 225*k**2 - 126*k**3 - 71*k**3 - 8 - 48*k**3 - 76*k = 0.
-2/5, -2/7
Let u be 4/(-6) - (-551)/435. Determine o so that -u*o**3 + 0*o + 0 - 3/5*o**2 = 0.
-1, 0
Factor -11*l**2 - 4 + 5*l - 8*l**3 + 6 + 0 + 12*l**3.
(l - 2)*(l - 1)*(4*l + 1)
Suppose 2*u + 5*l = -2*u - 59, -3*u - 38 = 5*l. Let b be (u/9 - -2)*-2. Factor 1/3*q**2 + q**3 - q + 1/3*q**4 - b.
(q - 1)*(q + 1)**2*(q + 2)/3
Suppose -3*c + 4 = -3*g - 5*c, -2*c - 18 = -4*g. Let f(u) be the third derivative of 1/12*u**4 - 1/40*u**5 + g*u**2 + 1/3*u**3 + 0*u + 0. Factor f(n).
-(n - 2)*(3*n + 2)/2
Let x(y) = -y**2 + y + 1. Let m(d) = 35*d**2 - 55*d - 30. Let i(c) = -m(c) - 30*x(c). Factor i(j).
-5*j*(j - 5)
Let r(d) be the second derivative of d**9/17640 - d**8/11760 - d**7/8820 - d**4/6 - 4*d. Let y(f) be the third derivative of r(f). Find u such that y(u) = 0.
-1/3, 0, 1
Let d(v) = -3*v**2 - 3*v. Suppose -5*g + 2*g = -12. Let b be 9/g + (-7)/28. Let t(k) = -3*k**2 - 3*k. Let m(n) = b*d(n) - 3*t(n). Factor m(p).
3*p*(p + 1)
Find k such that k**3 - k**3 - 2*k**5 + k**5 = 0.
0
Let s = -5 - 7. Let u(f) = f**3 - f**2 - f - 1. Let r(m) = -10*m**3 + 6*m**2 + 18*m + 10. Let w(b) = s*u(b) - r(b). Determine q, given that w(q) = 0.
1
Let d(t) be the second derivative of 3*t**6/35 - 6*t**5/7 + 19*t**4/7 - 12*t**3/7 - 27*t**2/7 - 21*t. Find k, given that d(k) = 0.
-1/3, 1, 3
Let t(x) be the third derivative of x**6/1800 - x**4/120 + x**3/3 + 2*x**2. Let y(p) be the first derivative of t(p). Factor y(m).
(m - 1)*(m + 1)/5
Factor -16*c**2 - 20*c**2 + 32*c**2 + 11 + 5.
-4*(c - 2)*(c + 2)
Let q(m) = -m**3 - m**2 + 3*m + 5. Let f be q(-2). Let l(o) be the first derivative of 3 + 1/12*o**f + 1/2*o**2 + o. Find b such that l(b) = 0.
-2
Let g = -28 + 34. Let q(u) be the first derivative of -4/3*u**3 + 1/3*u**g + 1/2*u**4 - u + u**5 - 2*u**2 + 2. Factor q(w).
(w - 1)*(w + 1)**3*(2*w + 1)
Let z(o) be the first derivative of 7*o**6/3 - 24*o**5/5 - 2*o**4 + 28*o**3/3 - 3*o**2 - 4*o + 20. Factor z(u).
2*(u - 1)**3*(u + 1)*(7*u + 2)
Let b be (-3)/2 + 1 + 1. Solve -2 + 2*v - b*v**2 = 0.
2
Factor -29*h**2 + 6*h**2 + 3*h**3 + 11*h**2.
3*h**2*(h - 4)
Let s(l) = -l**2 - l + 1. Let f(x) = -9 + 0*x**2 + 0*x**2 + 3*x**2. Let c(z) = -f(z) - 6*s(z). Factor c(j).
3*(j + 1)**2
Let v(h) be the first derivative of -h**6/1260 + h**5/420 + h**4/42 - 2*h**3/3 + 1. Let q(x) be the third derivative of v(x). Find a such that q(a) = 0.
-1, 2
Factor -h**2 - h**2 + 2*h**2 + 3*h - 2*h**2 + 2.
-(h - 2)*(2*h + 1)
Let b(o) be the second derivative of o**5/20 + o**4/3 + o**3/3 - o**2/2 - 2*o. Let w be b(-3). Factor 2/7*p**w - 6/7*p + 4/7.
2*(p - 2)*(p - 1)/7
Let d(c) be the first derivative of -c**5/6 + c**4/3 - c**3/18 - c**2/6 + 31. Factor d(b).
-b*(b - 1)**2*(5*b + 2)/6
Let b(q) = -q**2 + q + 2. Let s be b(0). Let l = 3 + -2. Factor 1 + 4*z**s + l - 6*z**2.
-2*(z - 1)*(z + 1)
Let c(s) be the second derivative of -s**5/50 + s**3/15 + s. Determine o, given that c(o) = 0.
-1, 0, 1
Let i(g) be the first derivative of -g**5/5 - 3. Factor i(v).
-v**4
Let a be (-20 - -19) + 0 + (-22)/(-18). Suppose a*h**2 - 2/9 + 0*h = 0. Calculate h.
-1, 1
Let r = 6 + -4. Find g, given that -2*g**5 + r*g**3 - 137*g**4 + 137*g**4 = 0.
-1, 0, 1
Let i be (-9)/9 + (-87)/(-81). Let y(h) be the first derivative of i*h**3 + 1/3*h**2 + 4/9*h + 3. Factor y(f).
2*(f + 1)*(f + 2)/9
Determine p, given that 0*p - 15/2*p**5 - 10*p**3 + 2*p**2 + 0 + 31/2*p**4 = 0.
0, 2/5, 2/3, 1
Factor 2/3*v**3 + 3/2*v**2 - 5*v - 4/3.
(v - 2)*(v + 4)*(4*v + 1)/6
Let -7/2*g**4 - 9/4*g - 3/4*g**5 + 15/2*g**2 + 0 - g**3 = 0. What is g?
-3, 0, 1/3, 1
Suppose -816*q + 810*q = 0. Suppose 4/5*h**3 + q*h**2 + 0*h - 2/5*h**4 + 0 = 0. Calculate h.
0, 2
Let d(u) be the first derivative of -u**4/18 + u**3/9 + 2*u**2/3 + 2*u - 3. Let z(r) be the first derivative of d(r). Factor z(j).
-2*(j - 2)*(j + 1)/3
Let s be (-16)/(-40) - (-22)/(-5). Let u be (0 + 2)*(-2)/s. Factor -y + 1/4*y**2 + u.
(y - 2)**2/4
Let k(g) be the first derivative of g**6/15 + g**5/10 + g + 1. Let v(j) be the first derivative of k(j). Solve v(i) = 0 for i.
-1, 0
Let p(x) be the first derivative of -2*x**3/3 + 5*x**2/2 +