*u**4/20 - 3*u**3/10 + 3*u**2/10 + 20*u. Let p(d) = 0. What is d?
1
Let m(j) be the third derivative of 0*j**3 + 0*j**4 + 2*j**2 + 0 - 1/15*j**5 + 0*j + 1/30*j**6 - 1/210*j**7. Suppose m(h) = 0. Calculate h.
0, 2
Suppose 37*i - 132 = -21. Factor 0 + 2/9*w**i + 0*w - 2/9*w**2.
2*w**2*(w - 1)/9
Let r(o) be the third derivative of -o**6/360 - o**5/180 - 5*o**2. Factor r(v).
-v**2*(v + 1)/3
Let y be (-24)/18*9/(-6). Factor -4/7*s**2 + 4/7 + y*s - 2*s**3.
-2*(s - 1)*(s + 1)*(7*s + 2)/7
What is f in -4/13 - 44/13*f**4 - 64/13*f**2 - 76/13*f**3 - 2*f - 10/13*f**5 = 0?
-1, -2/5
Let a(z) be the third derivative of -7*z**6/40 - 3*z**5/5 - 3*z**4/8 + z**3 - 8*z**2. Solve a(f) = 0.
-1, 2/7
Let j(p) be the third derivative of p**5/120 - p**4/24 - p**3/4 - 2*p**2 + 22*p. Determine u, given that j(u) = 0.
-1, 3
Let r = -1011/8 + 37487/296. Let j = 245/222 - r. Find t such that 5/6*t + 7/6*t**4 - j*t**3 - 3/2*t**2 + 1/3 = 0.
-1, -2/7, 1
Let m(w) be the second derivative of -w**4/42 - 13*w**3/21 - 12*w**2/7 - 2*w + 20. What is s in m(s) = 0?
-12, -1
Suppose -3 = -3*p - 3*y, 3*y + 1 - 12 = 5*p. Let z be p - (1 - 2 - 4). Determine x, given that -4*x + 6*x**z + 8*x**3 - x**2 - 2*x**2 + x**2 = 0.
-1, 0, 2/3
Let b(q) be the first derivative of 5*q**3/3 + 4*q**2 - 4*q - 2. Factor b(m).
(m + 2)*(5*m - 2)
Let c(a) be the second derivative of 2*a**2 - 2/3*a**4 - 2/5*a**5 + 2/3*a**3 + 2/21*a**7 + 2*a + 2/15*a**6 + 0. Solve c(r) = 0.
-1, 1
Suppose 3*w + 6 = 6*w. Let u(v) = 3*v - 2. Let r be u(2). Factor -w*s**3 + s**5 + 3*s + s**4 - 2*s - s**r.
s*(s - 1)**2*(s + 1)**2
Let c(t) be the second derivative of 3/25*t**5 + 4/5*t**3 + 0 - 4/5*t**2 - 13/30*t**4 - 1/75*t**6 + 4*t. Factor c(d).
-2*(d - 2)**2*(d - 1)**2/5
Let l(p) be the third derivative of p**6/30 - 2*p**5/5 + 4*p**4/3 - p**2 - 6. Find k, given that l(k) = 0.
0, 2, 4
Let d = 14 + -14. Factor 2 + r**3 - r - 2*r + 0 + d.
(r - 1)**2*(r + 2)
Let a(p) be the first derivative of -p**5/5 - p**4/4 + p**3 + 5*p**2/2 + 2*p - 17. Solve a(o) = 0.
-1, 2
Let l = 937/4 + -234. Find n such that -1/4*n + 0 - l*n**5 + 0*n**2 + 0*n**4 + 1/2*n**3 = 0.
-1, 0, 1
Let v(w) be the first derivative of 2 + 0*w + 1/4*w**4 + 1/6*w**2 + 1/3*w**3 + 1/15*w**5. Factor v(f).
f*(f + 1)**3/3
Let a(c) be the third derivative of c**5/90 + c**4/6 - 7*c**3/9 + 5*c**2. Solve a(x) = 0.
-7, 1
Let d(j) be the first derivative of 0*j**3 + 3/25*j**5 + 0*j + 3/20*j**4 + 0*j**2 - 1/5*j**6 - 1. Suppose d(w) = 0. Calculate w.
-1/2, 0, 1
Let f = 16 - 12. Let a(s) be the first derivative of -1/16*s**f + 1/8*s**2 + 3 + 0*s**3 + 0*s. Factor a(g).
-g*(g - 1)*(g + 1)/4
Let u(t) = t**3 + 9*t**2 + 9*t + 11. Let s be u(-8). Let g be 0 + (1 - -1) + s. Factor 2 + c - g*c**3 + 9*c**3 - 8*c**2 + c**3.
(c - 1)**2*(5*c + 2)
Suppose -3 = -s - 1. Let h(i) be the third derivative of 2*i**s + 0*i**6 + 1/120*i**5 + 0*i**4 + 0*i**3 + 0 + 0*i - 1/420*i**7. Solve h(g) = 0 for g.
-1, 0, 1
Let x(m) be the third derivative of -1/15*m**5 + 0*m**4 + 0*m - 2/105*m**7 + 0*m**3 + 0 - 1/15*m**6 + m**2. Factor x(z).
-4*z**2*(z + 1)**2
Let v = 10 - 2. Suppose -f = -5*f + v. Factor -2*z**3 - 3/2*z**f + 0 + 1/2*z.
-z*(z + 1)*(4*z - 1)/2
Let p(w) = w**3 - 9*w**2 - 10*w + 1. Let a be p(10). Let o(r) be the first derivative of -1/2*r**2 - a + 1/4*r**4 - 1/3*r**3 + r. Find b, given that o(b) = 0.
-1, 1
Let j(t) be the third derivative of -1/3*t**3 - t**2 + 0 + 0*t**4 + 1/30*t**5 + 0*t. Factor j(u).
2*(u - 1)*(u + 1)
Let x be (-8 + 4)/(2/(-5)). Let y be 6/10*x/9. Determine b, given that 8/9 + 0*b + 2/9*b**3 - y*b**2 = 0.
-1, 2
Let y(f) be the third derivative of -f**7/945 - f**6/540 + f**5/270 + f**4/108 + 18*f**2. Factor y(a).
-2*a*(a - 1)*(a + 1)**2/9
Let s(t) = 2*t**3 + 22*t**2 + 28*t + 12. Let i(h) = -h**3 + h**2. Let o(u) = -2*i(u) + s(u). Factor o(n).
4*(n + 1)**2*(n + 3)
Factor -2*f + 2*f**2 + 32 - 7*f - 2*f - 5*f.
2*(f - 4)**2
Let h(a) = a - 3 - 14*a + 5*a**3 + 4*a**3 + a - 5*a**2. Let x(s) = 14*s**3 - 8*s**2 - 18*s - 4. Let f(p) = 8*h(p) - 5*x(p). Let f(n) = 0. What is n?
-1, 2
Let c = -3 + 3. Suppose -2*o + 5*o = c. Factor 4/3*i**2 + 0*i + o*i**3 - 2/3 - 2/3*i**4.
-2*(i - 1)**2*(i + 1)**2/3
Let r(k) be the first derivative of 9*k**5/5 + 6*k**4 + 3*k**3 - 3*k**2 - 41. Factor r(w).
3*w*(w + 1)*(w + 2)*(3*w - 1)
Let r(u) be the second derivative of u**4/108 + 4*u. Factor r(p).
p**2/9
Suppose 0 = -2*o - 5*a + 38, -5*o + 61 = 4*a - 0. Let s = o + -5. Suppose z**s - 4*z**3 + 2*z**4 - z**4 + 2*z**2 = 0. What is z?
0, 1
Suppose 0 = 13*n - 3 - 23. Let f(q) be the third derivative of -3*q**n + 1/12*q**4 + 0 - 1/6*q**3 - 1/60*q**5 + 0*q. Suppose f(b) = 0. What is b?
1
Suppose 54 = 17*b - 14. Factor 0 + 0*o + o**2 - 1/2*o**b + 1/2*o**3.
-o**2*(o - 2)*(o + 1)/2
Let b be (-64)/(-36) + 4/18. Suppose 0 = 14*c - 5 - 37. Find y, given that -40/9*y**b - 8/9*y - 50/9*y**c + 0 = 0.
-2/5, 0
Solve 128/3*o + 58/3*o**2 + 7/3*o**3 + 32/3 = 0 for o.
-4, -2/7
Factor -5*d**2 + 2*d**2 - 3*d + 8*d + d.
-3*d*(d - 2)
Let h(q) be the third derivative of q**8/2520 - 2*q**7/1575 - q**6/225 + 4*q**5/225 - 10*q**2 + 1. Factor h(f).
2*f**2*(f - 2)**2*(f + 2)/15
Determine v, given that 78*v**3 + 344*v + 76*v**3 - 43*v**3 + 48 + 644*v**2 - 13*v**3 = 0.
-6, -2/7
Let f(x) = -126*x + 3. Let q be f(-7). Let t = q + -4403/5. Determine j so that -6/5*j**4 + 4/5 - 22/5*j**2 + 2/5*j + t*j**3 = 0.
-1/3, 1, 2
Find t such that -1/3*t**2 + 0 + 0*t**3 + 0*t + 1/3*t**4 = 0.
-1, 0, 1
Let g(u) be the first derivative of 2*u**5/15 - u**4/3 + 2*u**2/3 - 2*u/3 - 7. Factor g(d).
2*(d - 1)**3*(d + 1)/3
Let z(a) = 5*a**2 + 41*a + 11. Let h be z(-8). Find s such that 4/7*s**2 + 0*s - 4/7*s**4 + 10/7*s**h + 0 - 10/7*s**5 = 0.
-1, -2/5, 0, 1
Let w(r) be the second derivative of 0 - 1/54*r**4 + 5*r + 2/27*r**3 - 1/9*r**2. What is n in w(n) = 0?
1
Let b(s) be the third derivative of s**7/840 - s**6/1080 - s**5/120 + s**4/72 + s**3/6 - s**2. Let v(z) be the first derivative of b(z). Factor v(p).
(p - 1)*(p + 1)*(3*p - 1)/3
Let l be 3 - (0 + 6/2). Let s be (-3 - l/3) + 6. Factor -3*n**3 - n + n + s*n**2.
-3*n**2*(n - 1)
Let w = 7 - 6. Let p be w/2 + (-3)/(-2). Factor 1/3 + 2/3*y + 1/3*y**p.
(y + 1)**2/3
Let r(z) = -z**3 + 1. Let y(s) = -3*s**4 + 9*s**3 - 18*s**2 + 12*s. Let m(w) = -3*r(w) + y(w). Factor m(n).
-3*(n - 1)**4
Let m(z) be the third derivative of -6*z**2 + 0 - 1/180*z**6 + 0*z - 1/18*z**5 - 2/9*z**4 - 4/9*z**3. Factor m(l).
-2*(l + 1)*(l + 2)**2/3
Let z(v) = -3 + 2*v**2 - 2*v + 9 - v. Let f(d) = -9*d**2 + 15*d - 30. Let y(i) = -5*f(i) - 24*z(i). Find o, given that y(o) = 0.
-2, 1
Let m(i) = 13*i + 156. Let x be m(-12). Factor 0 + 0*j - 1/3*j**3 + x*j**2 - 2/3*j**4 - 1/3*j**5.
-j**3*(j + 1)**2/3
Let u(z) be the third derivative of 0*z - 3*z**2 - 7/60*z**5 + 1/6*z**3 - 1/12*z**4 - 1/30*z**6 + 0. Factor u(l).
-(l + 1)**2*(4*l - 1)
Let o = -15 + 7. Let f = 8 + o. Factor 0*z + 1/2*z**5 + 0 - 1/2*z**3 + 0*z**2 + f*z**4.
z**3*(z - 1)*(z + 1)/2
Let q(g) be the first derivative of g**4/24 + g**3/18 + 3. Determine u, given that q(u) = 0.
-1, 0
Let z(b) = b**2 + 12*b + 15. Let f be z(-11). Let h(s) be the third derivative of 0*s + 0*s**f + 0 - 1/120*s**5 + s**2 + 1/12*s**3. Suppose h(q) = 0. What is q?
-1, 1
Let f(p) be the first derivative of 0*p**2 + 0*p + 1/6*p**3 + 5. Factor f(t).
t**2/2
Let w = 1 + 1. Let 72*f**2 - 3 + 6 + f**3 - 75*f**w - f = 0. Calculate f.
-1, 1, 3
Suppose -101 = 5*w - 121. Let 7/3*m**5 + m**3 + 0 + 0*m - 4*m**w + 2/3*m**2 = 0. What is m?
-2/7, 0, 1
Let g(u) be the first derivative of 0*u**2 - 4/33*u**3 - 8/55*u**5 + 0*u + 5/22*u**4 - 1 + 1/33*u**6. Suppose g(v) = 0. What is v?
0, 1, 2
Let f be (0 + 3 - 3)/(6/6). Factor 0 + 4/7*a**2 + f*a + 6/7*a**5 - 2/7*a**3 - 8/7*a**4.
2*a**2*(a - 1)**2*(3*a + 2)/7
Let m(s) be the first derivative of -9*s**4/16 + s**3/4 + 9*s**2/8 - 3*s/4 + 38. Factor m(x).
-3*(x - 1)*(x + 1)*(3*x - 1)/4
Let x = 97 + -97. Determine m so that 3/2*m**2 + x - m - 1/2*m**3 = 0.
0, 1, 2
Factor -q**2 + 0*q**2 + 0*q**2.
-q**2
Let r = 233 - 230. Solve 0 + 10/9*k**2 + 4/9*k + 4/9*k**r = 0 for k.
-2, -1/2, 0
Suppose 0*s + 13 = s + 3*p, 0 = s - 4*p + 15. Let m = 2 + s. Factor 2*q**5 + q**2 - m*q**4 + q**2 + q**4 - 2*q**3.
2*q**2*(q - 1)**2*(q + 1)
Suppose -1 = -q + 1. Factor 4*t - t**3 + t**2 + 2 - t**q - t.
-(t - 2)*(t + 1