(u + 1)/3
Let d = 12/233 - 1234/69201. Let v = 4802/1485 - d. Determine p so that -v*p**5 + 8/5*p**3 + 1/5 - 1/5*p - 8/5*p**2 + 16/5*p**4 = 0.
-1/2, 1/2, 1
Suppose -30 = -w - 5*w. Let y(f) be the first derivative of 0*f**2 - 1/3*f**3 + 2*f**4 - 2 + 0*f - 16/5*f**w. Let y(j) = 0. Calculate j.
0, 1/4
Factor -1/2*c**2 + 0*c**3 + 1/2*c**4 + 0*c + 0.
c**2*(c - 1)*(c + 1)/2
Let x be (-2)/(-5) - 8/(-5). Suppose -5*a = 5*c - 70, -4*c = -3*a + 4 + 3. Factor -u**4 + 3 + 4*u**x - u**4 + 4 - a.
-2*(u - 1)**2*(u + 1)**2
Let l be 90/260 + (-2)/(-13). Factor l*h + 1/2 - h**2.
-(h - 1)*(2*h + 1)/2
Let q = 31/515 - -2/309. Let b(d) be the first derivative of 0*d**4 + q*d**5 - 1 - 2/9*d**3 + 0*d**2 + 1/3*d. Determine k so that b(k) = 0.
-1, 1
Let m = 32 + -44. Let l = -8 - m. Factor 0*r + 2/3*r**l - 2/3*r**2 + 0 + 0*r**3.
2*r**2*(r - 1)*(r + 1)/3
Let a(d) = 24*d**2 - 57. Let l(o) be the first derivative of -o**3 + 7*o - 7. Let w(g) = 4*a(g) + 33*l(g). Determine c, given that w(c) = 0.
-1, 1
Let o(t) = 3*t**2 + 4*t - 3. Let y(b) = 4*b**2 + 5*b - 4. Let n(m) = -5*o(m) + 4*y(m). Let x(i) = i**2 - 2. Let w(c) = 2*n(c) - x(c). Factor w(j).
j**2
Let d(b) be the third derivative of -b**7/630 + b**6/90 - b**5/30 + b**4/18 - b**3/18 - 3*b**2. Solve d(j) = 0 for j.
1
Let i(m) be the second derivative of m**7/42 - m**5/20 + 32*m. Factor i(n).
n**3*(n - 1)*(n + 1)
Determine o, given that 9*o + 10 + 3*o**3 - 30 + 15*o**2 - 7 = 0.
-3, 1
Let q(w) be the first derivative of 8/39*w**3 - 8/65*w**5 - 1/13*w**2 - 2 + 0*w + 1/26*w**4. Suppose q(a) = 0. Calculate a.
-1, 0, 1/4, 1
Factor 8*t**2 + 2*t**3 + 3*t**2 - 62 - 2*t - 3*t**2 + 54.
2*(t - 1)*(t + 1)*(t + 4)
Factor 0*c + 4/9*c**3 + 0 + 0*c**2.
4*c**3/9
Suppose 0 = -2*s + n - 4*n + 3, 0 = -3*s - 4*n + 4. Suppose s*w + w = 2. Let -2*r**3 - 2*r**3 + 4*r**3 - w*r**3 = 0. What is r?
0
What is j in -2/13*j**2 + 0 + 0*j = 0?
0
Let g(b) be the second derivative of b**4/36 + b**3/9 + 22*b. Solve g(v) = 0 for v.
-2, 0
Let m(x) be the first derivative of -3*x**4/4 - 5*x**3 - 12*x**2 - 12*x - 2. Factor m(a).
-3*(a + 1)*(a + 2)**2
Let a be (-1)/(-4)*16/54. Let d(x) be the third derivative of x**2 + 0*x + 0 + 1/108*x**4 - 1/270*x**5 + a*x**3. Factor d(y).
-2*(y - 2)*(y + 1)/9
Factor 2/11*d**5 + 2/11*d + 8/11*d**4 + 0 + 12/11*d**3 + 8/11*d**2.
2*d*(d + 1)**4/11
Let k = 39/6850 + 2/2055. Let z(q) be the third derivative of 0*q + 0 + 3*q**2 + k*q**5 + 1/30*q**4 + 1/15*q**3. Suppose z(b) = 0. What is b?
-1
Let w(t) be the first derivative of -t**4/18 - 4*t**3/27 - t**2/9 + 12. Solve w(r) = 0 for r.
-1, 0
Let h(p) be the second derivative of p**8/3360 + p**7/1260 - p**4/3 + 4*p. Let m(x) be the third derivative of h(x). What is t in m(t) = 0?
-1, 0
Factor -484/7 - 4/7*n**2 - 88/7*n.
-4*(n + 11)**2/7
Suppose -2*f + 8 - 8 = 0. Let j(t) be the second derivative of 1/36*t**4 - 2*t + 0 + f*t**2 + 1/9*t**3. Find m such that j(m) = 0.
-2, 0
Suppose -1490 + 1490 + 3*m + 12*m**2 = 0. What is m?
-1/4, 0
Let i(h) be the first derivative of h**3/21 - 8*h**2/7 + 15*h/7 + 45. Determine k so that i(k) = 0.
1, 15
Factor -3*g**2 + 24 - 8*g**2 + 52*g + 28*g**3 - 93*g**2.
4*(g - 3)*(g - 1)*(7*g + 2)
Suppose -f - 9 = -4*f. Suppose -9 = 4*k - k - 5*v, 0 = -v + f. Factor -7*y**k + 1 + 7*y**3 + 0*y - 3*y**3 + 2*y.
(y - 1)**2*(4*y + 1)
Let o(r) = -r**3 + 3*r**2 + r + 12. Let i be o(4). Let 6*c**4 + 3/2*c**2 + 0*c - 15/2*c**3 + i = 0. What is c?
0, 1/4, 1
Let s(y) = 6*y**5 + 2*y**4 - 11*y**3 - y**2 + 4*y + 7. Let t(m) = -3*m**5 - m**4 + 6*m**3 - 2*m - 3. Let q(w) = -6*s(w) - 14*t(w). What is f in q(f) = 0?
-2, -1/3, 0, 1
Let p be (-7)/(-4) + 2/8. Suppose -p = -2*w + 2. Solve -3/2*t**w - t + 0 = 0 for t.
-2/3, 0
Let y(o) be the third derivative of -1/8*o**3 + 0*o - 1/80*o**5 + 1/16*o**4 + 0 + 3*o**2. Determine i so that y(i) = 0.
1
Let m = 7 + -17/3. Let i(f) be the first derivative of 4*f - m*f**3 + 3 + 3/2*f**4 - 3*f**2. Factor i(h).
2*(h - 1)*(h + 1)*(3*h - 2)
Let h(n) = -16*n + 8. Let j(g) = -g**2 + 16*g - 9. Let q(p) = -3*h(p) - 4*j(p). Solve q(s) = 0.
1, 3
Let q(x) be the first derivative of -x**5/210 + x**4/42 - x**3/21 + 3*x**2/2 - 2. Let h(r) be the second derivative of q(r). Factor h(u).
-2*(u - 1)**2/7
Let n be (-5*1 - -2)*(-2 - -1). Let i(z) be the first derivative of -n - 1/2*z**2 + 2/3*z**3 + 0*z - 1/4*z**4. Factor i(q).
-q*(q - 1)**2
What is x in -12*x**4 + 26*x**2 - 11*x - 4*x**3 + 19*x**2 + 71*x - 11*x**3 + 12 = 0?
-2, -1, -1/4, 2
Let z(r) = -4*r**3 + 2*r**2 - 3. Let d(g) = 15*g**3 + 12 + 5 + 8*g**3 - 11*g**2. Let w(n) = -6*d(n) - 34*z(n). Factor w(b).
-2*b**2*(b + 1)
Let h(n) be the second derivative of -n**7/252 + n**5/120 + 10*n. Solve h(y) = 0.
-1, 0, 1
Let l(x) be the second derivative of x**6/15 - x**5/5 + 2*x**3/3 - x**2 - 2*x. Factor l(p).
2*(p - 1)**3*(p + 1)
Let x = 4 - 23/6. Let z(g) be the first derivative of -2 - 1/8*g**4 - x*g**3 + 1/4*g**2 + 1/2*g. Factor z(b).
-(b - 1)*(b + 1)**2/2
Factor -6/5*d + 0 + 3/5*d**5 + 3*d**2 - 9/5*d**3 - 3/5*d**4.
3*d*(d - 1)**3*(d + 2)/5
Let z(s) be the third derivative of -2*s**7/105 - s**6/15 + s**4/3 + 2*s**3/3 - 2*s**2. Solve z(a) = 0 for a.
-1, 1
What is g in 0 + 6/5*g**3 + 12/5*g**4 + 3/5*g**5 - 9/5*g - 12/5*g**2 = 0?
-3, -1, 0, 1
Factor 0*x**2 - 1/4*x + 1/8*x**4 + 1/4*x**3 - 1/8.
(x - 1)*(x + 1)**3/8
Let y(k) be the second derivative of k**7/126 - k**6/45 + k**4/18 - k**3/18 - 5*k. Suppose y(o) = 0. What is o?
-1, 0, 1
Suppose 5*m = 5 + 5. Solve -6*v - m*v + 3*v**3 - 4*v**4 + v + v**5 + 4*v**2 + 3*v = 0.
-1, 0, 1, 2
Let n(r) = -7*r**3 + r**2 - 11*r + 2. Let c(q) = -6*q**3 + 2*q**2 - 10*q + 2. Let j(a) = 5*c(a) - 4*n(a). What is u in j(u) = 0?
1
Let l(d) be the second derivative of -d**7/14 - d**6/10 + 3*d**5/20 + d**4/4 + d. Find v, given that l(v) = 0.
-1, 0, 1
Suppose 0 = -j + 5*j + 8. Let s = j - -5. Suppose 64/3*h - 32/3 + 16/3*h**s - 16*h**2 - 2/3*h**4 = 0. What is h?
2
Let t = -13 + 0. Let i = t - -13. Factor -4/9*r**3 + 4/9*r - 2/9*r**4 + 2/9 + i*r**2.
-2*(r - 1)*(r + 1)**3/9
Let g(z) be the first derivative of -2*z**3/3 - z**2 + 4*z + 7. Factor g(d).
-2*(d - 1)*(d + 2)
Let o(z) be the second derivative of z**5/10 - z**3/3 + 7*z. Find x such that o(x) = 0.
-1, 0, 1
Suppose 0 = 4*x - 6 - 10. Suppose -a = -2*i - 5, 0*i = 3*i + x*a - 20. Solve i - 3/5*d**3 + d**4 + 4/5*d**5 - d**2 - 1/5*d = 0 for d.
-1, -1/4, 0, 1
Let g = 0 - -4. Suppose 8 = g*b - 0. Suppose -2*d**2 + b*d + 5*d - 4 - d = 0. What is d?
1, 2
Let a = 6 - 0. Suppose -a*d = -d. Solve 3/2*w + d + 0*w**4 + 3/2*w**5 - 3*w**3 + 0*w**2 = 0 for w.
-1, 0, 1
Let w(f) be the first derivative of f**6/12 + 2*f**5/5 + 3*f**4/8 - 2*f**3/3 - f**2 + 5. Factor w(j).
j*(j - 1)*(j + 1)*(j + 2)**2/2
Let j(a) be the third derivative of -a**8/1680 + a**6/360 - 2*a**3/3 + 5*a**2. Let d(n) be the first derivative of j(n). Factor d(w).
-w**2*(w - 1)*(w + 1)
Let j(s) be the first derivative of 0*s**3 + 1/2*s**2 - 3 - 1/4*s**4 + 1/2*s - 1/10*s**5. Find v, given that j(v) = 0.
-1, 1
Let v(y) be the first derivative of 2*y**5/25 - y**4/2 + 6*y**3/5 - 7*y**2/5 + 4*y/5 - 5. Suppose v(j) = 0. Calculate j.
1, 2
Find q, given that 6/11*q**2 - 2/11*q**4 + 4/11*q**3 - 8/11*q - 8/11 = 0.
-1, 2
Let m(k) be the first derivative of -2/5*k**3 + 2/5*k**2 + 0*k + 2/25*k**5 - 7 + 0*k**4. Factor m(w).
2*w*(w - 1)**2*(w + 2)/5
Suppose -x = -0*v - v - 7, -3*x + 5 = v. Let h = 3 - x. Find d, given that -d**5 + d**4 - d**2 + h*d**5 + 2*d**5 - d**3 = 0.
-1, 0, 1
Let m = -62125/59 + 1053. Let f = 100/531 + m. Factor f*d + 0 - 2/9*d**4 + 2/3*d**3 - 2/3*d**2.
-2*d*(d - 1)**3/9
Let c(i) be the first derivative of -5*i**4/4 + 5*i**3/3 + 5*i**2/2 - 5*i + 15. Factor c(r).
-5*(r - 1)**2*(r + 1)
Suppose -14 + 4 = -5*g. Determine d, given that 4/3*d + 0 + 14/3*d**g = 0.
-2/7, 0
Let w = 1 + -1. What is l in 2/5*l**3 + w*l + 2/5*l**2 + 0 = 0?
-1, 0
Factor 0*y - 2/9*y**2 + 2/9.
-2*(y - 1)*(y + 1)/9
Let h(p) be the third derivative of -p**6/24 - p**5/3 - 25*p**4/24 - 5*p**3/3 + 11*p**2. Determine f so that h(f) = 0.
-2, -1
Let j(s) = -2*s**2 - 4*s - 4. Let c(t) = t**2 - t**2 - t**2. Let h(m) = -c(m) + j(m). Factor h(f).
-(f + 2)**2
Let g(u) be the first derivative of 3*u**4/20 - u**3/5 - 3*u**2/5 + 7. Solve g(q) = 0.
-1, 0, 2
Solve 2/7*t**5 - 4/7*t**3 + 2/7*t**4 + 2/7 + 2/7*t - 4/7*t**2 = 0.
-1, 