r f.
-2, 0, 1
Let u(h) be the first derivative of 5*h**6/6 + h**5 - 5*h**4/2 + 41. Determine s, given that u(s) = 0.
-2, 0, 1
Let s(a) be the first derivative of -3 + 1/9*a**3 + 1/3*a**2 + 0*a. Factor s(d).
d*(d + 2)/3
Let m(i) be the second derivative of 8*i + 2/3*i**3 - 1/6*i**4 + 0*i**2 + 0 - 1/10*i**5. Factor m(n).
-2*n*(n - 1)*(n + 2)
Let x be ((-6)/(-15))/((-1)/(-10)). Solve 3*c**2 + 0*c + 1 - c**3 + c - x*c = 0 for c.
1
Let i = -1/12 - 13/36. Let v = 2/3 + i. Factor v + 4/9*l**2 - 2/3*l.
2*(l - 1)*(2*l - 1)/9
Determine p, given that -13*p + 5*p + 24 - 6*p**2 + 3*p**3 - 4*p = 0.
-2, 2
Let g = 56/171 - -1/171. Suppose -2*r + 7 = 3. Factor g*q - 1/3*q**r + 0.
-q*(q - 1)/3
Let y(h) = -5*h + 5. Let p be y(-7). Let q be 26/p + 8/(-32). Factor 6/5*j**3 + 0 - q*j**4 + 2/5*j - 6/5*j**2.
-2*j*(j - 1)**3/5
Suppose -2*u + 1/4*u**2 + 4 = 0. What is u?
4
Suppose -278 = -5*z + h + 204, 0 = 4*z + 4*h - 376. Suppose 5*o - 2*o + z*o**2 + 0 + 12*o**2 - 6 = 0. What is o?
-1/4, 2/9
Let a(n) be the second derivative of n**5/30 + n**4/12 - 2*n**3/3 - 3*n**2/2 - n. Let y(k) be the first derivative of a(k). Let y(l) = 0. What is l?
-2, 1
Let u = 29 - 24. Let x(k) be the third derivative of -k**2 + 0 + 1/150*k**u + 1/300*k**6 + 0*k + 0*k**3 + 0*k**4. Factor x(i).
2*i**2*(i + 1)/5
Let l(t) = 2*t**4 - 2*t**3 - 2*t**2 + 2*t + 2. Let w(x) = 4*x**4 - 5*x**3 - 4*x**2 + 5*x + 5. Let c(m) = -5*l(m) + 2*w(m). Factor c(i).
-2*i**2*(i - 1)*(i + 1)
Determine x so that 8/7*x**3 + 16/7 + 4/7*x**4 - 12/7*x**2 - 16/7*x = 0.
-2, 1
Let a be (-3 + 12)*3/9. Let t(o) be the first derivative of -2/21*o**3 + a - 2/35*o**5 + 0*o**2 - 1/7*o**4 + 0*o. Find m such that t(m) = 0.
-1, 0
Let v(j) be the first derivative of -5*j**3 - 12*j**2 - 12*j - 1 - 3/4*j**4. Factor v(i).
-3*(i + 1)*(i + 2)**2
Let x(k) be the second derivative of 1/6*k**3 + 1/12*k**4 + 1/60*k**5 + 2*k - k**2 + 0. Let z(d) be the first derivative of x(d). Suppose z(g) = 0. What is g?
-1
Let l(i) be the second derivative of -i**6/195 - 2*i**5/65 - 5*i**4/78 - 2*i**3/39 + 5*i. Factor l(c).
-2*c*(c + 1)**2*(c + 2)/13
Let l(b) be the second derivative of 7*b**6/60 + 3*b**5/4 + 43*b**4/24 + 2*b**3 + b**2 - 2*b. Find a such that l(a) = 0.
-2, -1, -2/7
Let m be (1 + -1)*4/8. Suppose -5*x - v + 11 = m, 3*x + 0*v - 9 = -3*v. Factor 2*d**3 - 4*d**4 - x*d - 4*d**4 + 6*d**4 + 2*d**2.
-2*d*(d - 1)**2*(d + 1)
Let c(o) be the first derivative of -o**3/27 + o/9 - 5. Let c(h) = 0. Calculate h.
-1, 1
Suppose 3 = 5*w + 2*r - 7, -w - 2*r + 2 = 0. Factor 1/2*c**3 + 1/2*c**w + 0 - 1/2*c**4 - 1/2*c.
-c*(c - 1)**2*(c + 1)/2
Let c be 0 + 1 + 2 + (-7 - -6). Solve -1/3*z - 1/3*z**3 - 2/3*z**c + 0 = 0 for z.
-1, 0
Let v(x) = -2*x**2 - 27*x + 49. Let i be v(-15). Find y, given that 0 + 0*y**3 + 2/11*y**i - 6/11*y**2 + 4/11*y = 0.
-2, 0, 1
Let p(d) be the second derivative of 0 - 3/4*d**2 + 5*d + 3/20*d**5 + 1/20*d**6 + 0*d**4 - 1/2*d**3. Suppose p(r) = 0. What is r?
-1, 1
Let m = 1123/68 + -1/68. Let z = 1/4 - -1/4. What is y in -20*y**3 - 5*y + z + m*y**2 + 8*y**4 = 0?
1/4, 1
Suppose -14 = s - 14. Let o(b) be the third derivative of s*b + 0 + 4*b**2 - 1/210*b**5 + 0*b**3 + 1/42*b**4. Factor o(n).
-2*n*(n - 2)/7
Let h(c) be the first derivative of -2*c**3 - 1/2*c**4 - 2*c + 4 - 3*c**2. Factor h(w).
-2*(w + 1)**3
Let h(u) be the third derivative of u**8/23520 - u**6/2520 - u**4/4 - 7*u**2. Let d(a) be the second derivative of h(a). Determine o so that d(o) = 0.
-1, 0, 1
Let h(m) = -7*m**3 - 6*m**2 - 18*m - 2. Let b(u) be the first derivative of u**4/4 + u**2/2 - u + 2. Let g(j) = 6*b(j) + h(j). Factor g(w).
-(w + 2)**3
Let t be (-26)/8*(0 + (-8)/7). Factor 128/7*w**5 + 2/7*w - 32*w**4 + 0 - t*w**2 + 120/7*w**3.
2*w*(w - 1)*(4*w - 1)**3/7
Let m(x) be the third derivative of -x**6/60 + x**5/30 + x**2. Factor m(r).
-2*r**2*(r - 1)
Let j(m) be the third derivative of m**6/360 - 13*m**5/180 + 23*m**4/72 - 11*m**3/18 + 9*m**2. Let j(b) = 0. What is b?
1, 11
Let h(b) be the second derivative of -b**5/80 + b**4/12 - b**3/6 - 8*b. Factor h(v).
-v*(v - 2)**2/4
Let d be 20/90 + (-50)/(-18). Determine t, given that 0 - 8/5*t**5 - 2*t**d - 2/5*t**2 + 0*t - 16/5*t**4 = 0.
-1, -1/2, 0
Let u be (-6)/(-2) + (-6 - -7). Suppose 2*c + 6*c**3 - u*c**3 + 10*c**2 + 6*c**3 = 0. Calculate c.
-1, -1/4, 0
Solve 27/5*w**2 - 13/5*w + 7/5*w**4 - 23/5*w**3 + 2/5 = 0.
2/7, 1
Determine v, given that 2*v + 1 - 3*v + 2*v + 0*v - 2*v**2 = 0.
-1/2, 1
Let a(o) be the second derivative of o**5/20 - 5*o**4/12 + 4*o**3/3 - 2*o**2 - 21*o. What is c in a(c) = 0?
1, 2
Factor 9*z**2 - 4*z**3 - 3*z**5 + 7*z**5 + 9*z**2 - 6*z**2 - 12*z**4.
4*z**2*(z - 3)*(z - 1)*(z + 1)
Factor 4*o**3 - 4*o**2 - 3*o**4 + o**4 + 0*o**2 + 2*o**3.
-2*o**2*(o - 2)*(o - 1)
Find u such that -5*u**3 + 4*u**3 + 3*u**2 + u**3 - 3*u**3 = 0.
0, 1
Factor 0*b**2 - 4*b**2 - 27*b - b**2 + 2*b + 30.
-5*(b - 1)*(b + 6)
Let v(j) be the second derivative of -j**6/9 + 43*j**5/90 + j**4/9 - 20*j**3/9 - 8*j**2/9 - 66*j. Let v(t) = 0. What is t?
-1, -2/15, 2
Factor 2/9*t**2 - 2/9 + 0*t.
2*(t - 1)*(t + 1)/9
Let d(i) = -i**2 + i - 1. Let m(u) = -13*u - 2*u + 6*u**2 + 11 + 6*u. Let f be (-109)/(-5) + (-2)/(-10). Let n(z) = f*d(z) + 2*m(z). Factor n(a).
-2*a*(5*a - 2)
Let n be (16/12)/((-2)/(-6)). Let k be 3 - 2 - (-52)/n. Solve 49/5*d**3 + k*d**2 + 8/5 - 52/5*d = 0 for d.
-2, 2/7
Let u(v) be the second derivative of 1/20*v**5 + 0*v**2 - v - 1/12*v**4 + 0 + 0*v**3. Factor u(w).
w**2*(w - 1)
Suppose 2*u - p + 0*p - 3 = 0, 3*u + 4*p - 10 = 0. Find x such that 6*x - 18*x**3 + 8*x**u + 96/5*x**5 + 4/5 - 16*x**4 = 0.
-2/3, -1/4, 1
Factor 0 - 4/5*o**3 - 2/5*o**4 + 1/5*o**5 + 3/5*o + 2/5*o**2.
o*(o - 3)*(o - 1)*(o + 1)**2/5
Let c(b) = -6*b**2 - 24*b - 38. Let g(w) = -13*w**2 - 48*w - 77. Let m(q) = -5*c(q) + 2*g(q). Determine r, given that m(r) = 0.
-3
Let v(r) be the first derivative of -r**3/9 - r**2/3 + r - 16. Find y, given that v(y) = 0.
-3, 1
Determine a, given that -5/2*a - 1/2*a**5 - 1/2 - 5*a**2 - 5/2*a**4 - 5*a**3 = 0.
-1
Factor -1/5*v**3 + 0 + 0*v**2 + 0*v.
-v**3/5
Let i(t) be the second derivative of -t**7/105 + t**5/30 - t**2/2 + 3*t. Let x(r) be the first derivative of i(r). What is o in x(o) = 0?
-1, 0, 1
Let y(n) be the first derivative of 2*n**6 + 4*n**5 + n**4 - 4*n**3/3 - 4. Factor y(m).
4*m**2*(m + 1)**2*(3*m - 1)
Let l = -59/2 - -30. Solve 1 + l*s - 1/2*s**2 = 0 for s.
-1, 2
Suppose 0 = 3*f + 3, -7 = -5*m - 5*f + 8. Suppose -9*r**2 - 10*r - 7/2*r**3 - m - 1/2*r**4 = 0. Calculate r.
-2, -1
Let z(t) = -4*t + 2*t + 7 - 2*t + 5*t. Let s be z(-5). Factor -1/4*b + 1/4*b**3 + 1/4*b**s - 1/4.
(b - 1)*(b + 1)**2/4
Let s = 12 - 4. Factor 2*g**4 + 4*g**2 - 2*g - 2*g + 6*g**2 - s*g**3.
2*g*(g - 2)*(g - 1)**2
Suppose 2*m - 12 = 3*n + 4, 3*m = -n + 2. Let r(k) be the third derivative of 1/30*k**5 + 0 + 1/3*k**3 - 1/6*k**4 + 3*k**m + 0*k. Solve r(q) = 0 for q.
1
Let z(t) = 4*t + 14. Let m be z(-3). Factor -135*b**3 + 243/2*b**4 - 12*b + 0 - 81/2*b**5 + 66*b**m.
-3*b*(b - 1)*(3*b - 2)**3/2
Suppose -n + 351 = 348. Let 32/7*x**2 - 64/7 + 4/7*x**5 - 64/7*x + 64/7*x**n + 4*x**4 = 0. Calculate x.
-2, 1
Let k(b) be the third derivative of 1/30*b**4 + 0*b**3 - 3*b**2 + 0 + 3/350*b**7 + 0*b - 2/75*b**5 - 1/200*b**6. Factor k(w).
w*(w + 1)*(3*w - 2)**2/5
Let m = -10 - -34/3. Let w(c) be the first derivative of m*c + 4/9*c**3 - 3 - 5/3*c**2. Factor w(b).
2*(b - 2)*(2*b - 1)/3
Suppose 0 - 2/13*u + 4/13*u**2 - 2/13*u**3 = 0. Calculate u.
0, 1
Let p(c) be the first derivative of 2*c**3/9 - 2*c/3 + 36. What is h in p(h) = 0?
-1, 1
Factor 5*a**3 - 3*a**2 + 3*a**3 + 2*a**4 + 4*a**4 - 5*a**3.
3*a**2*(a + 1)*(2*a - 1)
Let b(x) be the third derivative of -x**5/60 + 2*x**4/3 - 32*x**3/3 + 38*x**2. What is r in b(r) = 0?
8
What is f in -6*f**3 - 11*f**4 - 4*f**2 + f**4 + 5*f**2 + 3*f**2 = 0?
-1, 0, 2/5
Let y(g) be the third derivative of g**5/120 + 5*g**4/16 + 7*g**3/6 + 2*g**2 - 1. Factor y(j).
(j + 1)*(j + 14)/2
Suppose 2*b = -4*b - 72. Let d be ((-117)/(-208))/((-1)/b). Let 6 + d*y**4 - 21/2*y**2 + 9*y - 45/4*y**3 = 0. Calculate y.
-2/3, 1, 2
Let b be ((-2)/(-3))/(-8 - 238/(-21)). Factor -b*w**3 - 2/5*w**2 - 1/5*w + 0.
-w*(w + 1)**2/5
Let q(a) be the first derivative of 0*a + 3 + 0*a**2 - 2/15*a**3 - 1/10*a**4. Factor q(v).
-2*v**2*(v + 1)/5
Let p be 0 - (