*n**2 + 0 + 0*n - 2/9*n**3.
-2*n**3*(n + 1)/9
Let u(h) be the first derivative of -h**5/10 - 17*h**4/2 - 506*h**3/3 + 1224*h**2 - 2592*h - 153. Factor u(x).
-(x - 2)**2*(x + 36)**2/2
Let u(x) = -x**2 - 7*x + 33. Let d be u(-10). Suppose -4*t = -t + 4*a + 10, t + 2 = -a. Factor -4*k**3 + 1 - 2*k**t - 1 - 3*k**d.
-k**2*(7*k + 2)
Let i(a) be the first derivative of -2*a**3/3 + 25*a**2 - 124. Find m such that i(m) = 0.
0, 25
Suppose -3*u + 5*l = -23, -4*u - u = -5*l - 45. Let c = u + -11. Find r, given that c*r + r**3 + 0 - 2/5*r**2 - 3/5*r**4 = 0.
0, 2/3, 1
Suppose -10*f - 5*f**4 + 3*f**4 + 3*f**4 + 24 + 0*f**4 - 9*f**3 + 30*f**2 - 34*f = 0. What is f?
2, 3
Find r, given that -776*r**3 - 775*r**3 + 4*r**2 + 1552*r**3 - 12*r = 0.
-6, 0, 2
Let j(b) = 4*b**2 + 7*b - 19. Let u be j(-7). Let o be u/30 - (-6)/15. Let 4/3*l**3 + o*l**4 - 4/3*l - 14/3*l**2 + 0 = 0. Calculate l.
-1, -2/7, 0, 1
Let n be (-33)/220*(-40)/105. Let f(j) be the first derivative of 0*j + 1/21*j**6 + 0*j**2 - 2/7*j**3 - 5/14*j**4 + 1 - n*j**5. Let f(a) = 0. Calculate a.
-1, 0, 3
Let o(f) = -5*f**2 - 7*f + 5. Let y(p) = -3*p**2 - 4*p + 3. Let c(q) = 4*o(q) - 7*y(q). What is h in c(h) = 0?
-1, 1
Let m(o) be the first derivative of o**8/1200 - 3*o**7/1400 + o**6/900 + 4*o**3 + 2. Let g(t) be the third derivative of m(t). Determine f, given that g(f) = 0.
0, 2/7, 1
Suppose -9 = 37*o - 40*o. Let s(l) be the third derivative of 0*l**4 - 3*l**2 - 1/240*l**5 + 0*l + 1/24*l**o + 0. Factor s(i).
-(i - 1)*(i + 1)/4
Find j such that 56/3 - 58/3*j + 2/3*j**2 = 0.
1, 28
Find u such that 1458/5 + 2/5*u**2 + 108/5*u = 0.
-27
Let f(v) be the first derivative of v**2/2 + v + 21. Let h be f(1). Determine u so that -4/3*u**h - 2/3*u + 0 - 2/3*u**3 = 0.
-1, 0
Find h, given that -225*h + 3*h**3 + 80*h**2 + 24*h**2 - 8*h**3 - 38*h**2 + 54*h**2 + 110 = 0.
1, 22
Let i be (-2 - (2 - -1)) + 7. Let r(j) be the first derivative of -j**4 + 0*j - 8 - 4/5*j**5 + 4/3*j**3 + 2*j**i. Determine h, given that r(h) = 0.
-1, 0, 1
Let l be -2*((-90)/(-4))/(-15). Let -12/5*g**2 + 8/5*g**l + 0*g + 4/5 = 0. What is g?
-1/2, 1
Let i(c) be the second derivative of c**7/70 + c**6/25 - 3*c**5/100 - c**4/10 - c - 45. Solve i(b) = 0.
-2, -1, 0, 1
Let p(v) = -v**3 + 4*v**2 - 4. Let g be p(2). Let k(t) be the first derivative of t**3 + 0*t + 9 - 3/4*t**g + 3*t**2. Suppose k(u) = 0. Calculate u.
-1, 0, 2
Suppose 11*n + 734 = 778. Let y(v) be the second derivative of -9*v + 0 + 0*v**3 + 3/40*v**5 + 3/8*v**n - 3*v**2. Determine j so that y(j) = 0.
-2, 1
Let v(m) = 17*m**2 + 142*m - 173. Let k(o) = 5*o**2 + 48*o - 57. Let f(p) = 14*k(p) - 4*v(p). Factor f(q).
2*(q - 1)*(q + 53)
Let y(z) be the third derivative of -z**8/294 - 13*z**7/735 - z**6/28 - z**5/30 - z**4/84 - 42*z**2 + 2. Factor y(b).
-2*b*(b + 1)**3*(4*b + 1)/7
Let c(s) be the second derivative of s**5/120 - 8*s**2 + 8*s. Let x(t) be the first derivative of c(t). Factor x(i).
i**2/2
Let i(f) = 11*f**3 - 29*f**2 - 23*f. Let v(d) = -2*d**3 + 5*d**2 + 4*d. Let k(o) = o**2 - 6*o - 1. Let m be k(7). Let x(s) = m*i(s) + 34*v(s). Factor x(a).
-2*a*(a + 1)**2
Suppose -208*n + 206 = -210. Factor 8/3*y**3 - 2/3*y + y**4 + y**n + 0.
y*(y + 1)*(y + 2)*(3*y - 1)/3
Let k(g) = -8*g**2 - 33*g + 12. Let l(i) = -i**2. Let h = 43 - 44. Let b(s) = h*k(s) - l(s). Factor b(f).
3*(f + 4)*(3*f - 1)
Let i(p) = 5*p**3 - 350*p**2 + 6130*p - 5. Let j(v) = 5*v**3 - 350*v**2 + 6129*v - 4. Let y(q) = -4*i(q) + 5*j(q). Factor y(w).
5*w*(w - 35)**2
Let t = 20 - 18. Let j be t*(-3)/((-3)/1). Factor -14*l**2 + 13*l**3 - 9*l**2 - 4*l**j + 12 + 8*l**3 - 36*l.
3*(l - 2)*(l + 1)*(7*l - 2)
Solve k**3 + 10 + 6*k**2 + 3*k**3 - 7*k**4 + 33*k**4 - 2 - 84*k**2 + 40*k = 0.
-2, -2/13, 1
Factor 832*c**2 - 12*c - 1695*c**2 + 855*c**2.
-4*c*(2*c + 3)
Let u(p) = -p**3 + 2*p**2 - 1. Let c(t) = t. Let b be c(-1). Let x be u(b). Factor -m + 28*m**3 - 23*m**3 - m - 3*m**x.
m*(m - 1)*(5*m + 2)
Let -3*c**4 + 0*c - 9/7*c**3 + 0 + 0*c**2 = 0. Calculate c.
-3/7, 0
Let d(c) be the third derivative of 1/70*c**7 + 0*c**3 + 0*c - 2*c**2 - 1/8*c**4 + 1/40*c**6 - 1/20*c**5 + 0. Suppose d(x) = 0. Calculate x.
-1, 0, 1
Suppose -2 = -4*p + 10. Let c = 31 - 28. Solve -3/2*t**5 + 0 - p*t**4 + 0*t**c + 3*t**2 + 3/2*t = 0.
-1, 0, 1
Let g(q) = -9*q**5 - 7*q**4 + 2*q**2 - q. Let y(o) = -2*o**5 - o**4. Let i(n) = 2*g(n) - 10*y(n). Factor i(x).
2*x*(x - 1)**3*(x + 1)
Let k(t) be the third derivative of -23*t**2 + 1/420*t**6 + 0 + 0*t - 1/3*t**3 + 5/28*t**4 - 3/70*t**5. Suppose k(c) = 0. Calculate c.
1, 7
Let l(q) be the first derivative of 0*q - 2/3*q**3 - 11 + 1/2*q**4 - 2/15*q**5 + 1/3*q**2. Factor l(v).
-2*v*(v - 1)**3/3
Let k be (-2 - 1)/(((-21714)/44)/47). Suppose -1/7*j + 1/7*j**2 - k = 0. What is j?
-1, 2
Let p(w) = -12*w**3 + 23*w**2 + 12*w + 5. Let d(r) = 42*r**3 - 81*r**2 - 42*r - 18. Let a = 15 + -33. Let x(i) = a*p(i) - 5*d(i). Factor x(y).
3*y*(y - 2)*(2*y + 1)
Suppose -27 = 2*t - 35. Solve -2*i**3 + 182*i**4 - 93*i**t + 2*i**2 - 90*i**4 + i**3 = 0 for i.
-2, 0, 1
Let h be ((32/(-20))/2)/((-8)/20). Solve -3*o**h - 29*o + 26*o + 0*o**2 + 3 + 3*o**3 = 0.
-1, 1
Let s(u) be the first derivative of 4*u - 1/2*u**4 + 4*u**2 - 1/5*u**5 + u**3 - 2. Determine n, given that s(n) = 0.
-2, -1, 2
Let o(g) be the second derivative of -g**9/15120 - g**8/6720 + g**7/2520 + g**6/720 - g**4/4 - 10*g. Let h(l) be the third derivative of o(l). Factor h(c).
-c*(c - 1)*(c + 1)**2
Let f(n) be the third derivative of n**5/210 + n**4/28 - 10*n**3/21 - 5*n**2 + 5. Solve f(w) = 0 for w.
-5, 2
Let t(q) = 7*q**3 - 67*q**2 - 26*q - 38. Let w be t(10). Factor -4/3*i**3 - 2*i - 3*i**w - 1/3.
-(i + 1)**2*(4*i + 1)/3
Let t(w) be the third derivative of w**8/2352 - w**7/1470 - w**6/420 + w**5/210 + w**4/168 - w**3/42 - 149*w**2. Factor t(i).
(i - 1)**3*(i + 1)**2/7
Let y(i) be the second derivative of 5*i**7/252 - 3*i**6/4 + 25*i**5/8 - 365*i**4/72 + 10*i**3/3 + 9*i + 8. Solve y(h) = 0.
0, 1, 24
Let b(n) be the first derivative of n**8/336 + n**7/210 - n**6/40 - n**5/60 + n**4/12 + 15*n**2 - 54. Let i(p) be the second derivative of b(p). Solve i(r) = 0.
-2, -1, 0, 1
Let b(p) be the second derivative of p**5/5 + 221*p**4 + 97682*p**3 + 21587722*p**2 - 80*p + 2. Factor b(m).
4*(m + 221)**3
Suppose 4*h + 2 + 6 = -4*i, 5*h + 3*i = -10. Let t be (4 - (-7)/(-2))*h*-2. What is x in 2/17*x**t + 0*x - 2/17 = 0?
-1, 1
Solve -28*q**5 + 10*q**4 + 60*q**5 + 27 - 27*q**5 + 43 - 235*q - 130*q**3 + 280*q**2 = 0 for q.
-7, 1, 2
Factor 48*o**2 + 3*o**3 + 2*o**3 - 245*o + 98 + 12*o**2 - 253 - 145.
5*(o - 4)*(o + 1)*(o + 15)
Suppose 2*w = 6*w + 40. Let q = w - -12. Find v such that -6*v + 0 + 5 - 1 + q*v**3 = 0.
-2, 1
Let y(b) be the first derivative of -14*b - 15/2*b**2 - 1/3*b**3 + 4. Factor y(a).
-(a + 1)*(a + 14)
Let t = 42966 + -302710/7. Let n = t + 279. Find q such that 4/7*q - n*q**5 + 15/7*q**3 + 0 + 16/7*q**2 - 2/7*q**4 = 0.
-1, -2/5, 0, 2
Let -81/8*t**3 + 3*t**4 - 549/8*t**2 - 57*t + 63/2 = 0. What is t?
-2, 3/8, 7
Let f(j) be the first derivative of j**6/120 + 11*j**5/40 + 5*j**4/4 + 13*j**3 + 9. Let g(t) be the third derivative of f(t). Factor g(z).
3*(z + 1)*(z + 10)
Let o = -26 - -28. Let d be 0*(-4)/16*o/(-4). Factor d - 1/3*y**2 + 2/3*y.
-y*(y - 2)/3
Determine o so that -o**4 - 6*o**3 + 2*o**5 - 14*o**3 + 18*o**3 + o**2 = 0.
-1, 0, 1/2, 1
Let g(q) be the first derivative of -3*q - 5/3*q**3 + 22 - 7/2*q**2 - 1/4*q**4. Factor g(n).
-(n + 1)**2*(n + 3)
Let x(i) be the first derivative of -2*i**3/27 + 38*i**2/9 - 74*i/9 - 32. Factor x(f).
-2*(f - 37)*(f - 1)/9
Let r(k) be the first derivative of k**5/20 - k**4 + 22*k**3/3 - 24*k**2 + 36*k - 73. Let r(x) = 0. What is x?
2, 6
Let q be ((-228)/380)/((-2)/10). Solve 1/2*u**q + 0 + u**2 + 1/2*u = 0.
-1, 0
Factor -1/6*s**2 + 82/3*s - 3362/3.
-(s - 82)**2/6
Factor 0*t**3 + 7203 + 9*t**3 + 2695*t + t**2 + 19*t**2 - 8*t**3 + 81*t**2.
(t + 3)*(t + 49)**2
Let v = -63 + 64. Let d be ((-17)/51)/(0 - v). Suppose c**2 + 4/3*c + d = 0. Calculate c.
-1, -1/3
Let m be 4/9 + 688/72. Let y be 100/m - (3 - -3). Let 4/9*b**3 - 4/9*b + 2/9 + 0*b**2 - 2/9*b**y = 0. Calculate b.
-1, 1
Let r(w) = 24*w - 504. Let b be r(21). Determine t, given that b*t**2 + 0 - t**3 + 1/3*t**4 + 0*t = 0.
0, 3
Let p(b) be the third derivative of 1/12*b**4 + 0*b + 0 + 