Suppose -23 = -k + 12. Suppose 10*g - 3*g - k = 0. Factor 2/9*x - 2/3*x**3 - 4/9*x**g + 2/9*x**2 - 10/9*x**4 + 0.
-2*x*(x + 1)**3*(2*x - 1)/9
Suppose 6 = -17*y + 20*y. Let b(n) be the second derivative of -1/10*n**3 + 0*n**y + 4*n - 1/10*n**4 + 0 - 3/100*n**5. Factor b(w).
-3*w*(w + 1)**2/5
Let b(p) be the first derivative of 2*p**3/3 + p**2 + 4*p - 79. Let t be b(0). Factor -6/7*z**3 + 2/7*z**5 + 0 + 10/7*z**2 - 2/7*z**t - 4/7*z.
2*z*(z - 1)**3*(z + 2)/7
Suppose -6*n = -2*n. Let v(b) be the second derivative of 1/2*b**3 - 9*b - 1/2*b**4 + n + 0*b**2 + 3/20*b**5. Suppose v(f) = 0. What is f?
0, 1
Let s(h) be the first derivative of -2*h**3/33 - 8*h**2 - 352*h + 531. Factor s(u).
-2*(u + 44)**2/11
Let y(l) be the first derivative of l**5/540 - l**4/108 - l**3/18 + 7*l**2 + 16. Let k(c) be the second derivative of y(c). Factor k(f).
(f - 3)*(f + 1)/9
Factor -17/5*o - 1/5*o**3 + 2*o**2 + 8/5.
-(o - 8)*(o - 1)**2/5
Factor 2/5*i**2 + 62/5*i - 64/5.
2*(i - 1)*(i + 32)/5
Let d(c) = c**3 + 7*c**2 + 10*c + 14. Let q be d(-7). Let l be q/10*(-4)/8. What is b in -2/5*b**2 + l*b**3 - 6/5*b + 0*b**4 - 8/5*b**5 + 2/5 = 0?
-1, 1/2, 1
Determine b so that 1/6*b**4 - 4/3*b**2 + 1/3*b**3 + 0*b + 0 = 0.
-4, 0, 2
Let w(a) = 231*a + 7394. Let g be w(-32). Let -11/3*i**g + 5/3*i + 2/3 + 4/3*i**3 = 0. What is i?
-1/4, 1, 2
Let i(y) = y**3 + 13*y**2 + 10*y + 5. Let z(v) = v**3 + 14*v**2 + 9*v + 6. Let r(u) = -6*i(u) + 5*z(u). What is d in r(d) = 0?
-5, -3, 0
Let f(q) be the first derivative of q**4/26 + 4*q**3/13 - q**2/13 - 12*q/13 - 184. Factor f(a).
2*(a - 1)*(a + 1)*(a + 6)/13
Suppose -12679*m = -12709*m + 2 - 2. Factor m*c**2 - 4/3 - 2/9*c**3 + 14/9*c.
-2*(c - 2)*(c - 1)*(c + 3)/9
Let y(t) = 14*t**4 - 10*t**3 - 12*t**2 - 8*t. Let j(m) = -16*m**4 + 12*m**3 + 12*m**2 + 8*m. Let s(v) = 5*j(v) + 6*y(v). Solve s(w) = 0.
-1, 0, 2
Let p(y) be the third derivative of 0*y + 0 - 1/8*y**4 + 1/10*y**5 + 1/40*y**6 + 17*y**2 - y**3. Factor p(r).
3*(r - 1)*(r + 1)*(r + 2)
Let u(l) = l**2 - 5*l - 63. Let r be u(11). Let x(s) be the first derivative of 6*s**3 + r*s**2 - 2*s - 1 + 5/2*s**4. Factor x(a).
2*(a + 1)**2*(5*a - 1)
Let o = 26/427 - -1370/5551. Find a such that 0 - 2/13*a**4 + o*a - 4/13*a**3 + 2/13*a**2 = 0.
-2, -1, 0, 1
Let q(b) be the first derivative of 13 + 24/5*b**2 + 121/20*b**4 - 11*b**3 - 4/5*b. Factor q(p).
(p - 1)*(11*p - 2)**2/5
Suppose l = 3*m - 47, 0 = 5*m - m - 4*l - 68. Suppose -2*d + 1 = -m. Suppose 21*b**3 + d*b**5 - 13*b**4 - 17*b**4 + 19*b**3 - 20*b**2 + 4 - 2 = 0. What is b?
-1/4, 1
Let c(x) be the first derivative of x**3/4 - 51*x**2/8 + 105*x/2 - 68. Suppose c(d) = 0. Calculate d.
7, 10
Let y = 975 - 971. Let q(a) be the second derivative of -1/12*a**3 + 0 - 4*a + 1/24*a**y - 1/2*a**2. Factor q(n).
(n - 2)*(n + 1)/2
Let z = -11690 + 11691. Find r, given that z + 3/2*r + 1/2*r**2 = 0.
-2, -1
Let p(r) = 8*r + 52. Let d be p(-7). Let w be (-3 + d + 2)*(-10)/25. What is v in -2/13*v - 2/13*v**w + 0 = 0?
-1, 0
Let v(j) be the first derivative of 5*j**4/8 + 55*j**3/3 + 765*j**2/4 + 810*j + 334. Find f, given that v(f) = 0.
-9, -4
Let v(i) = i**3 + 54*i**2 - 108*i + 228. Let l be v(-56). Let 0 - 2/3*w**l + 0*w - 8/3*w**3 - 8/3*w**2 = 0. What is w?
-2, 0
Let j(y) = y**2 - 4*y - 10. Let k be j(6). Let w = k - -3. Factor -w*a**4 + 2*a**4 + 6*a**2 + 3*a**4 - 9*a**3 + 3*a**5.
3*a**2*(a - 1)**2*(a + 2)
Factor -145*x**2 + 18*x**2 - 5*x**3 + 7*x**3 - 245*x**2.
2*x**2*(x - 186)
Let x(o) = -39 - 8*o**3 + 20*o + o**3 + 10*o**2 + o**3. Let a(m) = m**3 - 1. Let i(l) = a(l) + x(l). Factor i(f).
-5*(f - 2)**2*(f + 2)
Factor -28/5 - 1/5*x**3 - 44/5*x - 17/5*x**2.
-(x + 1)*(x + 2)*(x + 14)/5
Suppose 8*w + 16 = 56. Let l(k) be the first derivative of 1/6*k**3 - w + 0*k + 5/4*k**4 + 4/5*k**5 - 1/4*k**2. Let l(x) = 0. What is x?
-1, -1/2, 0, 1/4
Solve 0 - 6/5*k**3 + 8/5*k**4 - 1/5*k**5 - 8*k**2 - 5*k = 0 for k.
-1, 0, 5
Let g(i) be the second derivative of i**6/15 + 4*i**5/5 - 19*i**4/6 + 10*i**3/3 - i - 125. What is o in g(o) = 0?
-10, 0, 1
Let q(a) = -14*a**4 + 48*a**3 - 35*a**2 + 6*a. Let i(s) = 6*s**4 - 24*s**3 + 18*s**2 - 3*s. Let d(n) = 5*i(n) + 3*q(n). Factor d(g).
-3*g*(g - 1)*(2*g - 1)**2
Suppose -28 = -2*p - 0*p. Factor -2*r**3 + 3*r**3 + 4*r**3 + 19*r**4 - p*r**4.
5*r**3*(r + 1)
Find t such that 70/19*t - 64/19*t**2 - 6/19 = 0.
3/32, 1
Let p(s) = -3*s**3 - 3*s**2 - 3*s + 7. Suppose 2 = 3*m - 4. Let v(b) = -12*b**3 + 10*b**3 + 1 - m*b + 3 - b**2. Let l(f) = 4*p(f) - 7*v(f). Factor l(a).
a*(a - 2)*(2*a - 1)
Let g be (-367)/(-420) - 126/147. Let w(k) be the third derivative of 0*k - 1/300*k**5 + 0*k**3 + 0 + 5*k**2 - g*k**4. Factor w(p).
-p*(p + 2)/5
Let d = 1714 - 1709. Let r(i) be the second derivative of 1/50*i**d + 0 + 0*i**2 + 0*i**3 + 10*i + 1/150*i**6 + 1/60*i**4. Suppose r(u) = 0. What is u?
-1, 0
Let l = 33 - 25. Suppose 4*f - l = 4. Factor 4*p**5 + 4*p**2 - 4*p**4 - 4*p**5 + 4*p**5 - f*p**3 - p**3.
4*p**2*(p - 1)**2*(p + 1)
Let x(y) be the second derivative of -y**4/12 + 2*y**3 + 13*y**2/2 + 41*y. Factor x(s).
-(s - 13)*(s + 1)
Let z be (-81874)/(-15366) - (4 + 0 + 0). Let o = z - -1/197. Factor -1/3*x**2 - 8/3*x + 5/3*x**3 - o + 1/3*x**4 - 1/3*x**5.
-(x - 2)**2*(x + 1)**3/3
Let j(k) be the third derivative of 0*k + 0 + 1/270*k**6 - 5*k**2 - 4/135*k**5 + 2/945*k**7 + 7/108*k**4 - 2/27*k**3 - 1/1512*k**8. Find u, given that j(u) = 0.
-2, 1
Let t = -19 + 25. Let n(g) = 5*g**4 + 9*g**3 - 5*g - 3. Let q(y) = 4*y**4 + 8*y**3 - 6*y - 2. Let i(x) = t*q(x) - 4*n(x). Solve i(l) = 0.
-2, 0, 1
Suppose 0 = 17*l - 30 - 21. Let s(q) be the second derivative of 0*q**2 + 4*q - 1/27*q**l + 0 - 1/90*q**5 + 1/27*q**4. What is x in s(x) = 0?
0, 1
Let s = -66 - -68. Solve -3*k - 4 - 2*k**s + 2*k - k - 4*k = 0.
-2, -1
Suppose -13*w + 11 = -4*y - 10*w, -2*y + 12 = 2*w. Let l be (8/(-1) + 6)*(y - 2). Factor -2/9*f**l + 8/9*f + 0.
-2*f*(f - 4)/9
Let m(o) be the second derivative of -o**7/70 + o**6/15 + 7*o**5/50 - 8*o**4/15 - 17*o**3/10 - 9*o**2/5 + o + 14. Suppose m(p) = 0. What is p?
-1, -2/3, 3
Let m(v) be the first derivative of v**4/26 + 4*v**3 + 156*v**2 + 2704*v + 46. Factor m(a).
2*(a + 26)**3/13
Let h(p) be the third derivative of -p**7/35 + 19*p**6/80 + 13*p**5/40 - 47*p**4/8 - 6*p**3 + 677*p**2 - 2. Solve h(v) = 0.
-2, -1/4, 3, 4
Let -2/3 + 15*p**2 + 7/3*p + 80/3*p**4 - 184/3*p**3 = 0. Calculate p.
-1/5, 1/4, 2
Suppose 5*t + 0*t = -45. Let n(x) = -x**2 - 3*x + 4. Let b(y) = 2*y**2 + 6*y - 9. Let w(q) = t*n(q) - 4*b(q). Let w(l) = 0. Calculate l.
-3, 0
Factor 0*s**5 - 44*s**4 - 22*s**4 - 3*s**5 - 291*s**3 - 77*s**2 + 319*s**2 - 432*s + 550*s**2.
-3*s*(s - 1)**2*(s + 12)**2
Let v(h) = -2*h + 14. Let c be v(10). Let z be ((-26)/4 - -3 - -2)/c. Factor -z*p**3 + 0*p**2 - 1/2 + 3/4*p.
-(p - 1)**2*(p + 2)/4
Let 3/2*h**2 + 27/2 + 9*h = 0. What is h?
-3
Suppose 0 = 6*y - 20 - 58. Factor -y*a - 8 + 0*a - 20*a**2 - 15*a.
-4*(a + 1)*(5*a + 2)
Let p = -10 + 14. Suppose 2*d = -5*f + 133, -3*f - d + 76 = p*d. Determine i, given that 3*i**3 + 21*i**3 + 12*i**4 - f*i - 11*i**2 + 2*i**2 = 0.
-3/2, 0, 1
Suppose 8 = -5*m + 23. Suppose -5*z = 3*x - 7*x + 46, 0 = x + z - 7. Factor -2*w**4 - m*w**4 - 4*w**3 + 0*w**3 + x*w**4.
4*w**3*(w - 1)
Determine o, given that -4/3*o**4 - 419*o**2 + 833/3*o + 289/3 + 139/3*o**3 = 0.
-1/4, 1, 17
Factor 185*z**3 - 2*z**5 + 5*z**5 + 4*z**2 + z**5 - 4*z**4 - 189*z**3.
4*z**2*(z - 1)**2*(z + 1)
Let b(c) be the third derivative of c**7/1260 + c**6/720 - c**5/120 - c**4/144 + c**3/18 - 17*c**2. Suppose b(g) = 0. Calculate g.
-2, -1, 1
Let v(h) be the third derivative of -h**5/105 - 4*h**4/21 - 8*h**3/7 + 345*h**2. Factor v(w).
-4*(w + 2)*(w + 6)/7
Suppose -4*a - a - 4*z = -52, 0 = -4*a - 2*z + 38. Suppose a + 4 = 4*j. Factor -2*b**2 + 13*b - b**j - 9*b - b**3.
-2*b*(b - 1)*(b + 2)
Let w = 2 - -7. Factor -7*o**4 + 3 + 21*o**3 - 7*o**2 + 4*o**5 - w*o**4 - 5*o + 0.
(o - 1)**3*(2*o - 3)*(2*o + 1)
Let z(l) be the first derivative of -l**4/4 - 5*l**3 - 7*l**2 + 48. Solve z(d) = 0.
-14, -1, 0
Let i(n) be the second derivative of -1/40*n**5 + 1/84*n**7 + 1/60*n**6 + 0*n**2 + 0 - 1/24*n**4 + 0*n**3 + 5*n. Let i(r) = 0. What is r?
-1, 0, 1
Let o(d) be the third derivative of d**6/720 - d**5/180 + 78*d**2. Factor o(t).
t**2*(t - 2)/6
Let h(s) = -s**3 + 8*s**2 - 14*s - 