t = 0.
0, 1
Suppose -4*l = 3*h - 38 + 10, 0 = -5*l - 2*h + 28. Suppose -4*a + 2*a + l = 0. Factor 1/2*k**3 + 0*k - 1/2*k**4 + 0*k**a + 0.
-k**3*(k - 1)/2
Let x(c) be the first derivative of c**4/2 + 8*c**3/3 - 5*c**2 + 41. Find a, given that x(a) = 0.
-5, 0, 1
Let t(a) be the third derivative of a**6/1140 - 2*a**5/285 - 5*a**4/228 - 2*a**2 + 23*a. Factor t(s).
2*s*(s - 5)*(s + 1)/19
Let h(q) be the second derivative of 9*q**8/2240 - q**7/28 + 7*q**6/60 - q**5/5 - 4*q**4 - 30*q. Let y(g) be the third derivative of h(g). Factor y(a).
3*(a - 2)*(3*a - 2)**2
Let n(d) be the third derivative of d**5/60 - d**4/6 - 5*d**3/6 + 840*d**2. Find u such that n(u) = 0.
-1, 5
Let f(j) = 30*j**2 - 45*j - 135. Let z(m) = -7*m**2 + 12*m + 34. Let v(o) = -6*f(o) - 25*z(o). Factor v(h).
-5*(h + 2)*(h + 4)
Determine o, given that 32*o**4 + 69*o**2 - 46*o**4 + 11*o**4 + 30*o**3 + 36*o = 0.
-1, 0, 12
Let 118/5*s + 2/5*s**2 - 244/5 = 0. Calculate s.
-61, 2
Factor -254*r + 15*r**2 + 120 + 193*r + 91*r + 160*r.
5*(r + 12)*(3*r + 2)
Let v(n) = n**3 + 6*n**2 - 3*n - 8. Let b be v(-6). Suppose 2*r = -8, 4*i + 3*r + b = 3*i. Factor 2/3*g + 2/3*g**3 + 0 + 4/3*g**i.
2*g*(g + 1)**2/3
Let i be 7 - 14 - (-30)/(2/1) - 6. Find s, given that -1/2*s**i - 3/2*s - 1 = 0.
-2, -1
Let c(i) be the second derivative of i**5/10 + 8*i**4/33 - i**3/33 - 6*i**2/11 - 2*i + 6. Find t such that c(t) = 0.
-1, 6/11
Let j(h) be the third derivative of h**7/2100 - h**6/48 - 13*h**5/200 + 29*h**4/12 - 22*h**2. Let w(p) be the second derivative of j(p). Factor w(r).
3*(r - 13)*(2*r + 1)/5
Let x = -16 + 20. Let s be (2 - -1)/(6/x). Factor -6*c - 2*c**2 + 4*c - s*c**3 + 2*c.
-2*c**2*(c + 1)
Suppose 0 = 5*j - 1 - 9. Suppose j*h = -5*h + 28. Determine b so that -5*b**3 + b**3 - h*b**4 - 2*b**2 + 2*b**4 = 0.
-1, 0
Suppose 20/7*x + 0 + 6*x**2 + 4/7*x**3 = 0. What is x?
-10, -1/2, 0
Suppose 16*w - 280 = 21*w. Let r = -167/3 - w. Factor 0 + 1/3*u**2 - r*u.
u*(u - 1)/3
Let b be (105/(-18))/(-5) - (0 - 10/30). Let o = 35/2 - 16. Factor 0*w - b*w**3 + 0 + o*w**2.
-3*w**2*(w - 1)/2
Find u, given that -410/3*u**4 + 21632/3 + 63650/3*u**2 + 2/3*u**5 + 20390/3*u**3 + 64480/3*u = 0.
-1, 104
Let z(y) be the first derivative of 3*y**5/25 - 123*y**4/20 + 546*y**3/5 - 3234*y**2/5 - 8232*y/5 + 23. Find k, given that z(k) = 0.
-1, 14
Let x(s) be the second derivative of -5/3*s**4 + 14*s - 5/6*s**3 + 1/2*s**5 - 5/42*s**7 + 1/3*s**6 + 0 + 5*s**2. Find a such that x(a) = 0.
-1, 1, 2
Let u(q) = 14*q**2 + 12*q. Let m(x) = -34*x**2 - 30*x. Let w(c) = -5*m(c) - 12*u(c). Solve w(j) = 0.
-3, 0
Suppose -5*a + 20 = 0, 12*a - 10*a - 8 = -5*w. Factor 2/5*q**5 + 0 + 2/5*q**4 + w*q - 2/5*q**3 - 2/5*q**2.
2*q**2*(q - 1)*(q + 1)**2/5
Let n = 317/341 + 5/31. Let f(j) be the first derivative of -14/33*j**3 - 6 + 19/11*j**2 + n*j. Find q, given that f(q) = 0.
-2/7, 3
Let l = -48787/4930 - 2/493. Let m = -91/10 - l. Suppose -2*a - 18/5*a**3 + 32/5*a**2 - m = 0. What is a?
-2/9, 1
Factor -147*d**3 - 77*d + 368*d**2 - 3*d - 358*d**3 + 28*d**4 + 485*d**3 - 296*d**3.
4*d*(d - 10)*(d - 1)*(7*d - 2)
Let c(y) be the third derivative of -y**7/1260 + y**6/60 - 23*y**5/180 + 5*y**4/12 - 25*y**3/36 + 10*y**2. Factor c(h).
-(h - 5)**2*(h - 1)**2/6
Let f(s) be the third derivative of -s**10/151200 - s**9/60480 + 19*s**5/60 + 17*s**2. Let p(n) be the third derivative of f(n). Factor p(d).
-d**3*(d + 1)
Factor -4/3*f**2 - 32/3*f - 28/3.
-4*(f + 1)*(f + 7)/3
Let f(z) be the first derivative of -z**6/54 + 4*z**5/45 - 10*z**3/27 + z**2/18 + 2*z/3 - 10. Solve f(a) = 0 for a.
-1, 1, 2, 3
Let l = 218 - 155. Let x = 191/3 - l. Solve x*t**2 + 0*t + 0 - t**3 + 1/3*t**5 + 0*t**4 = 0.
-2, 0, 1
Let n(b) be the third derivative of -13/360*b**5 + 0*b**3 + 0 + 0*b - 7/240*b**6 - 1/72*b**4 + 7*b**2. Factor n(x).
-x*(3*x + 1)*(7*x + 2)/6
Let r(g) be the third derivative of g**6/144 - 19*g**5/180 - g**4/9 - 8*g**2 + 27*g. Factor r(q).
q*(q - 8)*(5*q + 2)/6
Let w(k) be the third derivative of -1/6*k**4 + 6*k**2 + 2/15*k**5 + 0*k + 1/30*k**6 - 4/3*k**3 + 0. Factor w(f).
4*(f - 1)*(f + 1)*(f + 2)
Let a = 3/82 + 16/123. Let n(q) be the third derivative of 1/16*q**4 + 0 + 0*q + a*q**3 + 1/120*q**5 - 2*q**2. What is j in n(j) = 0?
-2, -1
Let d = -52 + 60. Factor -1 - d*q - 3 + 0*q - 4*q**2.
-4*(q + 1)**2
Let u(s) be the second derivative of 13*s + 3/160*s**5 + 0 + 1/240*s**6 - 1/48*s**3 + 0*s**2 - 1/96*s**4 - 1/168*s**7. Suppose u(z) = 0. What is z?
-1, -1/2, 0, 1
Let t(l) be the third derivative of -2/75*l**5 + 0 + 6*l**2 + 0*l + 0*l**3 + 1/150*l**6 + 1/30*l**4. What is f in t(f) = 0?
0, 1
Let t(i) = -15*i**3 - 7225*i**2 - 1742425*i - 139975215. Let r(l) = 7*l**3 + 3613*l**2 + 871213*l + 69987607. Let o(g) = -5*r(g) - 2*t(g). Factor o(n).
-5*(n + 241)**3
Let a(m) be the third derivative of m**5/100 + m**2 - 32. Let a(d) = 0. What is d?
0
Let h(s) = -s**3 - s**2 - s + 2. Let f be h(0). Solve p + 5*p + 77*p**2 - 86*p**f = 0.
0, 2/3
Let d(l) = -l**3 - l - l**2 + 20 - 21 + 0*l**3. Let v(q) = -3*q**3 - 3*q - 2. Let o(k) = -6*d(k) + 3*v(k). Suppose o(i) = 0. What is i?
0, 1
Let h = 1 - -3. Let x(d) be the second derivative of 2*d + 0 - 4/11*d**3 + 5/66*d**h + 4/11*d**2. Find v such that x(v) = 0.
2/5, 2
Let l(w) be the second derivative of 13/3*w**3 + 0 + 1/6*w**4 + 25*w + 0*w**2. Suppose l(t) = 0. What is t?
-13, 0
Let y(s) be the second derivative of 5*s**8/84 - s**7/42 - s**6/6 + s**5/12 + 13*s**2/2 - 16*s. Let f(r) be the first derivative of y(r). Solve f(k) = 0 for k.
-1, 0, 1/4, 1
Let f(v) = 142*v - 138. Let j be f(1). Let s be -1 + 2/4*2. Factor s + 2/5*h**j + 2/5*h**5 + 0*h - 2/5*h**2 - 2/5*h**3.
2*h**2*(h - 1)*(h + 1)**2/5
Let k(y) be the second derivative of -1/30*y**4 + 0 + 0*y**2 + 7/15*y**3 + 19*y. Suppose k(h) = 0. What is h?
0, 7
Suppose -20 = -0*s - 5*s. Let j(v) be the third derivative of 1/20*v**5 - 1/8*v**s + 5*v**2 + 0 + 0*v + 0*v**3. Factor j(o).
3*o*(o - 1)
Suppose 3*d - 24 = r - 3, 2*r = 5*d - 44. Let n = r + 30. Factor 0 + 0*v - 5/7*v**5 - 9/7*v**n + 2/7*v**2 + 12/7*v**4.
-v**2*(v - 1)**2*(5*v - 2)/7
Let m(o) be the first derivative of -6*o**5/55 - 2*o**4/11 + 32*o**3/33 + 16*o**2/11 - 32*o/11 - 134. Suppose m(g) = 0. Calculate g.
-2, 2/3, 2
Let t(c) be the third derivative of -c**6/720 + c**5/72 + c**4/24 - 22*c**2. Factor t(v).
-v*(v - 6)*(v + 1)/6
Let x(g) = -2*g**2 + 23*g - 6. Let u be x(11). Suppose u*y - 2*y**5 - 12*y + 7*y = 0. What is y?
0
Let p(i) = -8*i**2 - 69*i - 46. Let c(g) = -g**2 + 4. Let y(v) = 5*c(v) - p(v). Factor y(k).
3*(k + 1)*(k + 22)
Let s(x) be the third derivative of x**8/168 - 2*x**7/315 - 7*x**6/180 - x**5/45 + x**2 - 16. Suppose s(b) = 0. What is b?
-1, -1/3, 0, 2
Suppose 15*u**4 - 287*u**3 + 25*u**2 - 28*u**2 - 12 + 266*u**3 + 24*u - 3*u**5 = 0. Calculate u.
-1, 1, 2
Factor 4/3*x**4 + 24*x**2 - 36 + 32/3*x**3 + 0*x.
4*(x - 1)*(x + 3)**3/3
Suppose t - 17 - 19 = 0. Let g = 41 - t. Factor -8*c + 8*c + 4*c**3 - g*c**4 + c**3.
-5*c**3*(c - 1)
Suppose -2*s = 3*s - 15. Suppose s*x = -3*p + 3, 7*x + 8 = -p + 3*x. Factor -4*r**4 - 8*r**3 + 6*r**3 - r**2 + 3*r**p.
-r**2*(r + 1)**2
Let d(k) be the second derivative of 2/33*k**3 + 1/110*k**5 + 0*k**2 + 0 - 7*k + 1/22*k**4. Solve d(g) = 0.
-2, -1, 0
Factor 26/9*q**3 - 200/9 + 70/9*q + 2/9*q**4 + 34/3*q**2.
2*(q - 1)*(q + 4)*(q + 5)**2/9
Suppose 0 = m - 4, -993*m + 18 = 3*s - 990*m. Suppose 0 + 3/2*g**s + 3*g = 0. What is g?
-2, 0
Let n(f) be the second derivative of 5*f**9/7056 + f**8/3920 + 5*f**3/6 + 6*f. Let s(o) be the second derivative of n(o). Let s(k) = 0. What is k?
-1/5, 0
Let -6/5*k**3 + 0 - 2/5*k**2 - 6/5*k**4 + 0*k - 2/5*k**5 = 0. Calculate k.
-1, 0
Let f(l) be the first derivative of -l**3 - 81*l**2 - 2187*l + 80. Factor f(u).
-3*(u + 27)**2
Solve -4/7*x**3 - 4/7*x**2 - 12/7 + 20/7*x = 0 for x.
-3, 1
Let v(x) be the third derivative of -1/60*x**5 + 11*x**2 - 6*x**3 - 1/2*x**4 + 0 + 0*x. Factor v(f).
-(f + 6)**2
Let a(m) be the first derivative of -4/19*m**3 - 1/38*m**4 + 0*m - 5/19*m**2 - 3. What is h in a(h) = 0?
-5, -1, 0
Suppose -7/2*o**4 + 0*o - 35/2*o**2 + 27*o**3 + 0 = 0. What is o?
0, 5/7, 7
Let c = 625 + -621. Let y(w) be the third derivative of 0 - 1/6*w**3 + 0*w - 6*w**2 - 1/12*w**c - 1/60*w**5. Factor y(z).
-(z + 1)**2
Solve -4/23*l - 6/23*l**2 - 2/23*l**3 + 0 = 0 for