1, 0
Let l(c) be the second derivative of -c**5/180 - c**4/18 + 5*c**3/18 - 9*c**2/2 + 20*c. Let i(a) be the first derivative of l(a). Factor i(s).
-(s - 1)*(s + 5)/3
Factor 54*q + 16/3 + 140*q**2 + 50/3*q**3.
2*(q + 8)*(5*q + 1)**2/3
Let m(u) = 70*u + 9174. Let i be m(-131). Determine t, given that -14/3*t - i - 2/3*t**2 = 0.
-6, -1
Let z(h) be the second derivative of -1/3*h**3 + 0 - 4*h + 1/10*h**5 - 2*h**2 + 1/3*h**4. What is c in z(c) = 0?
-2, -1, 1
Let b(v) be the third derivative of -v**7/525 - v**6/300 + v**5/50 + v**4/12 + 2*v**3/15 + v**2 + 37*v. Factor b(y).
-2*(y - 2)*(y + 1)**3/5
Let l(n) be the first derivative of -9*n**5/140 - n**4/7 - 2*n**3/21 - 46*n - 49. Let k(r) be the first derivative of l(r). Factor k(p).
-p*(3*p + 2)**2/7
Solve 0*u + 0 + 8/3*u**2 - 4/3*u**3 = 0 for u.
0, 2
Let r = 567 + -564. Let k(l) be the first derivative of 4*l - l**2 - 2/3*l**3 + r. Find a, given that k(a) = 0.
-2, 1
Let q(k) be the first derivative of 482*k**3/21 - 243*k**2/7 + 4*k/7 + 308. Determine u, given that q(u) = 0.
2/241, 1
Let y = 635/6888 - -1/328. Let f = 67/42 - y. Factor 3/4*n**2 - 3/4*n - f.
3*(n - 2)*(n + 1)/4
Let q(s) be the third derivative of -s**7/210 + s**6/60 + 7*s**5/60 - s**4/3 - 2*s**3 - 21*s**2. Solve q(j) = 0.
-2, -1, 2, 3
Suppose 136 = 6*y - 14. Suppose y = o + 5*q, 5*q - 20 = -0*q. Factor -3/4*s**3 + 0*s - 3/2*s**2 + 6*s**4 - 15/4*s**o + 0.
-3*s**2*(s - 1)**2*(5*s + 2)/4
Let r(j) be the first derivative of -j**6/660 - j**5/110 + 12*j**2 + 20. Let f(p) be the second derivative of r(p). Determine c, given that f(c) = 0.
-3, 0
Let u be 15/10*2 + 6. Factor 20*g + u*g**5 + 40*g**3 - 4 - 48*g**2 + 8*g**2 - 5*g**5 - 20*g**4.
4*(g - 1)**5
What is m in -79*m**4 - 20495*m**3 + 101261*m - 5*m**5 - 691485*m - 466*m**4 - 857500 - 340776*m - 289975*m**2 = 0?
-35, -2
Let d(n) be the first derivative of -n**6/30 - 4*n**5/15 - 5*n**4/6 - 4*n**3/3 + 5*n**2/2 + 13. Let a(s) be the second derivative of d(s). Factor a(r).
-4*(r + 1)**2*(r + 2)
Factor 160/11*k + 26*k**2 + 9/11*k**4 + 25/11 + 96/11*k**3.
(k + 5)**2*(3*k + 1)**2/11
Let u(t) be the third derivative of t**5/30 - 3*t**4/4 + 8*t**3/3 + 42*t**2 + 5*t. Factor u(r).
2*(r - 8)*(r - 1)
Let b(u) = u**3 + u**2 + u. Suppose 0 = -3*a - 4 - 8. Let i be (-2)/(a/(8/4)). Let f(w) = 4*w**3 + 2*w**2 + 4*w. Let p(t) = i*f(t) - 6*b(t). Factor p(s).
-2*s*(s + 1)**2
What is j in -2/3*j**2 - 26*j - 76/3 = 0?
-38, -1
Let k(x) be the third derivative of -x**6/20 + x**5/6 + x**4/6 - 581*x**2. Factor k(b).
-2*b*(b - 2)*(3*b + 1)
Factor -15/4*a**2 - 13/4*a - 1 - 1/4*a**4 - 7/4*a**3.
-(a + 1)**3*(a + 4)/4
Let w = 217/3 - 66. Let m = -5 + w. Determine x, given that 2/3*x**2 + 2*x + m = 0.
-2, -1
Let o be (0 + 69/(-6))/(4/(-24)). Suppose -3*y**2 - 50 - 30*y - o + 44 = 0. Calculate y.
-5
Let j(w) be the first derivative of -1/3*w**4 + 22/15*w**5 + 0*w**3 + 0*w + 0*w**2 - 17 - 4/3*w**6. Determine u so that j(u) = 0.
0, 1/4, 2/3
Let g(b) = 2*b**2 + 3*b + 3. Let k be g(-1). Suppose 0*j**2 + 22 - j**k - 4*j + 19 - 45 = 0. Calculate j.
-2
Let -7*n**2 + 192 + 130*n + 5*n**2 - 18*n**2 - 465*n - 107 = 0. Calculate n.
-17, 1/4
Find a such that 7*a - 33/2 - 1/2*a**2 = 0.
3, 11
Let w(i) be the second derivative of 1/54*i**4 + 0 + 10*i + 8/27*i**3 + 16/9*i**2. Find v such that w(v) = 0.
-4
Let a(s) be the third derivative of 1/72*s**4 + 0 + 1/90*s**5 + 0*s**3 + 1/360*s**6 + 2*s - 17*s**2. Find k such that a(k) = 0.
-1, 0
Let f(s) be the second derivative of -s**6/105 + 3*s**5/35 + s**4/42 - 2*s**3/7 + 126*s. Factor f(z).
-2*z*(z - 6)*(z - 1)*(z + 1)/7
Suppose 8*l + 87 - 127 = 0. Let s(k) be the second derivative of 11/48*k**4 - k + 9/80*k**l + 0 - 1/2*k**2 + 1/60*k**6 + 0*k**3. Suppose s(n) = 0. What is n?
-2, -1, 1/2
Let w be 5/4*5*32/40. Let v(h) be the first derivative of 0*h**2 + 1/3*h**3 + 0*h - 5/8*h**4 + 3/10*h**w - 6. Find f such that v(f) = 0.
0, 2/3, 1
Let p(t) = t**3 + 24*t**2 + 44*t + 5. Let x be p(-22). Suppose -36 = -x*b - 4*b. Factor 4/3*m**3 - 2/3*m - 2/3 + 4/3*m**2 - 2/3*m**b - 2/3*m**5.
-2*(m - 1)**2*(m + 1)**3/3
Let q(k) be the second derivative of -5*k**7/42 + 47*k**6/30 - 163*k**5/20 + 253*k**4/12 - 28*k**3 + 18*k**2 - 25*k - 7. Let q(s) = 0. Calculate s.
2/5, 1, 2, 3
Let y be 286/154*(-8)/(-104). Factor 4/7*r + 4/7 + y*r**2.
(r + 2)**2/7
Let m(a) be the first derivative of a**6/300 + a**5/30 - 7*a**2 - 13. Let w(z) be the second derivative of m(z). Factor w(o).
2*o**2*(o + 5)/5
Suppose 794 - 400 - 466 = -18*f. Factor -1/3*w + 1/3*w**5 - 2/3*w**2 + 2/3*w**f + 0 + 0*w**3.
w*(w - 1)*(w + 1)**3/3
Suppose 2015 = 3*r + 10*r. Let a be ((-62)/r)/(12/(-10)). Factor a - 1/3*x**2 - 1/3*x + 1/3*x**3.
(x - 1)**2*(x + 1)/3
Let 0*v**2 - 1 - 1/2*v**3 + 3/2*v = 0. What is v?
-2, 1
Let a(w) be the second derivative of -1/36*w**4 + 11*w - 1/180*w**5 - 1/18*w**2 + 0 - 1/18*w**3. Determine d so that a(d) = 0.
-1
Let d(k) be the first derivative of k**6/24 - k**5/4 - k**4/2 + k**3 + 398. Solve d(x) = 0 for x.
-2, 0, 1, 6
Let k = 82276/483 + 52/161. Let j = k - 170. Let -4*l**2 - j*l + 0 - 8/3*l**4 - 6*l**3 = 0. Calculate l.
-1, -1/4, 0
Let i(h) = -27*h - 21. Let t be i(-1). Let y(d) be the second derivative of 2*d - 2/165*d**t - 1/231*d**7 + 0 + 0*d**3 + 0*d**5 + 0*d**2 + 0*d**4. Factor y(k).
-2*k**4*(k + 2)/11
Let m(r) be the first derivative of r**3/3 - 13*r**2/2 + 355. Factor m(x).
x*(x - 13)
Suppose 2*s = -6*s - s. Let b be s - (-1 + 3/(-1)). Solve 0 + 2/5*g - 4/5*g**2 + 6/5*g**5 - 8/5*g**3 + 4/5*g**b = 0.
-1, 0, 1/3, 1
Let u(d) be the second derivative of -5/42*d**7 - 10/3*d**4 + 5/2*d**3 + 19*d + 0*d**6 + 0*d**2 + 0 + 3/2*d**5. Factor u(z).
-5*z*(z - 1)**3*(z + 3)
Let j = 13009/6 - 2168. Let h(y) be the third derivative of -1/420*y**7 + 1/80*y**6 + 0 + 0*y + j*y**3 - 1/120*y**5 + 8*y**2 - 1/16*y**4. What is r in h(r) = 0?
-1, 1, 2
Let c(x) = -2*x**2 - x + 3. Let d(r) = -3*r**2 - 3*r + 6. Let s = 24 + -41. Let h = 12 + s. Let g(o) = h*d(o) + 9*c(o). Suppose g(u) = 0. Calculate u.
1
Let j(m) = -m**5 + m**4 + 4*m**3. Let f(r) = -6*r**5 + 6*r**4 + 22*r**3. Let h(o) = -2*f(o) + 11*j(o). Determine a, given that h(a) = 0.
0, 1
Let t(n) be the third derivative of -n**5/30 - 2*n**4/3 - 7*n**3/3 + 60*n**2. Factor t(q).
-2*(q + 1)*(q + 7)
Suppose 2*u = -3*u + 3*d - 52, -u = 5*d + 16. Let h(z) = z**3 + 11*z**2 - 3*z - 29. Let x be h(u). Factor -2/7*c**x - 4/7 - 2*c - 10/7*c**3 - 18/7*c**2.
-2*(c + 1)**3*(c + 2)/7
Let i be (2/(-165))/(-2*(-4)/(-40)). Let y(f) be the first derivative of -4/11*f + 1/11*f**2 + i*f**3 + 4. Factor y(q).
2*(q - 1)*(q + 2)/11
Let h(y) = -9*y**3 - 1. Let c be h(1). Let z be c/(-6) + (-3)/(-9). Factor 12*a + 4*a**2 - 2 + 10 + 0*a**z.
4*(a + 1)*(a + 2)
Let v(l) be the first derivative of l**3/9 - 13*l**2/6 - 124. Factor v(b).
b*(b - 13)/3
Let u be (8/(-28)*4)/(-1). Suppose 3 = -6*l + 15. Find w, given that 32/7*w + 6/7*w**3 - 26/7*w**l - u = 0.
1/3, 2
Suppose 6*l - 3*l = -12. Let u be 1*(l/2 - -4). Find g such that -g**4 + 20*g - 18*g**2 + 0 - 2 - 8 + u + 7*g**3 = 0.
1, 2
Factor 1/3*g - g**2 + 2/3*g**3 + 0.
g*(g - 1)*(2*g - 1)/3
Let g = 2 - -10. Suppose -3*q + g = -q. Determine i so that -2*i**4 + q*i**4 + 24*i**3 + 8*i**2 - i**5 - 20*i - 12 + 0*i**3 - 3*i**5 = 0.
-1, 1, 3
Let h(n) be the second derivative of 0 - 1/165*n**6 - 11*n + 0*n**2 + 0*n**3 + 0*n**4 + 1/110*n**5. Factor h(m).
-2*m**3*(m - 1)/11
Let o(a) = -a**3 + 12*a**2 - 34*a - 3. Let w be o(5). Let -75/4 - 15/2*f - 3/4*f**w = 0. Calculate f.
-5
Let s(i) = 2*i**3 + i**2 - 3. Let a(f) = 5*f**3 + 2*f**2 - 8. Let p = -60 - -63. Let w(v) = p*a(v) - 8*s(v). Find t, given that w(t) = 0.
-2, 0
Suppose 3*b + 4*f = -72 + 13, -4*b - 92 = 2*f. Let v = 35 + b. Factor -x**4 + 14*x - v*x**2 - x**4 - 4 + 10*x**3 - 8*x**2.
-2*(x - 2)*(x - 1)**3
Suppose -39*z - 8*z**2 - 4*z**2 - 24 + 5*z**2 - 8*z**2 = 0. What is z?
-8/5, -1
Let d = 861 + -858. Find p such that 1/3*p**4 + 0 + 1/3*p - 1/3*p**2 - 1/3*p**d = 0.
-1, 0, 1
Suppose -3*f + 2*f = -n - 7, 0 = 4*f + n - 3. Let r be 22/99 + 1/(-9)*f. Let m + r - 1/3*m**2 = 0. What is m?
0, 3
Let n(x) = -x**3 + 4*x**2 + 17*x - 2. Let i be n(-3). Let o(q) be the first derivative of i + 8/5*q - 32/15*q**3 - q**4 - 2/5*q**2. Factor o(k).
-4*(k + 1)**2*(5*k - 2)/5
What is t in -40/11 - 2/11*t**2 + 24/11*t = 0?
2, 10
Factor 