he third derivative of -1/24*l**4 + 1/20*l**5 - 1/40*l**6 + 0*l + 0*l**3 + 1/210*l**7 + 0 - 5*l**a. Factor v(s).
s*(s - 1)**3
Suppose 7*d = 2*d + 10. Let s(g) be the first derivative of -d + 1/4*g - 1/4*g**3 + 1/4*g**2. Suppose s(h) = 0. Calculate h.
-1/3, 1
Let x(s) be the second derivative of s**8/3360 - s**7/840 + s**6/720 + s**3/2 - 11*s. Let p(h) be the second derivative of x(h). Factor p(y).
y**2*(y - 1)**2/2
Let s be ((-3472)/(-372))/(5/36). Factor 48/5*z**3 - 147/5 + s*z - 234/5*z**2 - 3/5*z**4.
-3*(z - 7)**2*(z - 1)**2/5
Let c(z) be the third derivative of 0*z**3 + 0*z + 0 - 3*z**2 - 1/60*z**4 + 1/150*z**5. Factor c(i).
2*i*(i - 1)/5
Let z(m) be the second derivative of m**5/80 - 25*m**4/24 + 28*m**3 - 144*m**2 - 54*m - 5. Find u such that z(u) = 0.
2, 24
Let w(h) be the first derivative of -5*h**3/3 + 455*h**2 - 41405*h + 626. Find b, given that w(b) = 0.
91
Let -2/11*s**3 - 16/11*s - 2/11*s**4 + 20/11*s**2 + 0 = 0. What is s?
-4, 0, 1, 2
Let h(m) be the second derivative of -m**4/36 - 17*m**3/18 - 8*m**2/3 + 140*m. Solve h(y) = 0.
-16, -1
Suppose -1/5*z**4 + 2*z**2 + 0*z + 3/5*z**3 + 0 = 0. Calculate z.
-2, 0, 5
Let c(d) be the second derivative of d**5/60 - d**4/12 + d**3/6 - 9*d**2/2 - 2*d. Let y(m) be the first derivative of c(m). Factor y(x).
(x - 1)**2
Let l(h) be the first derivative of -h**6/18 + 4*h**5/3 - 40*h**4/3 + 640*h**3/9 - 640*h**2/3 + 1024*h/3 + 174. Factor l(x).
-(x - 4)**5/3
Let g = -198 - -206. Let t be ((-96)/30)/g*-1. Solve 0*i + t*i**3 + 0 - 2/5*i**2 = 0.
0, 1
Let s = -38453 - -38453. Solve s - 3/5*o**4 + 0*o + 6/5*o**2 + 3/5*o**3 = 0 for o.
-1, 0, 2
Let d(w) be the third derivative of -w**7/6720 + w**6/960 + w**5/960 - w**4/64 - w**3 - 11*w**2. Let f(i) be the first derivative of d(i). Factor f(b).
-(b - 3)*(b - 1)*(b + 1)/8
Let p(o) be the second derivative of -o**6/6 + o**5/2 - 5*o**4/12 - 52*o - 1. Suppose p(s) = 0. Calculate s.
0, 1
Suppose -28 = 14*m, 23*c + 3*m + 6 = 20*c. Find z such that -6/7*z + c + 2/7*z**2 = 0.
0, 3
Let g be ((-4 + 3)*-3)/1. Let q(s) = -s**2 + 6*s - 5. Let a be q(g). What is j in 0*j**4 + j**4 + 3*j**2 - a*j**4 = 0?
-1, 0, 1
Let z(k) = 12*k - 9 + 29 - 9*k**2 - 11 - 11 - k**2. Let l(j) = -2 - 7*j**2 - 2 + 8*j + 3. Let m(b) = -7*l(b) + 5*z(b). Factor m(t).
-(t - 3)*(t - 1)
Let m(y) be the second derivative of -y**4/20 + 17*y**3/10 - 63*y**2/5 + 46*y. Factor m(p).
-3*(p - 14)*(p - 3)/5
Let k(f) be the first derivative of 5*f + 17/3*f**3 + 11 - 31/2*f**2. Let h(c) = 16*c**2 - 32*c + 4. Let s(n) = 3*h(n) - 4*k(n). Suppose s(x) = 0. Calculate x.
2/5, 1
Let r(h) be the first derivative of h**5/5 - 9*h**4/4 - 10*h**3/3 + 122. Solve r(a) = 0.
-1, 0, 10
Let h be 2 + 0 + -2*1. Let r = 12 + -9. Let h*t**4 - 2*t**r + 4*t**5 - 6*t**5 - 4*t**4 = 0. What is t?
-1, 0
Find s, given that -s**2 + 0 - 1/3*s + 4/3*s**3 = 0.
-1/4, 0, 1
Let x(t) = 9*t - 59. Suppose 34 = 2*k - 4*c, -c + 25 = 5*k + c. Let o be x(k). Factor 0*f**3 - 4/5*f**2 - 2/5*f**5 + 4/5*f**o + 2/5*f + 0.
-2*f*(f - 1)**3*(f + 1)/5
Let y(p) be the second derivative of p**4/4 + 11*p**3 + 63*p**2/2 - 79*p. Factor y(k).
3*(k + 1)*(k + 21)
Suppose 0 = -2*g + 3 + 1. Let u be ((-2)/20)/((-3)/72*g). Find v, given that u + 36/5*v**2 + 33/5*v - 27/5*v**3 = 0.
-1/3, 2
Let v(z) = -2*z + 19. Let c be v(8). Factor 18*i**4 + 10*i**3 + 36*i**c + 32 + 112*i + 15*i**3 + 23*i**3 + 146*i**2.
2*(i + 1)**2*(3*i + 4)**2
Let s(v) be the first derivative of -v**4/3 - 4*v**3 - 28*v**2/3 - 170. Let s(c) = 0. Calculate c.
-7, -2, 0
Let b(c) be the first derivative of c**6/15 + 3*c**5/25 - c**4/10 - 4*c**3/15 + c/5 + 29. Determine i, given that b(i) = 0.
-1, 1/2, 1
Let t(c) be the first derivative of c**4/16 + 3*c**3/4 + 3*c**2/4 - 4*c - 685. What is l in t(l) = 0?
-8, -2, 1
Suppose -13 = -9*k + 5*k + t, -4*k - 3*t - 7 = 0. Suppose -14/3*a**k + 2/3*a**5 + 16/3 - 22/3*a**3 - 2/3*a**4 + 20/3*a = 0. Calculate a.
-2, -1, 1, 4
Let u(v) be the first derivative of 1/36*v**6 + 0*v**5 + 0*v**2 - 1/8*v**4 + 0*v + 1/9*v**3 + 17. Determine i, given that u(i) = 0.
-2, 0, 1
Let r(b) be the third derivative of 1/20*b**5 + 3/4*b**4 - 7/2*b**3 + b**2 + 0 - 29*b. Factor r(v).
3*(v - 1)*(v + 7)
Let m(b) be the first derivative of -b**6/60 - b**5/30 + 3*b**3 + 1. Let l(s) be the third derivative of m(s). Find f, given that l(f) = 0.
-2/3, 0
Let q(j) be the second derivative of -3*j**5/20 + 5*j**4/4 - 4*j**3 + 6*j**2 + 2*j - 113. Factor q(p).
-3*(p - 2)**2*(p - 1)
Suppose 3*p - 289 + 283 = 0. Let o(d) be the first derivative of 6*d**3 + 3/2*d**4 - p*d**5 + 1/3*d**6 + 0*d + 4 + 0*d**2. Factor o(l).
2*l**2*(l - 3)**2*(l + 1)
Let k(a) = a**3 - 8*a**2 + 21*a - 10. Let c be k(8). Let r = 1108/7 - c. Factor 0 + 4/7*u**4 + r*u**5 - 4/7*u**2 - 2/7*u + 0*u**3.
2*u*(u - 1)*(u + 1)**3/7
Let b(m) = -4*m**2 - 18*m + 62. Let w(d) = 3*d - 1. Let n(t) = b(t) - 2*w(t). Factor n(c).
-4*(c - 2)*(c + 8)
Let w = 31 + -37. Let b(a) = 8*a**4 + 4*a**2. Let c(j) = -7*j**4 - j**3 - 4*j**2. Let z(v) = w*c(v) - 5*b(v). Factor z(u).
2*u**2*(u + 1)*(u + 2)
Suppose 4*q + 6*q - 12*q = 0. Suppose 2/7*d**3 + 2/7*d**2 + 0*d + q = 0. Calculate d.
-1, 0
Let a = -56/5 + 12. Factor 0*v + 2/5*v**2 + a*v**3 + 2/5*v**4 + 0.
2*v**2*(v + 1)**2/5
Suppose 5530*u**2 - 593*u + 331 + 109 - 245*u**3 - 2507*u = 0. Calculate u.
2/7, 22
Let o = 5 + -3. Factor -19*g**2 + 104 - 14 + 15*g - g**o + 0*g**2 - 5*g**3.
-5*(g - 2)*(g + 3)**2
Let t = 37/961 + 1737/4805. Solve t*f + 2/5*f**3 - 3/5*f**2 - 1/10*f**4 - 1/10 = 0.
1
Let a(g) be the third derivative of -g**8/4200 + g**6/900 + g**3/6 - 7*g**2. Let y(i) be the first derivative of a(i). Factor y(s).
-2*s**2*(s - 1)*(s + 1)/5
Suppose -4*u = 5*w - 16 - 1, -5*u = 5*w - 20. Factor w - 23*n - 9*n - 10 + 18*n**2 + 1.
2*(n - 2)*(9*n + 2)
Let k(t) be the third derivative of t**7/70 + 3*t**6/40 - t**5/20 - 3*t**4/8 - 2*t**2 - 32*t. Determine i, given that k(i) = 0.
-3, -1, 0, 1
Let a(z) be the second derivative of z**5/40 - 6*z**4 + 576*z**3 - 27648*z**2 + 617*z. Let a(o) = 0. What is o?
48
Suppose -u + y = 38, 5*u + 0*y + 158 = -3*y. Let a = u - -36. Factor 0 + 1/4*v + 0*v**a - 1/4*v**3.
-v*(v - 1)*(v + 1)/4
Let t = 1144/225 - 126/25. Let o(r) be the second derivative of -1/63*r**7 + 0 + t*r**6 - 1/9*r**4 + 8*r + 0*r**2 + 0*r**5 + 1/9*r**3. Factor o(c).
-2*c*(c - 1)**3*(c + 1)/3
Let h(j) = j**3 - 4*j**2 - 37*j - 18. Let x be h(-4). Suppose 1/5*w**x - 1/5*w**5 - 1/5*w**4 - 2/5*w + 3/5*w**3 + 0 = 0. What is w?
-2, -1, 0, 1
Let k(j) be the first derivative of -3/10*j**6 + 0*j**2 + 0*j**4 - 2 - 21/20*j**5 + 2*j**3 + 3*j. Let d(p) be the first derivative of k(p). Solve d(h) = 0.
-2, -1, 0, 2/3
Let v(w) = -w**4 - 11*w**3 - 72*w**2 - 75*w - 38. Let q(x) = 2*x**4 + 16*x**3 + 108*x**2 + 112*x + 58. Let k(a) = -5*q(a) - 8*v(a). Factor k(b).
-2*(b - 7)*(b + 1)**3
Let l(t) be the second derivative of t**4/90 + 181*t**3/45 + 708*t. Find u, given that l(u) = 0.
-181, 0
Let a = -449/2 - -225. Let x(g) be the second derivative of -1/48*g**4 + 1/6*g**3 - 2*g + 0 - a*g**2. Let x(q) = 0. What is q?
2
Suppose 3*l - 4*l = 5*f - 28, 0 = 3*l - 3*f + 6. Let j(p) = p**3 - 8*p**2 + 9*p - 2. Let o be j(7). Factor z**4 - 4*z**4 + 23*z**3 - 13*z**l - o*z**3 - z**5.
-z**3*(z + 1)*(z + 2)
Let a = 7 + -4. Let f(i) be the second derivative of 0*i**6 + 1/5*i**a - 7/50*i**5 + 5*i + 1/5*i**2 + 0 - 1/30*i**4 + 4/105*i**7. Solve f(y) = 0.
-1, -1/2, 1
Factor 0*c - 6/5*c**3 + 0 + 0*c**4 + 2/5*c**5 - 4/5*c**2.
2*c**2*(c - 2)*(c + 1)**2/5
Let b be ((-1)/(14/413))/((-20)/8) - 7. Factor b*t - 16/5 - 9/5*t**2 + 1/5*t**3.
(t - 4)**2*(t - 1)/5
Suppose -c + 52 = 48. Let g = -1066/5 + 214. Factor 0*y**2 - g + 4/5*y**c - 8/5*y**3 + 8/5*y.
4*(y - 1)**3*(y + 1)/5
Let a(o) = 9*o**2 + 5. Let i(j) = 5*j**2 + 3. Suppose 9*v + 37 - 1 = 0. Let p(n) = v*a(n) + 7*i(n). Factor p(l).
-(l - 1)*(l + 1)
Let n(h) be the second derivative of 0*h**2 + 0*h**3 + 3*h - 1/150*h**6 + 1/20*h**4 + 0 - 1/50*h**5. Suppose n(z) = 0. Calculate z.
-3, 0, 1
Let c(j) be the second derivative of 0*j**3 + 29*j + 0*j**4 + 0 - 1/168*j**7 + 1/30*j**6 - 3/80*j**5 + 0*j**2. What is z in c(z) = 0?
0, 1, 3
Suppose -l + 2*l = 3*n + 14, -5*l - 2*n = -19. Factor 1/5*m**l - 3/5*m**3 - 4/5*m + 8/5*m**2 - 2/5*m**4 + 0.
m*(m - 2)*(m - 1)**2*(m + 2)/5
Let j be 129/(-301)*(15/9 - 2). Factor j