d derivative of 1/21*f**3 + 1/21*f**5 - 5/84*f**4 + 10*f**2 + 0*f + 0 + 1/147*f**7 - 1/1176*f**8 - 1/42*f**6. Factor w(i).
-2*(i - 1)**5/7
Suppose 0 = -2*a + 4*i + 22, 0 = -2*a - 5*i - 7 - 7. Let b = 161 - 161. Solve -1/7*x**2 + 2/7*x + b - 1/7*x**a = 0.
-2, 0, 1
Let a = 3054009/13 + -234567. Let q = a + -356. Determine t, given that q*t**2 + 6/13 - 2/13*t**3 - 14/13*t = 0.
1, 3
Let b(x) be the third derivative of 1/42*x**7 + 0 + 5/2*x**3 + 1/12*x**6 - 5/12*x**4 - 17*x**2 - 1/3*x**5 + 0*x. Factor b(a).
5*(a - 1)**2*(a + 1)*(a + 3)
Let f be (-6)/(-24) + (-22)/(-8). Suppose -4*c = f*u + 5 - 4, c + 4*u + 10 = 0. Let g**2 + 3*g**3 + 4*g - 2*g**3 - 5*g**c = 0. Calculate g.
0, 2
Let s be -2*((-15)/12)/5*-247. Let q = -123 - s. Factor p + q + 1/2*p**2.
(p + 1)**2/2
Let d(s) be the first derivative of s**5/120 + s**4/16 - s**3/3 - 3*s**2/2 + 9. Let b(i) be the second derivative of d(i). Determine m so that b(m) = 0.
-4, 1
Let t(i) = -4*i - 1. Let l be t(-7). Let c = l - 23. Find m such that 2*m**2 - m + 6*m**3 - m**c + 3*m**4 - 5*m - 4 = 0.
-2, -1, 1
Let p(o) = -o**3 - 8*o**2 - 2*o - 9. Let l be p(-8). Let l*g - 204 + 220 + 7*g - 2*g**2 = 0. Calculate g.
-1, 8
Let d = 88153/5 - 17629. Find m such that -2/5*m**4 + 4/5*m**2 - 18/5 + d*m**3 - 24/5*m = 0.
-1, 3
Let o(h) be the second derivative of h**5/10 - 32*h**4 - 129*h**3 - 194*h**2 - 848*h. Solve o(b) = 0.
-1, 194
Solve -100/3*c**2 + 0 - 4/3*c**3 + 104/3*c = 0 for c.
-26, 0, 1
Factor -24*y**3 - 20*y**4 + 44/5*y**2 + 48/5*y - 16/5.
-4*(y + 1)**2*(5*y - 2)**2/5
Suppose -7 + 199 = 48*v. Let o(n) be the second derivative of 1/9*n**4 - v*n + 0*n**3 + 0*n**2 + 0 + 1/10*n**5 + 1/45*n**6. Find q, given that o(q) = 0.
-2, -1, 0
Determine o, given that 8/7*o + 2/7*o**5 + 1/7*o**2 - 24/7*o**3 + 0 + 13/7*o**4 = 0.
-8, -1/2, 0, 1
Let z be (1/18)/(15*31/1860). Factor -2/9*d**5 + 0*d**3 + z*d**4 + 0 + 0*d + 0*d**2.
-2*d**4*(d - 1)/9
Suppose 11 = 2*w - 0*w + g, 2*g = 10. Let t be (10 - 1236/126)/((-9)/(-42)). Factor 2/9*y**4 + 4/3*y**2 - 8/9*y**w + 2/9 - t*y.
2*(y - 1)**4/9
Let j(f) be the first derivative of f**7/5460 - f**6/2340 + 3*f**3 - 3. Let y(b) be the third derivative of j(b). Factor y(q).
2*q**2*(q - 1)/13
Let p(z) be the second derivative of z**10/60480 - z**9/30240 - z**8/6720 + 5*z**4/3 - 22*z. Let f(o) be the third derivative of p(o). Factor f(r).
r**3*(r - 2)*(r + 1)/2
Let p(t) be the second derivative of -t**5/40 + t**3/4 + t**2/2 + 50*t. Factor p(x).
-(x - 2)*(x + 1)**2/2
Let g be (1*-4)/(7 + -25). Let w = g + 4/9. What is p in -4/3*p + 2/3*p**2 + w = 0?
1
Suppose -4*k + 4*i = -804, 2*k - 7*i - 399 = -8*i. Let j = k - 200. Factor 2/11*n - 2/11*n**2 + j.
-2*n*(n - 1)/11
Let z(v) = -v**2 + v. Let c(m) be the second derivative of -m**4/6 + 5*m**3 + 18*m**2 - 5*m. Let i(o) = -c(o) + 6*z(o). Factor i(y).
-4*(y + 3)**2
Let d(n) be the first derivative of -n**5/4 - 5*n**4/4 + 14*n - 19. Let i(p) be the first derivative of d(p). Factor i(m).
-5*m**2*(m + 3)
Let b(z) be the second derivative of 3*z**7/14 - z**6/2 - 11*z**5/12 - 5*z**4/12 - 41*z**2/2 - 29*z. Let l(a) be the first derivative of b(a). Factor l(w).
5*w*(w - 2)*(3*w + 1)**2
Suppose 5*r - 4*r - 2916 = 0. Let r*x**3 + 32 + 83*x + 355*x + 1944*x**2 - 6*x = 0. What is x?
-2/9
Let a be (2 + (-144)/68)*5*1. Let q = 84/85 + a. Let 2/5*d**5 + q*d**4 - 4/5*d**2 + 2/5 - 4/5*d**3 + 2/5*d = 0. Calculate d.
-1, 1
Let f(w) be the third derivative of w**7/630 - w**6/36 + 2*w**5/15 + 3*w**4/8 - 8*w**2. Let a(y) be the second derivative of f(y). Factor a(r).
4*(r - 4)*(r - 1)
Let c(g) be the third derivative of g**7/1050 - g**6/200 - g**5/150 + g**4/10 - 4*g**3/15 - 85*g**2. Factor c(v).
(v - 2)**2*(v - 1)*(v + 2)/5
Let x(n) be the third derivative of 0 + 1/630*n**7 + 1/72*n**6 - 1/36*n**5 + 0*n - 15*n**2 - 1/18*n**4 - 1/1008*n**8 + 2/9*n**3. Suppose x(v) = 0. Calculate v.
-2, -1, 1, 2
Let s(x) = x**2 + x - 1. Let q be s(2). Suppose y - q = -0. Factor 4*d**y + 5*d**4 + d**4 + 6*d**4 - 4*d**4 + 4*d**3.
4*d**3*(d + 1)**2
Let o = -264 - -268. Let u(i) be the first derivative of 0*i**2 + 2/9*i**3 + 0*i - 3 - 2/15*i**5 + 0*i**o. Factor u(w).
-2*w**2*(w - 1)*(w + 1)/3
Let f(r) be the first derivative of -343*r**6/18 - 98*r**5/5 + 259*r**4/12 + 286*r**3/9 + 14*r**2 + 8*r/3 - 251. Find o such that f(o) = 0.
-1, -2/7, 1
Let w(u) be the second derivative of u**4/24 + 4*u**3 - 25*u**2 - 172*u. Suppose w(p) = 0. Calculate p.
-50, 2
Suppose 21 = 10*r - 3*r. Suppose 4*q = -2 - 26. Let i(v) = 2*v**2 + 3*v - 5. Let f(d) = 5*d**2 + 6*d - 11. Let z(s) = q*i(s) + r*f(s). What is t in z(t) = 0?
1, 2
Let 2/3*w + 1/3*w**4 - 1/3*w**2 - w**3 + 0 + 1/3*w**5 = 0. What is w?
-2, -1, 0, 1
Let i(y) = y**2 - 5*y + 19. Let r be i(7). Let u be 8/(-12) + 28/r. Suppose 2/11*s**4 - 4/11*s**2 + 2/11*s + 2/11*s**5 - 4/11*s**3 + u = 0. Calculate s.
-1, 1
Suppose 3*g = 8 + 10. Find s such that -g*s + 3*s + 0*s - 15*s**2 = 0.
-1/5, 0
Suppose q + c = -3, 4*q - c - 4 + 1 = 0. Find z, given that 2*z**4 + q + 5*z**3 - 17*z**4 + 10*z**2 + 0 = 0.
-2/3, 0, 1
Let s(r) be the third derivative of -r**6/600 + r**4/30 - 80*r**2. Factor s(n).
-n*(n - 2)*(n + 2)/5
Let g(o) = -25*o**2 - 8*o + 3. Let q(u) = 224*u**2 + 72*u - 28. Let l be (0 + 1)/(2 - (-228)/(-112)). Let b(h) = l*g(h) - 3*q(h). Suppose b(p) = 0. Calculate p.
-2/7, 0
Let l(r) be the second derivative of -3*r**5/20 - r**4/2 - r**3/2 - 247*r. Determine d so that l(d) = 0.
-1, 0
What is a in 14*a - 17*a - 1168 + 1168 - 6*a**2 = 0?
-1/2, 0
Let p(w) be the third derivative of w**5/300 + 7*w**4/120 + w**3/5 - 428*w**2. Suppose p(d) = 0. What is d?
-6, -1
Let u(c) be the first derivative of c**4/10 - 2*c**3/15 - 2*c**2 - 16*c/5 - 56. Let u(x) = 0. What is x?
-2, -1, 4
Solve 598 - 780*m - 8*m**4 - 42*m**3 - 114*m**3 - 1916*m**2 - 88*m**3 + 302 = 0 for m.
-15, -1, 1/2
Suppose 36*b - 43*b = -42. Let l(r) be the second derivative of 0 + 0*r**4 - 5*r + 0*r**2 - 1/10*r**5 - 1/5*r**b + 0*r**3. Factor l(f).
-2*f**3*(3*f + 1)
Let h(m) be the second derivative of m**4/4 + 3*m**3 + 27*m**2/2 - 2*m + 47. Find u such that h(u) = 0.
-3
Let r(z) be the second derivative of z**6/90 - z**5 + 75*z**4/2 + 5*z**3/6 - 19*z. Let m(c) be the second derivative of r(c). Factor m(p).
4*(p - 15)**2
Let t = 6 - -4. Let i(a) = 25*a**5 + 5*a**4 - 25*a**3 - 15*a**2. Let v(g) = -8*g**5 - 2*g**4 + 8*g**3 + 5*g**2. Let l(w) = t*v(w) + 3*i(w). Factor l(f).
-5*f**2*(f - 1)*(f + 1)**2
Factor -3/7*q**2 + 0 - 30/7*q.
-3*q*(q + 10)/7
Let p be (-9)/15 - 196/(-35). Find r such that -4*r**4 - r**4 + 5*r**3 - 3*r**2 - 8*r**5 + 3*r**p + 8*r**2 = 0.
-1, 0, 1
Let k(l) be the third derivative of -4/45*l**3 - 1/45*l**4 + 0*l - 1/450*l**5 + 0 - 9*l**2. Factor k(b).
-2*(b + 2)**2/15
Factor -25*h**2 + 6*h**4 + 32*h**3 - 64 - 32*h - h**4 - 2*h**4 + h**4 + 85*h**2.
4*(h - 1)*(h + 1)*(h + 4)**2
Let i(w) be the third derivative of -w**7/42 + w**6/6 + w**5/2 - 5*w**4/6 - 25*w**3/6 - 74*w**2. Factor i(b).
-5*(b - 5)*(b - 1)*(b + 1)**2
Let u = 54 - 24. Suppose u + 2 = 8*b. Factor -41*y**b + 6*y**5 - 10 - y**5 - 80*y**2 + 11*y**4 + 70*y**3 + 45*y.
5*(y - 2)*(y - 1)**4
Let s(d) be the second derivative of d**4/4 + 86*d**3 + 11094*d**2 - 4*d + 13. Find l such that s(l) = 0.
-86
Let j(y) be the first derivative of 2*y**3 + 0*y**2 + 0*y + 27 - 1/2*y**4. Factor j(l).
-2*l**2*(l - 3)
Let a(h) be the first derivative of h**7/420 + h**6/60 + h**5/60 - h**4/12 - h**3/4 + 5*h**2/2 - 2. Let z(k) be the second derivative of a(k). Factor z(r).
(r - 1)*(r + 1)**2*(r + 3)/2
Let t(b) be the second derivative of -16*b - 1/4*b**4 - 3/16*b**5 + 0*b**2 - 1/20*b**6 - 1/8*b**3 + 0. Solve t(q) = 0 for q.
-1, -1/2, 0
Let x(n) = -n + 8. Let s = 15 + -9. Let t be x(s). Factor 2*d**2 + 4 - 5*d**t + 3 + 5.
-3*(d - 2)*(d + 2)
Let w = 18416 - 18411. Factor w*v - 25/6 - 5/6*v**2.
-5*(v - 5)*(v - 1)/6
Suppose 0 = 3*y - 4*d + 11, 0*y - 2*y + 31 = 5*d. Suppose -3*m = 3*o - 15, -m - 2*m = 5*o - 19. What is a in 14*a - 4 + 5/2*a**y - 11*a**o = 0?
2/5, 2
Let c = -362 + 366. Let o(w) be the second derivative of -1/7*w**3 - 2*w + 0 - 1/7*w**2 + 2/21*w**c. Factor o(f).
2*(f - 1)*(4*f + 1)/7
Suppose 3*c - 5*z = 6*c - 32, 3*z - 24 = -3*c. Let f(y) be the first derivative of -1/3*y**3 + y - 3 - 1/2*y**2 + 1/4*y**c. Factor f(p).
(p - 1)**2*(p + 1)
Suppose -