- 115)*(g - 1)/6
Let j = 2353/2 - 1150. Let y = j + -263/10. Determine t so that 3/5*t**3 - 1/5*t**4 + y*t - 3/5*t**2 + 0 = 0.
0, 1
Let z(x) be the first derivative of x**9/12096 + x**8/3360 - x**7/3360 - x**6/720 + 28*x**3/3 + 34. Let f(h) be the third derivative of z(h). Factor f(i).
i**2*(i - 1)*(i + 1)*(i + 2)/4
Suppose -48 - 257 = -208*s + 319. Factor 4/5*z**4 + 0 + 2/5*z**5 + 2/5*z**s + 0*z**2 + 0*z.
2*z**3*(z + 1)**2/5
Let m(r) = -r**3 - 11*r**2 - 3*r - 31. Let c be m(-11). Factor 36 - 6*i - 22*i**3 - 3*i**2 - 5*i**c + 24*i**3.
2*(i - 3)**2*(i + 2)
Let c(x) be the second derivative of -x**8/17920 + 9*x**4/4 + 2*x. Let z(t) be the third derivative of c(t). Suppose z(g) = 0. Calculate g.
0
Let o be (-81)/(-28) + 3/(-21). Let y = -69/28 + o. Factor -2/7 + y*l**2 - 2/7*l + 2/7*l**3.
2*(l - 1)*(l + 1)**2/7
Let u = -197 + 200. Let w(l) be the second derivative of 0 - 1/3*l**2 - u*l - 2/3*l**4 - 3/20*l**5 - 13/18*l**3. Determine m so that w(m) = 0.
-2, -1/3
Let b(c) be the second derivative of -c**7/315 - 101*c**6/225 - 479*c**5/30 + 7801*c**4/90 - 8008*c**3/45 + 2704*c**2/15 - 833*c. Let b(s) = 0. What is s?
-52, 1
Let u(v) be the first derivative of v**5/100 - 2*v**4/5 + 32*v**3/5 + 4*v**2 - 4*v - 31. Let g(z) be the second derivative of u(z). Let g(l) = 0. What is l?
8
Let v be (-2)/8*(-6 + 24/4). Let i be 4 + (3 + v - 5). Suppose -2/5*m - 6/5*m**3 + 0 + 6/5*m**i + 2/5*m**4 = 0. Calculate m.
0, 1
Let 30/11*b**5 - 4*b + 122/11*b**4 + 0 + 14/11*b**3 - 122/11*b**2 = 0. What is b?
-11/3, -1, -2/5, 0, 1
Let m(n) = 3*n - 10. Let x be m(4). Suppose -3*i + 4*v + 1 = 0, 0 = -i - x*i - 3*v + 15. Factor 2*b - 4 - 5*b**2 + i*b + 9 - 5*b**3.
-5*(b - 1)*(b + 1)**2
Let t(w) = -4*w**2 - 108*w - 248. Let y(s) = -3*s**2 - 72*s - 165. Let p(n) = 5*t(n) - 8*y(n). Solve p(v) = 0 for v.
-5, -4
Let s(h) be the first derivative of h**6/3 - 8*h**5/5 - h**4 + 16*h**3/3 + h**2 - 8*h - 36. Find n, given that s(n) = 0.
-1, 1, 4
Let h be 3 - (-14)/((12 - 4)/(-1)). Solve 0 - 5/4*j**3 + 5*j + 5*j**2 - h*j**4 = 0 for j.
-2, -1, 0, 2
Let z(l) = l**2 + 2*l - 9. Let c be z(-5). Factor -c*x**4 + x**3 + 4*x**2 + 4*x - 5*x**3 + 2*x**4.
-4*x*(x - 1)*(x + 1)**2
Suppose -6*n + 12 = -10*n. Let y be 112/40*(n + 23/7). Factor 8/5*k**2 + 4/5*k**5 + 8/5*k**3 - 12/5*k + y - 12/5*k**4.
4*(k - 1)**4*(k + 1)/5
Let q(m) be the third derivative of -m**8/110880 - m**7/6930 - m**6/1320 - m**5/6 + 11*m**2. Let v(a) be the third derivative of q(a). Factor v(x).
-2*(x + 1)*(x + 3)/11
Let n(i) be the third derivative of i**8/1176 + 2*i**7/105 + 5*i**6/84 + 2*i**5/35 + 471*i**2. What is y in n(y) = 0?
-12, -1, 0
Let s(o) be the second derivative of -o**5/5 - 29*o**4/36 + 10*o**3/9 - o**2/2 + 8*o + 2. Let s(v) = 0. Calculate v.
-3, 1/4, 1/3
Suppose 2*j = -5*w - 31, 172 - 201 = 3*j + 5*w. Suppose 4/5*c**j - 8/5 + 4/5*c = 0. What is c?
-2, 1
Let a(p) be the first derivative of -34 + 1/19*p**2 - 1/38*p**4 + 2/95*p**5 - 2/57*p**3 + 0*p. Factor a(t).
2*t*(t - 1)**2*(t + 1)/19
Let i(d) be the third derivative of 0*d**3 + 0*d**4 + 1/84*d**8 - 1/30*d**6 + 0*d + 7*d**2 + 4/105*d**7 + 0 - 2/15*d**5. Suppose i(j) = 0. What is j?
-2, -1, 0, 1
Factor -j**4 + 12*j**3 + 64 - j**4 - 8*j**2 - 13479*j + 13431*j.
-2*(j - 4)*(j - 2)**2*(j + 2)
Let p = 2/7769 - -209759/15538. Factor p*n**2 - 3 - 21/2*n.
3*(n - 1)*(9*n + 2)/2
Let o(y) = -y + 15. Let d be o(7). Suppose 0 = 4*b - 4*c - 2 - 14, 3*b - d = c. Solve -4/5 + 4/5*j**b - 2/5*j + 2/5*j**3 = 0.
-2, -1, 1
Let c(a) be the first derivative of -1/6*a**2 - 2/15*a**5 + 1/18*a**6 + 0*a + 0*a**4 + 2/9*a**3 + 3. Factor c(d).
d*(d - 1)**3*(d + 1)/3
Let k(t) be the third derivative of t**5/210 - 83*t**4/84 + 82*t**3/21 - 12*t**2 - 12. Determine p, given that k(p) = 0.
1, 82
Suppose 0 = 3*g - y - 46, 3*y + 38 - 108 = -4*g. Suppose -12*o + 3*o = g*o. Factor 2/5*r**2 + 0*r + o.
2*r**2/5
Let f = -20 + 24. Factor 0*w**f - 2*w**2 + 6*w**4 + 0*w**3 - 2*w**3 - 2*w**4.
2*w**2*(w - 1)*(2*w + 1)
Let d(y) be the second derivative of -y**6/60 - 17*y**5/40 - y**4 - y**3/3 - 18*y. Let o(g) be the second derivative of d(g). Factor o(c).
-3*(c + 8)*(2*c + 1)
Let z(u) be the first derivative of 3*u**5/10 - 5*u**4/8 - 13*u**2/2 + 7. Let y(m) be the second derivative of z(m). Factor y(h).
3*h*(6*h - 5)
Let i(v) = -v**2 + 27*v + 4. Let f be i(27). Let g(s) be the first derivative of -8/5*s**5 - 16/3*s**3 + 5*s**f - 1 + 2*s**2 + 0*s. Suppose g(r) = 0. What is r?
0, 1/2, 1
Let q(g) be the first derivative of -g**7/56 + 7*g**6/120 - g**5/20 + 8*g**3/3 + 7. Let u(c) be the third derivative of q(c). Solve u(j) = 0 for j.
0, 2/5, 1
Let o(i) = i**2 + 88*i + 2. Let r be o(0). Let -1/3*k**4 + 2/3 - k + k**3 - 1/3*k**r = 0. Calculate k.
-1, 1, 2
Suppose 0 = -5*n + b + b + 73, -3*n - 3*b = -27. Let f be 4/(-5)*n/(-26). Suppose f + 4/5*o + 2/5*o**2 = 0. What is o?
-1
Suppose -5*f - 4 = 31. Let h be (-21)/f + (-22)/10. Find r, given that 8/5*r + h + 4/5*r**2 = 0.
-1
Factor 0*z + 2/9*z**3 - 2/9*z**4 + 8/3*z**2 + 0.
-2*z**2*(z - 4)*(z + 3)/9
Factor 0 + 39/4*t**3 + 507/8*t**2 + 3/8*t**4 + 0*t.
3*t**2*(t + 13)**2/8
Let c(v) = 8*v**3 + 29*v**2 + 23*v - 15. Let n(l) = 9*l**3 + 31*l**2 + 24*l - 16. Let k(z) = -4*c(z) + 3*n(z). Factor k(p).
-(p + 2)*(p + 3)*(5*p - 2)
Let q(h) be the first derivative of -5*h**6/6 + 2*h**5 - 10*h**3/3 + 5*h**2/2 - 136. Factor q(j).
-5*j*(j - 1)**3*(j + 1)
Let o(s) be the third derivative of -20*s**2 + 0 + 1/4*s**4 + 0*s - 1/30*s**5 - 2/3*s**3. Factor o(q).
-2*(q - 2)*(q - 1)
Suppose 12*n - n = 0. Let p(v) be the second derivative of 0*v**2 - v + 1/24*v**4 + 0*v**3 + n + 1/40*v**5. Factor p(c).
c**2*(c + 1)/2
Let t be 378/78 - 4/(-26). Suppose 2 + 20 = o - t*a, -5*a = o + 18. Factor 1/2*g - 1/3 - 1/6*g**o.
-(g - 2)*(g - 1)/6
Let f = 76 + -72. What is u in -u**3 - f*u**4 - 124*u**2 + 124*u**2 + 2*u**3 = 0?
0, 1/4
Let s(c) = -c**2 - 66*c + 58. Let m(p) = -p**2 - 130*p + 116. Let n(r) = 6*m(r) - 10*s(r). Suppose n(z) = 0. What is z?
1, 29
Let s be ((-2)/(-12) - (-11)/6)*2. Factor 4*v**2 + s*v**2 - 2*v + 6*v**2 - 30*v**3 + 18*v**4.
2*v*(v - 1)*(3*v - 1)**2
Suppose -5*k + 3*c + 29 = 6*c, 3*c - 17 = -2*k. Solve -4*q**2 + 4*q - k*q**2 + 12*q**2 = 0.
-1, 0
Let y(r) be the first derivative of -r**7/42 - r**6/15 - r**5/20 + 3*r + 2. Let d(g) be the first derivative of y(g). Factor d(n).
-n**3*(n + 1)**2
Let r(m) be the second derivative of -1/24*m**3 + 9*m + 0*m**2 - 1/48*m**4 + 0. Solve r(j) = 0 for j.
-1, 0
Let c(k) be the second derivative of k**6/120 + 3*k**5/80 + k**4/16 + k**3/24 + 133*k. Factor c(j).
j*(j + 1)**3/4
Let h(a) = a**3 - 2*a**2 - 14*a - 10. Let g be h(-2). Suppose -2/15*k**4 - 2/5*k**g - 2/5*k**3 + 0 - 2/15*k = 0. What is k?
-1, 0
Factor -30*t**2 + 14*t**3 + 3*t**4 + 26*t + 2*t**4 - 4*t**4 - 8 - 3*t**4.
-2*(t - 4)*(t - 1)**3
Suppose 3*j + 3 = -9, -j = 4*n - 44. Suppose -10 - 2*h**3 + 2*h - 10 + n + 7*h**2 + h**2 = 0. Calculate h.
-1, 1, 4
Let v(i) be the third derivative of i**5/60 - i**4/6 + 2*i**3/3 + 4*i**2 - 6. Factor v(k).
(k - 2)**2
Let z(r) be the third derivative of r**8/2184 + 4*r**7/1365 - r**6/390 - 2*r**5/65 + 3*r**4/52 - 45*r**2 - 2*r. Factor z(l).
2*l*(l - 1)**2*(l + 3)**2/13
Let n(r) be the first derivative of 3*r**4/20 + 5*r**3 + 252*r**2/5 + 432*r/5 + 64. Suppose n(q) = 0. What is q?
-12, -1
Let x(t) be the third derivative of t**8/131040 - t**7/4680 + 7*t**5/10 - 37*t**2. Let g(i) be the third derivative of x(i). Let g(w) = 0. What is w?
0, 7
Let f(i) = 30*i**2 - 10*i + 40. Let s(m) = 2*m**2 + m. Let x(b) = -2*f(b) + 28*s(b). Factor x(o).
-4*(o - 10)*(o - 2)
Let c(q) be the first derivative of -5*q**6/6 + q**5 + 15*q**4/2 + 10*q**3/3 - 25*q**2/2 - 15*q + 65. Factor c(p).
-5*(p - 3)*(p - 1)*(p + 1)**3
Let y(d) be the third derivative of 0*d - 1/20*d**6 + 1/30*d**5 + 0 + 1/105*d**7 - 2/3*d**3 + 1/4*d**4 + 12*d**2. Factor y(u).
2*(u - 2)*(u - 1)**2*(u + 1)
Let q = -2393 - -11971/5. Solve 0 + q*v**2 - 3/5*v**3 - 3/5*v = 0.
0, 1
Factor -520*b**5 - 10*b**3 + 0*b**3 + 515*b**5 + 15*b**4.
-5*b**3*(b - 2)*(b - 1)
Let d(o) be the third derivative of 0 + 35*o**2 + 0*o + 1/6*o**3 - 1/12*o**4 + 1/60*o**5. Factor d(x).
(x - 1)**2
Let -9/2*o**4 + 127*o**2 - 1/2*o**5 + 11*o**3 - 245/2 - 21/2*o = 0. What is o?
-7, -1, 1, 5
Let k(n) be the second derivative of 3*n**5/20 - 26