**3 + 5*t**3 + 3*t**4 + n*t**4 + 3*t**2 - 3*t**3.
3*t**2*(t + 1)**2
Let c(m) be the third derivative of -1/45*m**5 + 0 + 0*m**3 - 1/36*m**4 + 1/504*m**8 + 2/315*m**7 + 0*m + 0*m**6 + 11*m**2. Determine y, given that c(y) = 0.
-1, 0, 1
Let v = -7 - -11. Suppose 3*t = v*m + 14, t + 4*m = m - 4. Factor 10*w**2 - 40*w + 28*w**2 - 8*w**3 + 8 - 4*w**t.
-2*(w - 2)**2*(4*w - 1)
Let c(y) be the third derivative of -y**8/30240 - y**7/1260 - y**6/120 - 13*y**5/60 + 27*y**2. Let p(f) be the third derivative of c(f). Factor p(r).
-2*(r + 3)**2/3
Let i(v) be the third derivative of 0*v**4 - 1/120*v**5 + 1/240*v**6 + 0 + 0*v + 9*v**2 + 0*v**3. Factor i(d).
d**2*(d - 1)/2
Let o(r) be the third derivative of r**5/420 + r**4/168 - r**3/21 - 149*r**2. Factor o(f).
(f - 1)*(f + 2)/7
Let t(g) = -g**3 - 5*g**2 + 28*g + 102. Let k be t(-7). Factor -4/7*w**k + 0 + 6/7*w**5 + 0*w**3 + 0*w + 0*w**2.
2*w**4*(3*w - 2)/7
Let m(r) = 4*r**2 - 3*r - 7. Let g(v) = -4*v**2 + 4*v + 8. Let z be (-20)/(4 + 1) - -1. Let s(j) = z*g(j) - 4*m(j). Determine p, given that s(p) = 0.
-1, 1
Let m(w) be the first derivative of -7/12*w**3 - 1/2*w + 9/8*w**2 + 18. Factor m(k).
-(k - 1)*(7*k - 2)/4
Let m = -38840 + 271881/7. Factor 0*a - m*a**2 + 1/7.
-(a - 1)*(a + 1)/7
Factor 0 + 4/11*n**2 + 6/11*n - 2/11*n**3.
-2*n*(n - 3)*(n + 1)/11
Let g(a) be the second derivative of -3*a**7/35 - a**6/5 + 16*a**5/25 + 4*a**4/5 - 16*a**3/5 + 16*a**2/5 + a + 271. Solve g(l) = 0 for l.
-2, 2/3, 1
Factor 72/5 + 2/5*t**2 - 24/5*t.
2*(t - 6)**2/5
Let 0*o - 15/7*o**3 - 12/7*o**4 - 6/7*o**2 - 3/7*o**5 + 0 = 0. Calculate o.
-2, -1, 0
Let o be ((-32)/12 - -2)*3. Let c be (o - 0) + (-1 - 15/(-3)). Factor -1 - 81/4*k**c + 9*k.
-(9*k - 2)**2/4
Let v(r) = -3*r - 35. Let i be v(-15). Suppose -7*b + 12*b = i. Let 2/7*u - 2/7*u**4 + 0 + 2/7*u**b - 2/7*u**3 = 0. Calculate u.
-1, 0, 1
Let p be (-6)/4 - (27 + -15)/(-4). What is t in 0 + 3/2*t + p*t**2 = 0?
-1, 0
Let q(l) be the third derivative of -l**8/224 + 3*l**7/70 - 13*l**6/80 + 3*l**5/10 - l**4/4 - 3*l**2 - 12. Factor q(o).
-3*o*(o - 2)**2*(o - 1)**2/2
Suppose 135 = 4*t - 3*v, -3*v + 11 = 5*t - 178. Let r be ((-24)/t)/((-44)/(-6))*-2. Factor 2/11*z - 2/11*z**2 + r - 2/11*z**3.
-2*(z - 1)*(z + 1)**2/11
Let q(h) be the first derivative of -h**4/24 + 94*h**3/9 - 2209*h**2/3 - 15. Factor q(i).
-i*(i - 94)**2/6
Let q(g) be the first derivative of g**7/420 + g**6/105 + g**5/140 - g**4/42 + 7*g**3/3 - 8. Let i(b) be the third derivative of q(b). Factor i(c).
2*(c + 1)**2*(7*c - 2)/7
Let v(n) be the third derivative of -n**5/90 - 97*n**4/36 - 32*n**3/3 + n**2 + 67. What is o in v(o) = 0?
-96, -1
Let t(z) = z**2 - 22*z + 46. Let v(d) = -4*d**2 + 108*d - 228. Let p(c) = 28*t(c) + 6*v(c). Determine f, given that p(f) = 0.
-10, 2
Let j(x) = x**2 - x + 23. Let k be j(0). Let a = k + -11. Solve a*t**4 + 6*t - 4*t**2 - 6*t**3 - 3*t**4 + 0*t**2 - 5*t**2 = 0 for t.
-1, 0, 2/3, 1
Let v(d) be the third derivative of 2/3*d**3 + 1/21*d**7 - 7/30*d**5 - 10*d**2 + 0 + 1/4*d**4 - 1/20*d**6 + 0*d. Factor v(f).
2*(f - 1)**2*(f + 1)*(5*f + 2)
Let s(w) be the second derivative of w**5/100 + 13*w**4/60 + 13*w**3/10 + 27*w**2/10 - 393*w. Suppose s(f) = 0. Calculate f.
-9, -3, -1
Let t(d) be the second derivative of -d**4/2 + 6*d**3 - 31*d**2 - 6*d. Let o(b) = 4*b**2 - 24*b + 41. Let h(m) = 8*o(m) + 5*t(m). Solve h(i) = 0 for i.
3
Suppose -2*v - 2 = 2*n, 3*v - 5*n = -2*v - 15. Let m be v + (-25)/(-2 + -3). Factor -1/4*l**4 - 1/2*l**m - 1/4*l**2 + 0 + 0*l.
-l**2*(l + 1)**2/4
Let 0*f**4 + 4*f**4 - 20*f - 28*f**3 + 58*f**2 - 52*f**2 + 38*f**2 = 0. Calculate f.
0, 1, 5
Let o(u) = -u**3 + 4*u**2 - 3*u. Let n be o(3). Suppose n = 5*m - 4*m - 2. Factor -6 - 9*h - 7*h - 22*h**m + 18*h**2 - 6.
-4*(h + 1)*(h + 3)
Let p be (-4)/6 + (-18)/(-27). Suppose p*s + 9 = 3*s. Determine n, given that n**4 + 24*n**3 - 11*n**s - 16*n**3 + 2*n**2 = 0.
0, 1, 2
Factor 0*k - 8/3*k**2 - 2/3*k**4 + 8/3*k**3 + 0.
-2*k**2*(k - 2)**2/3
Let x(w) = -475*w**2 + 245*w - 10. Let g(y) = -475*y**2 + 246*y - 8. Let h(z) = -5*g(z) + 6*x(z). Factor h(j).
-5*(5*j - 2)*(19*j - 2)
Let w(m) = -m**3 + 6*m**2 - 3*m - 6. Let f = 8 - 3. Let x be w(f). Solve 3*y**2 + 5 - x*y + 4 + 16*y = 0 for y.
-3, -1
Let d(t) be the second derivative of t**7/21 - 13*t**6/15 + 23*t**5/5 + 5*t**4/3 - 175*t**3/3 - 125*t**2 - 72*t. Solve d(s) = 0 for s.
-1, 5
Let h(s) be the third derivative of -1/40*s**5 + 0*s**3 + 1/48*s**4 + 1/80*s**6 + 0 + 9*s**2 + 0*s - 1/420*s**7. Factor h(i).
-i*(i - 1)**3/2
Let h(i) be the third derivative of -i**6/10 + 7*i**5/3 - 26*i**4/3 + 40*i**3/3 + 2*i**2 - 71*i. Factor h(w).
-4*(w - 10)*(w - 1)*(3*w - 2)
Let o(w) = 6*w**2 + 15*w + 11. Let q(a) = a**2 + 1. Let y(i) = o(i) - q(i). Determine x so that y(x) = 0.
-2, -1
Let y(o) be the second derivative of -o**8/1120 + o**7/280 + o**6/240 - o**5/40 - o**3/3 + 12*o. Let w(p) be the second derivative of y(p). Factor w(t).
-3*t*(t - 2)*(t - 1)*(t + 1)/2
Let c = 113 + -111. Let i(u) be the third derivative of -1/8*u**4 + 0*u + 4*u**c - 1/20*u**5 + 1/28*u**8 + 0 - 11/70*u**7 + 0*u**3 + 9/40*u**6. Factor i(n).
3*n*(n - 1)**3*(4*n + 1)
Let d(y) be the first derivative of 4*y**3/9 - 76*y**2/3 + 1444*y/3 + 14. Factor d(k).
4*(k - 19)**2/3
Let j(q) be the third derivative of 2*q**7/525 + 8*q**6/75 + 13*q**5/75 - q**4 + 157*q**2 + 2. Factor j(t).
4*t*(t - 1)*(t + 2)*(t + 15)/5
Let y(r) be the second derivative of 0*r**2 - 1/12*r**3 + 1/80*r**5 - 5*r + 1/16*r**4 + 0 + 1/168*r**7 - 1/40*r**6. What is j in y(j) = 0?
-1, 0, 1, 2
Factor -8*z**2 - 4 + 4/3*z**4 + 0*z**3 + 32/3*z.
4*(z - 1)**3*(z + 3)/3
Suppose 0 = -2*p + 1 + 11. Suppose 9*b = 6*b + p. Suppose 11 - 7*f + 7*f**4 + 8*f**3 - 4*f**5 + 3*f + 1 + 5*f**4 - 24*f**b = 0. What is f?
-1, 1, 3
Let c be ((-3)/(-4))/(9/6). Let l be (-20)/8*(-102)/85. Find w, given that -1/2*w**4 + 3/4*w**l + 0 - 3/4*w**5 + 0*w + c*w**2 = 0.
-1, -2/3, 0, 1
Let y(z) = z**3 + 4*z**2 - 4. Let o be y(-3). Let b be (-40)/(-400)*o/3. Let 1/3 - b*m - 1/6*m**2 = 0. Calculate m.
-2, 1
Suppose h - 363 = 3*u - 6*u, -4*h + 605 = 5*u. Let c be -2 + 0 - u/(-44). Solve 3/4*f**2 + 3/4*f**3 - 3/4*f - c = 0.
-1, 1
Let b(h) be the third derivative of 3*h**5/35 + 11*h**4/21 + 26*h**3/21 + 68*h**2 - 2. Factor b(j).
4*(j + 1)*(9*j + 13)/7
Let w(c) be the third derivative of c**10/126000 + c**9/28350 - c**8/37800 - c**5/20 + 2*c**2. Let p(l) be the third derivative of w(l). Solve p(t) = 0.
-2, 0, 2/9
Let l be ((-9)/(-6)*-32)/(-2). Let r be 2/5 - l/(-15). Factor -3/7*w**r - 2/7 - w.
-(w + 2)*(3*w + 1)/7
Let n be 3 + ((-6)/(-4))/(9/(-237)). Let g = n + 37. Factor 5/4*x**3 + 1/2*x**2 - 5/4*x - g.
(x - 1)*(x + 1)*(5*x + 2)/4
Let y be (2 + 0)*(-3)/(-2). Let j be 8/68 + 198/51. Factor -10*p**y + 10*p**3 + p**4 + p**j.
2*p**4
Let h(t) be the third derivative of -t**6/165 - 8*t**5/165 - 13*t**4/132 - t**3/11 - t**2 + 70. Factor h(p).
-2*(p + 3)*(2*p + 1)**2/11
Let x(o) = -3*o**3 - 2*o**2 - 9*o + 14. Let k(f) = -3*f + 3. Let g(n) = -4*k(n) + x(n). Factor g(a).
-(a - 1)*(a + 1)*(3*a + 2)
Let i(p) = p**3 + 17*p**2 - 38*p + 4. Let y be i(-19). Let n = 35 - 25. Find w such that -y*w + 10*w**4 + 4*w**4 + n*w**2 + 12*w**2 - 32*w**3 = 0.
0, 2/7, 1
Let r(u) = 75*u**2 + 63*u + 27. Let x(m) = -11*m**2 - 9*m - 4. Let c(g) = -4*r(g) - 27*x(g). Solve c(d) = 0.
-3, 0
Let p = 10 + -2. Let d be ((-12)/p)/(-3)*8. Factor 4*q**2 + 3 - d*q + 0*q - 3.
4*q*(q - 1)
Let y(d) = -d**3 - d**2 - d. Let q(l) = -l**4 + 8*l**3 + 2*l**2 + 6*l. Let m be (-6)/12*(28 + 2). Let n(o) = m*y(o) - 3*q(o). Factor n(s).
3*s*(s - 1)**3
Let t(r) be the second derivative of 2 - 1/10*r**5 + 8*r - 8/3*r**4 - 64/3*r**3 + 0*r**2. Solve t(u) = 0 for u.
-8, 0
Let o(i) be the first derivative of -i**6/180 - i**5/45 - i**4/36 + 25*i**2 - 40. Let k(a) be the second derivative of o(a). Factor k(u).
-2*u*(u + 1)**2/3
Let r(s) be the third derivative of -s**6/360 - s**5/180 + s**4/36 + 99*s**2 - 2. Factor r(t).
-t*(t - 1)*(t + 2)/3
Let k be 7/2*6496/140. Let c = k - 156. Determine o, given that -2/5*o**2 - c - 16/5*o = 0.
-4
Suppose -25 = -4*u + 55. Suppose -4 = -5*k + 9*t - 8*t, u = -5*t. Suppose -1/7*g**3 + k*g + 4/7 - 3/7*g**2 = 0. What is g?
-2, 1
Let z(t) be the third derivative of t**5/300 - 11*t**4/120 - 2*t**3/5 - 3*t**2 + 4*t. Find q, given that 