-10))/(3/((-1380)/(-8))). Factor -8*z**2 + 2*z**3 - 46 + 8*z + v.
2*z*(z - 2)**2
Let h(a) be the first derivative of -5*a**4/4 - 55*a**3/3 - 60*a**2 + 180*a - 41. Factor h(m).
-5*(m - 1)*(m + 6)**2
Let a be 0*((-66)/24)/(-11). Let p(d) be the third derivative of -1/30*d**5 + 6*d**2 + a*d + 1/21*d**3 + 0 - 1/42*d**4 - 1/105*d**6. Let p(u) = 0. Calculate u.
-1, 1/4
Factor -4/5*u**2 - 36/5*u + 8.
-4*(u - 1)*(u + 10)/5
Solve -4/3*j**4 + 20*j**3 - 64/3 - 20*j + 68/3*j**2 = 0 for j.
-1, 1, 16
Let q(a) be the first derivative of 10 + a**3 - 1/2*a**2 + 0*a. Factor q(z).
z*(3*z - 1)
Let x(w) be the third derivative of -2/9*w**3 + 0*w + 0 + 5/72*w**4 - 31*w**2 - 1/180*w**6 + 7/180*w**5. Let x(b) = 0. Calculate b.
-1, 1/2, 4
Let p = 174 + -150. Let q(g) = -g**2 - 27*g - 60. Let y be q(-24). Factor -3/2*k**2 - p + y*k.
-3*(k - 4)**2/2
Let o(a) = -a**2 - 19*a + 40. Let c be o(-21). Let v be c - -4 - 40/28. Solve -3/7*x - 2/7 + v*x**4 + 16/7*x**2 - 15/7*x**3 = 0 for x.
-1/4, 1, 2
Factor 11*s**4 + 4*s**3 - 3*s**4 + 369*s**5 - 365*s**5.
4*s**3*(s + 1)**2
Suppose 16 = -4*n + 4*i, 3*n + 27 = 5*i + 7. Factor n - 2/9*k**2 + 0*k.
-2*k**2/9
Let v be 77/55 - 198/165. Suppose v*m**2 + 4/5*m - 1 = 0. Calculate m.
-5, 1
Let s(n) be the third derivative of n**8/420 + n**7/42 + n**6/15 - 2*n**5/15 + 7*n**4/24 - 33*n**2. Let g(z) be the second derivative of s(z). Factor g(h).
4*(h + 2)**2*(4*h - 1)
Let g(o) be the second derivative of o**4/18 + 41*o**3/9 + 103*o. Determine c, given that g(c) = 0.
-41, 0
Let t(i) be the second derivative of 0*i**3 - 7/10*i**5 + 0*i**2 + 0 + 2/3*i**4 + 2/15*i**6 + 1/21*i**7 - 32*i. Solve t(w) = 0 for w.
-4, 0, 1
Let f(w) be the third derivative of -w**9/181440 - w**8/60480 + 2*w**5/15 - 24*w**2. Let c(t) be the third derivative of f(t). Factor c(v).
-v**2*(v + 1)/3
Solve -2/17*f**2 - 8/17*f + 0 = 0 for f.
-4, 0
Let p = 2008/3 + -669. What is q in 1/9*q**4 + 1/9*q + p*q**2 + 0 + 1/3*q**3 = 0?
-1, 0
Let f(n) be the first derivative of n**5/20 - n**4/16 - n**3/3 + n**2/2 - 102. Solve f(h) = 0.
-2, 0, 1, 2
Let n(x) = -4*x**2 - x + 20. Let p(l) = 12*l**2 + 8*l - 60. Let f(c) = 8*n(c) + 3*p(c). Factor f(b).
4*(b - 1)*(b + 5)
Let i(h) = h**3 + 8*h**2 + 5*h - 7. Let z be i(-7). Let k be -4 + z - (0 + 1). Factor -5*l + 0*l + 4*l + k*l**2 - l**3.
-l*(l - 1)**2
Suppose -81*q = -5*q - 152. Factor -1/6*a**q + 0*a - 7/2*a**4 + 4/3*a**3 + 3*a**5 + 0.
a**2*(2*a - 1)*(3*a - 1)**2/6
Factor 24/5*h**2 + 26/5*h + 0 - 2/5*h**3.
-2*h*(h - 13)*(h + 1)/5
Let 3*x**2 - 3*x**5 + 2*x - 4 + 5*x**5 - 4*x**3 + 9*x**4 - x**2 + 6*x**2 - 13*x**4 = 0. What is x?
-1, 1, 2
Let f(l) be the third derivative of -l**6/600 + 13*l**5/100 - 133*l**4/40 + 361*l**3/30 - 111*l**2. Suppose f(d) = 0. Calculate d.
1, 19
Factor -5/2*k + 5/2*k**2 + 0.
5*k*(k - 1)/2
Factor -16 + 204/5*t - 2*t**2.
-2*(t - 20)*(5*t - 2)/5
What is j in -20*j**2 - 8*j**3 - 131*j + 24*j**3 + 274*j - 4*j**4 - 135*j = 0?
0, 1, 2
Let a(m) be the second derivative of m**6/6 + 5*m**5/4 + 5*m**4/2 - 309*m. Factor a(r).
5*r**2*(r + 2)*(r + 3)
Let k be (25 - (-1230)/(-50))/(8/5). Factor -1/4 + 1/4*i + k*i**2 - 1/4*i**3.
-(i - 1)**2*(i + 1)/4
Let -242836*w**3 - 10*w**4 - 175*w**4 - 3*w**5 + 242638*w**3 - 16*w**4 = 0. Calculate w.
-66, -1, 0
Let i(m) = 100*m**2 - 2599*m - 21. Let j be i(26). Factor -7*p**2 + 1/2*p**j - 3 + 2*p**4 + 0*p**3 - 17/2*p.
(p - 2)*(p + 1)**3*(p + 3)/2
Let l(j) be the second derivative of j**4/24 - 5*j**3/4 + 7*j**2/2 - 40*j + 1. Let l(k) = 0. Calculate k.
1, 14
Let j be ((-291)/(-6))/(-2 - (-10)/4). Let c = j + -97. Let -1/4*x**3 - 5/4*x**2 - 3/4*x + 1/4*x**4 + c = 0. What is x?
-1, 0, 3
Let s = 205 + -370. Let y = -165 - s. Factor -1/2*n**2 + 1/2*n**5 + 0 + 3/2*n**3 + y*n - 3/2*n**4.
n**2*(n - 1)**3/2
Let v be (-5 - (-8 - -2))/((-2)/74). Let q = -35 - v. Factor 1/2*g**3 + 27/2 + 27/2*g + 9/2*g**q.
(g + 3)**3/2
Let o be 2/(-13) + 670/130. Suppose -o*w + 29 - 19 = 0. Suppose 9/2 + 1/2*y**w - 3*y = 0. Calculate y.
3
Let o(b) be the third derivative of b**8/112 + 2*b**7/35 + 3*b**6/40 - b**5/5 - b**4/2 + 49*b**2. Factor o(h).
3*h*(h - 1)*(h + 1)*(h + 2)**2
Factor -78*g**2 - 2*g**3 - 9*g**3 - g**3 + 0*g**3 + 15*g**3.
3*g**2*(g - 26)
Let d(o) = 28*o**2 + 72*o + 4. Let u(m) = -m**3 - 29*m**2 - 70*m - 3. Let q(v) = 3*d(v) + 4*u(v). Let q(x) = 0. What is x?
-4, 0
Suppose 2*j = 4*y - 8, -2*j - 8 = -4*y - j. Suppose 17 - 23 = -y*v. Factor 6/7*u**2 + 36/7*u - 27/7 - 12/7*u**v - 3/7*u**4.
-3*(u - 1)**2*(u + 3)**2/7
Let t(g) be the second derivative of 35*g + 70/3*g**3 - 245/12*g**4 - 10*g**2 + 0. Factor t(q).
-5*(7*q - 2)**2
Let b(k) = -3*k**2 - 13*k + 2. Let s(g) = -g - 1. Let q(h) = b(h) + 2*s(h). Factor q(f).
-3*f*(f + 5)
Solve 1/2*f**4 + 1/2*f**2 - 3/2*f - 1 + 3/2*f**3 = 0.
-2, -1, 1
Suppose 12*j - 51*j = 60*j - 26*j. Factor j - 4/9*p**3 + 2/9*p**4 + 2/9*p**2 + 0*p.
2*p**2*(p - 1)**2/9
Let z = 1/40 - -13/120. Let r = z + 6/5. What is u in 14/3*u**2 - r + 10/3*u = 0?
-1, 2/7
Let c(u) = -5*u**2 - 9*u - 10. Let a(z) = -7*z**2 + z + 2. Let k be a(-1). Let t(l) = -9*l**2 - 17*l - 19. Let p(q) = k*t(q) + 11*c(q). Factor p(v).
-(v - 4)*(v + 1)
Determine o, given that 141 - 3*o**2 + 3*o**4 - 5*o**3 + 21*o + 0*o**4 - 141 - 16*o**3 = 0.
-1, 0, 1, 7
Suppose 0 = -9*w + 11*w - 24. Suppose 4*q = -16, 0 = -d - 3*d - q + w. Factor 3/4*k - 15/2*k**2 + 0 + 99/4*k**3 + 12*k**5 - 30*k**d.
3*k*(k - 1)**2*(4*k - 1)**2/4
Let v(m) be the third derivative of m**7/5040 - m**6/1440 + 5*m**4/12 - 4*m**2. Let a(n) be the second derivative of v(n). Factor a(c).
c*(c - 1)/2
Let o(s) = 2*s**2 - 4*s + 1. Let h(l) = 0*l**2 - 1 - 4*l**2 + l + 5*l**2. Let d(m) = -h(m) - o(m). Suppose d(i) = 0. Calculate i.
0, 1
Suppose -60 = -13*n - 2*n. Let g(t) be the first derivative of -2*t**3 + 3/5*t**5 - n + 0*t - 3/4*t**4 + 0*t**2. Factor g(p).
3*p**2*(p - 2)*(p + 1)
Let -4/9*w**2 - 44/9*w - 8 = 0. What is w?
-9, -2
Let j(w) be the second derivative of -3*w**5/100 - 3*w**4/10 - w**3/2 - 64*w. Find l, given that j(l) = 0.
-5, -1, 0
Let d(k) = -4*k**2 + 3*k + 5 + 2*k - 9. Let w(y) = y**2 - y + 1. Let f(u) = -2*d(u) - 6*w(u). Factor f(x).
2*(x - 1)**2
Let p(s) be the first derivative of 3*s**4/4 - 13*s**3 + 54*s**2 - 257. Let p(h) = 0. What is h?
0, 4, 9
Let l(u) be the third derivative of -u**6/60 - u**5/6 + 11*u**4/6 - 16*u**3/3 - 916*u**2. Determine j so that l(j) = 0.
-8, 1, 2
Factor -6*q**3 + 0 + 0*q + 81*q**2 + 1/9*q**4.
q**2*(q - 27)**2/9
Let i(d) be the first derivative of -d**6/21 - 16*d**5/35 - 8*d**4/7 + 12*d**3/7 + 81*d**2/7 + 108*d/7 - 47. Solve i(t) = 0 for t.
-3, -1, 2
Let o(s) be the second derivative of -s**9/3024 - s**8/840 + s**6/180 + s**5/120 - 2*s**3 - 4*s. Let u(c) be the second derivative of o(c). Factor u(r).
-r*(r - 1)*(r + 1)**3
Let k(n) = -5*n + 14. Let b be k(-12). Suppose i = -4*p, -b - 31 = -5*i + p. Factor -8 - 12*w - 54*w**3 + 29*w**4 - 122*w**2 + 72*w + i*w**4 + 75*w**3.
(w - 1)*(w + 2)*(7*w - 2)**2
Let l(w) = -7*w**3 + 24*w**2 - 47*w + 34. Let n(g) = 6*g**3 - 24*g**2 + 48*g - 33. Let v(h) = 3*l(h) + 4*n(h). Find c such that v(c) = 0.
1, 2, 5
Let t(j) be the second derivative of j + 1/72*j**5 + 0 - 1/36*j**4 + 7/1080*j**6 + j**3 + 0*j**2. Let n(o) be the second derivative of t(o). Factor n(k).
(k + 1)*(7*k - 2)/3
Determine r, given that 25600 - 547*r**2 + 1094*r**2 - 640*r - 543*r**2 = 0.
80
Let o(h) be the second derivative of -4/21*h**3 + 1/210*h**6 + 0 + 6*h - 2/7*h**2 - 1/28*h**4 + 1/70*h**5. Factor o(s).
(s - 2)*(s + 1)**2*(s + 2)/7
Let j(d) = d**2 + d. Let r(w) = 7*w**2 - 5*w + 18. Let q(h) = -6*j(h) + r(h). Let b be q(9). Suppose 0*g + b - 1/4*g**4 + 0*g**2 + 0*g**3 = 0. Calculate g.
0
Let i = 1806 - 1804. Solve -3/2 - 1/2*y**2 - i*y = 0 for y.
-3, -1
Let s = -21 - -31. Let z = -8 + s. Factor 2191*v + 26*v**3 + 54*v**3 - 1280 - 5*v**4 - 480*v**z - 911*v.
-5*(v - 4)**4
Let n(t) = 2*t**3 + 6*t**2 - 18*t + 2. Let o(c) = c**3 - c**2 - c - 1. Let a = -31 + 32. Let i(m) = a*n(m) - 4*o(m). Determine k, given that i(k) = 0.
1, 3
Find i, given that 10/9*i**4 - 22/9*i - 8/9 - 2/9*i**2 + 26/9*i**3 - 4/9*i**5 = 0.
-1, -1/2, 1, 4
Let x(w) be the second derivative of -3*w**5/140 + 11*w**4/28 - 2*w**3/7 - 90*w**2/7 - 582*w. Factor x(i).
-3*(i - 10)*(i - 3)*(i + 2)/7
Suppose -3*f = -4*r + 24, -3*f = -5*r - 2*f + 19. Let u be 