/160 + h**4 + 65*h**3/16 - 445*h**2. Factor m(p).
-3*(p - 65)*(p + 1)/8
Let m(s) be the first derivative of -s**6/15 + s**4/5 - s**2/5 - 56. Factor m(c).
-2*c*(c - 1)**2*(c + 1)**2/5
Let c(n) = -11*n**4 + 4*n**3 + 21*n**2. Let y = -133 - -132. Let l(g) = -g**4 - g**3 + g**2. Let h(s) = y*c(s) + 6*l(s). Solve h(p) = 0.
-1, 0, 3
Let u = -58 + 72. Let b be (-2 + 36/u)/1. Factor b*s + 0 - 2/7*s**2.
-2*s*(s - 2)/7
Let b be 2/(-16)*-26 + (-1)/4. Suppose -4*x + b = -13. Factor -1/3*a**3 + 0*a**2 - 1/6 + 1/6*a**x + 1/3*a.
(a - 1)**3*(a + 1)/6
Let k(a) be the second derivative of a**4/6 + 122*a**3/3 + 3721*a**2 + 17*a. Suppose k(o) = 0. What is o?
-61
Let f(g) be the third derivative of g**6/160 + g**5/2 + 39*g**4/32 + 2*g**2 - 199. Factor f(t).
3*t*(t + 1)*(t + 39)/4
Factor -7/4*n - 3 - 1/4*n**2.
-(n + 3)*(n + 4)/4
Let f(v) be the third derivative of v**5/40 - 2*v**4 + 2*v**2 - 4*v. Suppose f(a) = 0. Calculate a.
0, 32
Suppose 3*i = 4*m - 11, -5*m = -4*m + i - 1. Factor 0 + 15/2*k - 3/2*k**m.
-3*k*(k - 5)/2
Let 0 + 44/3*m - 2/3*m**3 - 6*m**2 = 0. Calculate m.
-11, 0, 2
Let w(c) be the second derivative of c**5/10 + 17*c**4/6 + 16*c**3/3 + 21*c + 3. Factor w(a).
2*a*(a + 1)*(a + 16)
Let m be 30/(-45)*1*-2*1. Determine t, given that 1/3*t**5 + 4/3*t**4 + t**3 + 0 - 4/3*t - m*t**2 = 0.
-2, -1, 0, 1
Let y(m) be the second derivative of m**4/12 + 10*m**3/3 - 21*m**2/2 - 14*m - 3. Determine h, given that y(h) = 0.
-21, 1
Let b(w) = -w**3 - w**2 + 268*w - 66. Let s be b(-17). Factor 2/3*h**s + 4 + 14/3*h.
2*(h + 1)*(h + 6)/3
Let y(f) = 17*f**4 - 7*f**3 + 6*f + 6. Let m(k) = 37*k**4 - 16*k**3 + 13*k + 13. Let w(n) = -6*m(n) + 13*y(n). Solve w(v) = 0 for v.
0, 5
Let q be (-40)/(-100) - (16/5)/(-2). Factor -f + 1/3*f**q + 2/3.
(f - 2)*(f - 1)/3
Suppose -1 + 6 = -s, w + 4*s = -17. What is l in -9 + w*l**5 + 0*l**2 + 15*l - 4*l**4 + 6*l**2 - 18*l**3 + 7*l**4 = 0?
-3, -1, 1
Let o(k) be the second derivative of k**6/70 + 3*k**5/28 - k - 23. Suppose o(h) = 0. What is h?
-5, 0
Factor 8*p**5 + 48*p**2 + 86*p**3 + 18*p**4 - 44*p**3 + 6 - 5*p**5 + 27*p.
3*(p + 1)**4*(p + 2)
Let k(n) be the second derivative of -n**7/14 + 3*n**6/5 - 39*n**5/20 + 3*n**4 - 2*n**3 - n + 37. Factor k(x).
-3*x*(x - 2)**2*(x - 1)**2
Let l = 53 - 35. Let c = l + -16. Factor 0*u**c + 5*u**3 + 3*u - 5*u - 6*u**3 - 3*u**2.
-u*(u + 1)*(u + 2)
Solve 4/5*g**5 + 12/5*g**4 - 28/5*g**3 + 32/5 + 24/5*g - 44/5*g**2 = 0.
-4, -1, 1, 2
Let f(k) = -2*k**2 - k. Let n(h) = -5*h**2 + 15*h + 81. Let g(l) = -3*f(l) + n(l). Factor g(a).
(a + 9)**2
Let n = 1 + 1. Suppose 0 = -n*k - k + 36. Factor -3*f**3 + k - f**2 - f**4 - 10 + 0*f**2 + 3*f.
-(f - 1)*(f + 1)**2*(f + 2)
Suppose -4*h = -3*w - 33, 2*h + 3*w - 8*w = 27. Let m = h + -2. Factor -6*u**5 + 8*u**5 + u**m + 2*u**3 + 3*u**4.
2*u**3*(u + 1)**2
Let h(l) be the first derivative of l**6/120 + l**5/20 + 7*l**2 + 4. Let c(i) be the second derivative of h(i). Factor c(s).
s**2*(s + 3)
Let w(v) be the first derivative of -2*v**3/9 + 4*v**2 - 18*v - 257. Factor w(l).
-2*(l - 9)*(l - 3)/3
Let s(t) be the third derivative of -t**6/360 - t**5/45 + 2*t**4/9 + 32*t**3/9 + 95*t**2. Solve s(q) = 0 for q.
-4, 4
Let n(q) be the second derivative of 1/6*q**3 + 20*q + 0*q**2 + 1/16*q**4 + 0 - 1/80*q**5. Factor n(h).
-h*(h - 4)*(h + 1)/4
Let g be 162/10 + (-2 + -1 - 2). Let 56/5*m**3 - 8/5 + 98/5*m**4 - g*m - 18*m**2 = 0. Calculate m.
-1, -2/7, 1
Let i(z) be the first derivative of -z**6/18 - 38*z**5/15 - 44*z**4 - 3146*z**3/9 - 6655*z**2/6 - 785. Let i(n) = 0. What is n?
-11, -5, 0
Let p(d) be the second derivative of -5*d**5/12 - 5*d**4/18 + 14*d**3/3 + 12*d**2 - 19*d + 1. Factor p(f).
-(f - 2)*(5*f + 6)**2/3
Suppose 9 - 1 = 2*d. What is c in 0*c**3 + 0*c**2 - c**d + 0*c**3 + c**2 = 0?
-1, 0, 1
Let o be (-3240)/(-2100) + (-2)/5. Factor 6/7*u**2 - o*u**3 + 8/7*u + 2/7*u**4 - 8/7.
2*(u - 2)**2*(u - 1)*(u + 1)/7
Factor 84*i**2 - 5*i**4 + 12*i**4 + 20*i**4 - 102*i**3 + 0*i**4 + 24*i.
3*i*(i - 2)**2*(9*i + 2)
Let w = 115 - 114. Let j = -2 - -4. Factor 1 - 4*t - w + 18*t - 4*t**j - 14*t**3 + 4.
-2*(t - 1)*(t + 1)*(7*t + 2)
Let p(c) be the third derivative of -c**5/105 - 5*c**4/3 - 350*c**3/3 - 4*c**2 - 15. Find i such that p(i) = 0.
-35
Let l(p) be the first derivative of 2/3*p**3 + 1/6*p**2 - 23 - 4/15*p**5 - 1/3*p**4 - 2/3*p + 1/6*p**6. Factor l(b).
(b - 1)**3*(b + 1)*(3*b + 2)/3
Let z(t) = t**4 - 2*t**2 + 1. Let q(c) = -8*c**4 - 88*c**3 - 620*c**2 - 1584*c - 1300. Let g(l) = q(l) + 4*z(l). Let g(r) = 0. Calculate r.
-9, -2
Find u, given that -4*u**5 - 6*u**4 - 16*u**2 + 3*u**5 + 528 - 530 - 9*u - 14*u**3 = 0.
-2, -1
Suppose 31*v - 99 = -6. Let d(o) be the first derivative of -3/16*o**4 - 1 - 1/4*o**v + 3/4*o + 3/8*o**2. Factor d(y).
-3*(y - 1)*(y + 1)**2/4
Let c(l) be the first derivative of -4*l**3/3 - 268*l**2 - 17956*l + 42. Let c(k) = 0. What is k?
-67
Let g(s) be the first derivative of s**4/4 - 7*s**3/3 + s**2 - 10*s + 2. Let p be g(7). Factor -2/5*q**3 + 0 + 0*q**2 + 1/5*q**p + 0*q.
q**3*(q - 2)/5
Let g(v) be the third derivative of 0*v**5 + 1/480*v**6 + 0 + 0*v**4 - 6*v**2 - 1/840*v**7 + 0*v + 0*v**3. Find b, given that g(b) = 0.
0, 1
Suppose 5*k - 5*v - 25 = 0, 3*k - 7*v = -12*v + 23. Let m(d) be the third derivative of 1/7*d**3 - k*d**2 - 1/42*d**4 - 1/210*d**5 + 0 + 0*d. Factor m(y).
-2*(y - 1)*(y + 3)/7
Factor 6*n**2 - n**2 - 8*n - 4*n**2 + 7 + 3*n**2 - 3*n**2.
(n - 7)*(n - 1)
Factor 44/3 + 65/3*s**3 + 51*s**2 + 7/3*s**4 + 139/3*s.
(s + 1)**3*(7*s + 44)/3
Let q(u) be the third derivative of -u**7/1260 - u**6/240 + u**5/60 + 7*u**4/36 + 2*u**3/3 + u**2 + 13. Let q(c) = 0. What is c?
-2, 3
Let i be -3 + (-3 - -5) - -11. Let n be (3 + -8)*(-54)/i. Find f, given that 12*f - 4/3 - n*f**2 = 0.
2/9
Factor -2*t + 1/2*t**2 + 0 + 1/4*t**4 + 5/4*t**3.
t*(t - 1)*(t + 2)*(t + 4)/4
Suppose 0 = -10*m - 3*m + 26. Suppose -12*b**m + 3*b - 4 - 15*b + 0 - 4*b**3 = 0. What is b?
-1
Let m = 57421/24233 - 13/2203. Find f such that 169/11 + m*f + 1/11*f**2 = 0.
-13
Let y(j) be the first derivative of 2*j**5/5 + 5*j**4/12 - 5*j**3/9 - 5*j**2/6 - j/3 + 70. Solve y(t) = 0.
-1, -1/2, -1/3, 1
Suppose -5*f = -5*u - 5, -f = -4*u + 2*u - 4. Let x be ((3 + -3)/2)/u. What is q in 1/3*q**2 + x + 0*q**3 + 0*q - 1/3*q**4 = 0?
-1, 0, 1
Let c be 90/24 - 6/8. Let f = c + -1. Factor 3*x**5 - 8*x**2 + f*x**2 + 9*x**3 - 6*x**5.
-3*x**2*(x - 1)**2*(x + 2)
Let i(v) = v + 12. Let c be i(-7). Suppose -4*z = 5*u - 27, 20 - 2 = c*u + z. What is s in -3/2*s - u - 3/2*s**4 + 3/2*s**3 + 9/2*s**2 = 0?
-1, 1, 2
Let o(i) be the second derivative of i**5/80 - i**4/16 + i**2/2 - 2*i + 17. Factor o(u).
(u - 2)**2*(u + 1)/4
Suppose 2*n**3 + 192/7 + 124/7*n**2 + 320/7*n = 0. What is n?
-4, -6/7
Let j(c) be the first derivative of 0*c + 4*c**2 - 2 + 8/3*c**3 + 1/2*c**4. Factor j(z).
2*z*(z + 2)**2
Let i be ((-319)/145 + 3)/4. Let l(p) = -p**2 + 2*p + 2. Let d be l(2). Factor 1/5*w + 0 + i*w**d.
w*(w + 1)/5
Let z = 4514/9 + -500. Let r = -18283/3 - -6095. Factor -r - z*b - 2/9*b**3 - 10/9*b**2.
-2*(b + 1)**2*(b + 3)/9
Let r be (7/(-57))/((-2304)/(-885) - 3). Let f = r - 1/513. Factor 2/13*t**5 + 2/13*t + 2/13*t**4 - 4/13*t**2 + 2/13 - f*t**3.
2*(t - 1)**2*(t + 1)**3/13
Let o(a) be the third derivative of -a**8/5040 - a**7/315 + a**6/36 - a**5/6 + 13*a**2. Let t(y) be the third derivative of o(y). Factor t(m).
-4*(m - 1)*(m + 5)
Let p(q) be the first derivative of 1/12*q**4 - 22 - 2/9*q**3 - 1/2*q**2 + 0*q. Find d such that p(d) = 0.
-1, 0, 3
Suppose 5*d - 70 = -2*c, -d + 17 = -0*d + c. Factor -2*v**2 - 45 - v**2 + d*v + 33.
-3*(v - 2)**2
Let j be (-60)/(-50)*20/6. Suppose j*u - 12 = u. Find l such that 1/2*l**u - 1/4*l**5 - 1/2 + 1/2*l**3 + 7/4*l - 2*l**2 = 0.
-2, 1
Let r(l) be the second derivative of 1/105*l**6 - 31*l + 0 - 1/3*l**4 - 1/147*l**7 + 3/35*l**5 + 11/21*l**3 - 3/7*l**2. Factor r(a).
-2*(a - 1)**4*(a + 3)/7
Let y(o) be the third derivative of -o**6/60 + 13*o**5/15 - 75*o**4/4 + 216*o**3 - 696*o**2. Let y(n) = 0. Calculate n.
8, 9
Let o(u) be the second derivative of 5*u**7/42 + u**6/3 - u**5/2 - 10*u**4/3 - 35*u**3/6 - 5*u**2 + 20*u. Factor o(z).
5*(z - 2)*(z + 1)**4
Let w(n) be the second derivative of -n**6/1080 - n**5/180 - 8*n**3/3 - 21*n. Let o(t) be the second derivative of w(t). Factor o(j).
-j*(j + 2)/3