Suppose z - 15 = -3*f + 6*z, 4*f = -3*z + 20. Let t(a) be the third derivative of -1/330*a**f + 0*a - 5*a**2 + 0 - 3/11*a**3 + 1/22*a**4. Factor t(m).
-2*(m - 3)**2/11
Let j be (23/45*12 - 9/27) + -5. Factor 2/5*t - 2/5*t**3 + 4/5*t**2 - j.
-2*(t - 2)*(t - 1)*(t + 1)/5
Let a(x) be the second derivative of -x**6/15 + 79*x**5/20 - 337*x**4/6 - 707*x**3/2 - 441*x**2 + 82*x + 3. Solve a(o) = 0 for o.
-2, -1/2, 21
Let a(i) be the third derivative of 0 + 0*i**3 - 2/21*i**7 + 1/15*i**6 - 20*i**2 - 1/28*i**8 + 0*i**4 + 0*i + 0*i**5. Factor a(q).
-4*q**3*(q + 2)*(3*q - 1)
Suppose -4*w = -2*a - 208, 4*a - 3*w + 416 = w. Let v = a + 106. Factor 0*g**v + 2/3 + 4/3*g - 4/3*g**3 - 2/3*g**4.
-2*(g - 1)*(g + 1)**3/3
Let r be (-24)/45*(-1)/((-36)/(-15)). Let c(f) be the first derivative of -1 + 1/3*f**2 - r*f**3 + 0*f. Factor c(x).
-2*x*(x - 1)/3
Factor 86 + 106 - 29*u**2 - u**4 - 2345*u**3 + 176*u + 2331*u**3.
-(u - 3)*(u + 1)*(u + 8)**2
Find c, given that 113*c**3 + 278*c**4 + 142*c**4 + 50*c**2 + 29*c**5 - 408*c**3 + 16*c**5 + 0*c**5 = 0.
-10, 0, 1/3
Let w = 1063/1599 + 1/533. Find k, given that 2/3*k**3 + 0*k**2 - w*k + 0 = 0.
-1, 0, 1
Let w(r) = 7*r**3 + 116*r**2 + 350*r + 352. Let p(x) = -3*x**3 - 56*x**2 - 176*x - 176. Let b(d) = -5*p(d) - 2*w(d). Find y such that b(y) = 0.
-44, -2
Let h(l) be the first derivative of 2*l**3/3 + 7*l**2 - 10*l + 41. Let w(j) = -j. Let n(t) = -2*h(t) - 12*w(t). Factor n(m).
-4*(m - 1)*(m + 5)
Let c = 1220 + -1217. Factor 0 + 0*g + 2/7*g**c + 4/7*g**2.
2*g**2*(g + 2)/7
Factor -212/9*h**2 - 44/3*h - 16/9 + 31*h**3 + 9*h**4.
(h - 1)*(h + 4)*(9*h + 2)**2/9
Let p(v) be the third derivative of -v**7/1470 - v**6/315 + v**5/210 + v**4/21 - 7*v**3/3 + 8*v**2. Let w(f) be the first derivative of p(f). Factor w(m).
-4*(m - 1)*(m + 1)*(m + 2)/7
Suppose a = 2*c + 2*a - 31, -5*a = -c - 1. Suppose y = 4, -g - y + c = 4*g. Factor g*u**2 - 9*u**2 - u + 6*u**2.
-u*(u + 1)
Let u(q) = 6*q + 74. Let m be u(0). Solve 10 + m*w**2 - 140*w**2 + 81*w**2 + 45*w - 20*w**3 = 0.
-1, -1/4, 2
Let d = -211 + 214. Let n(z) be the first derivative of 0*z - 1/12*z**4 + d + 0*z**2 - 2/9*z**3. Determine q, given that n(q) = 0.
-2, 0
Let n(x) be the first derivative of -x**6/45 - 148*x**5/75 - 228*x**4/5 + 148*x**3/45 + 1369*x**2/15 + 203. Determine t, given that n(t) = 0.
-37, -1, 0, 1
Let p(t) = 3*t**2 + 74*t + 116. Let q be p(-23). Let r(m) be the first derivative of 4/21*m**3 + q + 0*m - 1/14*m**4 - 1/7*m**2. Factor r(y).
-2*y*(y - 1)**2/7
Let i(u) = -u**3 + 2*u**2 + u + 1. Let k(m) = 7*m**3 + 24*m**2 + 6*m + 2. Let s(g) = 10*i(g) - 5*k(g). Factor s(l).
-5*l*(l + 2)*(9*l + 2)
Let w(g) = -9*g**4 - 80*g**3 - 159*g**2 - 120*g - 32. Let q(l) = 19*l**4 + 160*l**3 + 317*l**2 + 240*l + 64. Let p(z) = -3*q(z) - 5*w(z). What is m in p(m) = 0?
-4, -1, -2/3
Let j(q) = -q**3 - q**2 - 2*q - 4. Let v be j(-2). Suppose -3*h + 17*h = 0. Find t such that t**3 + h + 0*t - 1/2*t**v - 1/2*t**2 = 0.
0, 1
Let f(q) = q**3 + 20*q**2 + 17*q - 1. Let g(x) = -2*x - 1. Let p(k) = f(k) - g(k). Factor p(a).
a*(a + 1)*(a + 19)
Let w(y) be the second derivative of -y**7/105 + y**5/50 + 207*y. Solve w(d) = 0 for d.
-1, 0, 1
Let c(b) be the second derivative of -b**4/6 + 7*b**3 + 22*b**2 + 52*b. Suppose c(a) = 0. What is a?
-1, 22
Let v(p) be the third derivative of 25*p**6/6 + 30*p**5 + 90*p**4 + 144*p**3 + p**2 + 12. Solve v(u) = 0 for u.
-6/5
Factor -8*k - 12*k + 6848*k**3 + 5*k**4 - 6878*k**3 + 45*k**2.
5*k*(k - 4)*(k - 1)**2
Factor 6*m**2 + m**3 - 17 - 20*m + 2*m**2 - 5*m**2 - 7 - 5*m**2.
(m - 6)*(m + 2)**2
Let k(q) be the first derivative of -6*q**3/7 - 223*q**2/7 + 100*q/7 + 1059. Factor k(c).
-2*(c + 25)*(9*c - 2)/7
Let d(b) = 2*b**4 - 13*b**3 - 2*b**2 + 13*b. Let r(s) = s**4 - 6*s**3 - s**2 + 6*s. Let i(n) = 4*d(n) - 7*r(n). Factor i(g).
g*(g - 10)*(g - 1)*(g + 1)
Let i(q) be the second derivative of q**7/42 - q**6/10 + 3*q**5/20 - q**4/12 - 29*q - 2. Factor i(m).
m**2*(m - 1)**3
Find m, given that 72*m - 358/5 - 2/5*m**2 = 0.
1, 179
Let p(o) be the third derivative of -7*o**7/60 + 21*o**6/80 - o**5/8 + o**4/48 + 2*o**2 - 130. Find h such that p(h) = 0.
0, 1/7, 1
Factor -13*n**3 - 18*n**3 - 137*n**5 + 11*n**3 - 16*n**3 - 40*n**4 + 133*n**5.
-4*n**3*(n + 1)*(n + 9)
Let g(q) be the third derivative of -q**5/30 + 2*q**4/3 - 16*q**3/3 - 2*q**2 - 56*q. Factor g(t).
-2*(t - 4)**2
Suppose 4*r - 7*v = -26, 4*r - 28 = 190*v - 192*v. Factor 4/3*i + 0*i**2 - 4/3*i**3 + 2/3 - 2/3*i**r.
-2*(i - 1)*(i + 1)**3/3
Let n = -794/21 - -274/7. Let k(y) be the first derivative of -y**2 + n*y + 2/9*y**3 - 3. Factor k(h).
2*(h - 2)*(h - 1)/3
Let q(d) be the second derivative of -d**7/21 + 7*d**6/15 - 7*d**5/10 - 23*d**4/6 + 44*d**3/3 - 20*d**2 - d - 153. Let q(z) = 0. Calculate z.
-2, 1, 2, 5
Suppose 2*p = -2*h - 0*h + 2, -2*h = 3*p + 1. Factor 6*b - 4 + 3*b**4 - 6*b**3 - b**h + 2*b**2 + 0*b**3.
2*(b - 2)*(b - 1)**2*(b + 1)
Let u(x) be the first derivative of x**2 - 31. Let r be u(0). Let r - 2/5*p**2 + 4/5*p**3 + 0*p - 2/5*p**4 = 0. Calculate p.
0, 1
Let h(m) be the second derivative of -m**5/10 - 5*m**4/6 + 2*m**3/3 + 24*m**2 + 142*m - 2. Solve h(y) = 0 for y.
-4, -3, 2
Let u be (249/15 + -17)/(4/(-5)). Let o(l) = l**3 - 5*l**2 - 5*l - 4. Let x be o(6). Factor -1/2*i**x - i - u.
-(i + 1)**2/2
Let x(v) be the second derivative of v**6/10 - 7*v**5/20 - 37*v**4/12 - 17*v**3/6 + 5*v**2 + v + 26. Find c, given that x(c) = 0.
-2, -1, 1/3, 5
Find i, given that -8*i - 25*i + 9*i + 2*i**4 - 4*i**2 + 6*i**3 - 16 = 0.
-2, -1, 2
Suppose 48/5*q + 44/5*q**2 + 18/5 + 2/5*q**4 + 16/5*q**3 = 0. Calculate q.
-3, -1
Solve 20 + 18 + 20*p - 22 + 4*p**2 = 0 for p.
-4, -1
Let g(o) be the first derivative of -2/3*o**2 - 1 - 2/27*o**3 + 0*o. Let g(t) = 0. What is t?
-6, 0
Let w(l) be the third derivative of l**7/630 - l**6/180 - 4*l**5/45 + l**4/36 + 5*l**3/6 + 302*l**2 - 1. Suppose w(y) = 0. What is y?
-3, -1, 1, 5
Let l = -18 - -16. Let u(x) = 19*x**4 + 91*x**3 + 51*x**2 + 11*x. Let m(d) = 4*d**4 + 18*d**3 + 10*d**2 + 2*d. Let z(j) = l*u(j) + 11*m(j). Factor z(r).
2*r**2*(r + 2)*(3*r + 2)
Let k(t) be the second derivative of -t**7/840 - t**6/72 - t**5/15 - t**4/6 - 11*t**3/2 - 8*t + 2. Let s(g) be the second derivative of k(g). Factor s(x).
-(x + 1)*(x + 2)**2
Let d(p) be the first derivative of -1/3*p**4 - 8/27*p**3 + 0*p - 2 - 1/54*p**6 + 0*p**2 - 2/15*p**5. Solve d(k) = 0 for k.
-2, 0
Let w(j) be the third derivative of -36*j**2 - 1/33*j**4 - 1/231*j**7 + 1/165*j**6 + 0*j + 1/55*j**5 - 1/33*j**3 + 0. Find m such that w(m) = 0.
-1, -1/5, 1
Let k(w) be the first derivative of 2*w**5/5 + 2*w**4 + 4*w**3/3 - 4*w**2 - 6*w - 155. Factor k(p).
2*(p - 1)*(p + 1)**2*(p + 3)
Let c = 8/1491 - -7439/2982. Factor -1/2*x**2 + c*x - 2.
-(x - 4)*(x - 1)/2
Let f = 60 - 54. Suppose -q + 3*q**3 + f*q - 13 - 8*q**3 + 5*q**2 + 8 = 0. What is q?
-1, 1
Let l = -1471 - -1476. Let o(c) be the first derivative of 1/4*c**2 + 9 + 0*c**4 - 1/3*c**3 - 1/12*c**6 + 1/5*c**l + 0*c. Factor o(b).
-b*(b - 1)**3*(b + 1)/2
Factor -8/13*x**2 + 12/13 - 2/13*x - 2/13*x**3.
-2*(x - 1)*(x + 2)*(x + 3)/13
Let s be (-66)/(-198)*((-6)/4)/(-1). Let j(u) be the second derivative of -2*u + 0 - 1/12*u**4 - s*u**2 - 1/3*u**3. Factor j(i).
-(i + 1)**2
Suppose 8*h - 24/7 + 14*h**2 - 2*h**4 + 4/7*h**3 = 0. What is h?
-2, -1, 2/7, 3
Suppose -4*n = -n + y - 22, -4*n - 5*y = -44. Let h be (20/8)/(3/n). Factor 3 + 42*t**2 - 41*t**2 - t - h.
(t - 2)*(t + 1)
Let z = 34976 + -209855/6. Factor -z*i**3 - i**2 + 0 - 3/2*i.
-i*(i + 3)**2/6
Let y(o) be the third derivative of -o**9/1512 + o**7/140 + o**6/90 - 7*o**3 + 18*o**2. Let s(f) be the first derivative of y(f). Factor s(i).
-2*i**2*(i - 2)*(i + 1)**2
Let b be 1*(-2)/(-4)*4. Let g be b*3/(25 - -2). Factor 2/9*r**5 + 0 - 4/9*r**2 + 4/9*r**4 - g*r + 0*r**3.
2*r*(r - 1)*(r + 1)**3/9
Let v(h) be the third derivative of h**6/30 - h**5/15 - h**4/6 + 2*h**3/3 + 33*h**2. Let v(u) = 0. What is u?
-1, 1
Let f(d) = -d**5 + d**4 + d**3 + d - 1. Let o(b) = -6*b**5 - 5*b**4 - 12*b**3 - 14*b**2 - 2*b - 5. Let r(k) = -12*f(k) + 3*o(k). Factor r(v).
-3*(v + 1)**4*(2*v + 1)
Let m = 43 - 41. Factor 5*s**3 + 0 + 0*s**3 - 4*s**m - 12*s**2 - 2 + 13*s.
(s - 2)*(s - 1)*(5*s - 1)
Let l = 45138 - 45136. Factor 1/2*s**3 + 1/2*s**l + 1/6*s**4 + 0 + 1/6*s