 be the second derivative of -n**4/12 - 413*n**3/24 - 103*n**2/8 - 125*n + 1. Factor r(f).
-(f + 103)*(4*f + 1)/4
Let f(u) be the third derivative of u**6/150 + 2*u**5/75 - u**4/6 - 4*u**3/5 + u**2 + 247. Factor f(h).
4*(h - 2)*(h + 1)*(h + 3)/5
Let o(x) be the second derivative of -1/6*x**4 + 0 - 5*x**2 - 2*x**3 + 20*x. Find t such that o(t) = 0.
-5, -1
Solve -32*r**2 + 131*r - 131*r - 30*r**3 + 10*r**4 - 8*r**4 = 0 for r.
-1, 0, 16
Let y(q) be the third derivative of q**7/2100 + q**6/300 + q**5/600 - q**4/40 - 75*q**2. Determine u so that y(u) = 0.
-3, -2, 0, 1
Solve 6 + 24*i**2 + 141/7*i - 3/7*i**5 + 78/7*i**3 + 6/7*i**4 = 0.
-2, -1, 7
Let d(h) = -3*h**2 + 76*h + 52. Let l be d(26). Factor 0*r**2 + 0 - 1/5*r**4 - 2/5*r**3 + l*r.
-r**3*(r + 2)/5
Let u = 83 + -78. Let o(c) be the first derivative of 0*c + 7 + 1/8*c**4 - 1/12*c**6 + 1/6*c**3 + 0*c**2 - 1/10*c**u. Determine r so that o(r) = 0.
-1, 0, 1
Let c = -4702 - -4704. Factor 0*p**c + 1/11*p + 0 - 1/11*p**3.
-p*(p - 1)*(p + 1)/11
Let w(y) = -2*y - 10. Let u be w(-7). Let j be 0/1*u/8. Factor j*v - 1 + 4*v - 4*v**3 - 2*v**4 + 1 + 2*v**2.
-2*v*(v - 1)*(v + 1)*(v + 2)
Let q(j) be the second derivative of -1/3*j**4 + 6*j + 4 + 2*j**3 - 4*j**2. Let q(g) = 0. Calculate g.
1, 2
Let d = 112 - 127. Let n be (-19 - d)*(1 + 18/(-8)). Find a such that 0*a - 42/5*a**4 - 8/5*a**2 - 98/5*a**n + 0 + 48/5*a**3 = 0.
-1, 0, 2/7
Let o be ((-45)/21)/((-138)/(-805))*(-8)/30. Determine b, given that 0*b**2 + 0 + 0*b + 2/3*b**5 + 0*b**3 + o*b**4 = 0.
-5, 0
Let f = 9 - 7. Find n, given that -607 + 9*n + 607 + 6*n**f - 3*n**3 = 0.
-1, 0, 3
Let h(t) be the first derivative of -t**3/7 - 51*t**2/7 - 867*t/7 + 130. Let h(l) = 0. Calculate l.
-17
Suppose -68 + 2*w - 3*w**2 - 2*w - 48*w - 97 = 0. Calculate w.
-11, -5
Let d = 129 - 65. Let g be (d/(-90))/(-4) + 18/81. Find h, given that 2/5*h - 2/5*h**2 + g - 2/5*h**3 = 0.
-1, 1
Factor -2/3*h**2 + 2/9*h**3 + 0 - 8/9*h.
2*h*(h - 4)*(h + 1)/9
Factor 38/3*j - 13 + 1/3*j**2.
(j - 1)*(j + 39)/3
Let s(n) = -n**2 + 2*n - 1. Let g be s(3). Let a = 8 + g. Determine z so that 0*z**3 + 8*z**3 + z**a - 2*z**2 - 8*z**3 + 1 = 0.
-1, 1
Let p(v) be the second derivative of -1/27*v**3 + 45*v - 1/135*v**6 + 0 - 1/18*v**4 - 1/30*v**5 + 0*v**2. Let p(w) = 0. What is w?
-1, 0
Let m(k) = 8*k**3 + 20*k**2 - 63*k - 6. Let r(b) = 9*b**3 + 20*b**2 - 64*b - 8. Let w(d) = 4*m(d) - 3*r(d). Determine o so that w(o) = 0.
-6, 0, 2
Suppose -5*x - 13 - 7 = 2*k, 2*x = -k - 9. Let h be (x + 7)*2*(-1)/(-15). Factor 2/3*p**4 + h*p - 2/9 - 4/9*p**2 - 2/9*p**5 - 4/9*p**3.
-2*(p - 1)**4*(p + 1)/9
Solve 12*s - 144 + 1/4*s**3 + 5*s**2 = 0 for s.
-12, 4
Let r(n) = 9*n - 32. Let c be r(4). Let p(m) be the first derivative of 1/4*m**c - 2 + 0*m**2 + 0*m + 0*m**3 + 0*m**5 - 1/6*m**6. Suppose p(i) = 0. What is i?
-1, 0, 1
Let c(b) be the second derivative of 4*b + 0 - 9*b**2 - 1/24*b**4 + b**3. Let c(d) = 0. What is d?
6
Let m be ((-80)/210)/(72/(-126)). Factor 1/3*x**3 + m*x**2 + 0*x + 0.
x**2*(x + 2)/3
Let x(b) be the first derivative of b**6/2 + 3*b**5/5 - 9*b**4/2 - 4*b**3 + 12*b**2 + 2. What is n in x(n) = 0?
-2, 0, 1, 2
Determine z, given that 0*z**3 + 8/3 + 2/3*z**4 - 10/3*z**2 + 0*z = 0.
-2, -1, 1, 2
Let y(i) = i**2 - i. Let m be y(2). Suppose -20*x + 10*x = -40. Factor -x*c**m + 2*c - c + 11*c.
-4*c*(c - 3)
Determine r so that -21*r**4 - 33*r**5 - 6*r**3 + 9*r**5 + 9*r**5 = 0.
-1, -2/5, 0
Let d(i) be the first derivative of 19 - 6/25*i**5 + 0*i**2 + 0*i - 1/5*i**4 + 0*i**3 - 1/15*i**6. Let d(z) = 0. Calculate z.
-2, -1, 0
Suppose 2/7*k**2 + 0 - 32/7*k = 0. Calculate k.
0, 16
Factor 2*s**3 + 2*s**3 + s**4 + 2*s**2 - 166*s - 172*s - 3 + 334*s.
(s - 1)*(s + 1)**2*(s + 3)
Let b = 2394/265 + -182/53. Determine t so that 32/5*t - b - 4/5*t**2 = 0.
1, 7
Let v(x) = 12*x**2 - 240*x + 472. Let s(w) = -w**2 - w + 1. Let d(p) = -8*s(p) - v(p). Let d(c) = 0. Calculate c.
2, 60
Let h(x) = 2*x**3 - 82*x**2 + 163*x - 271. Let b be h(39). Factor -4/3 - 1/3*s**b + 4/3*s.
-(s - 2)**2/3
Let p = 7 + 0. Let w = 10 - p. Factor -1 + 3*u**4 - u**4 + 4*u + 0*u**4 - w*u**4 - 6*u**2 + 4*u**3.
-(u - 1)**4
Let r(u) be the first derivative of u**4/10 - 2*u**3/3 - 8*u**2/5 + 24*u/5 + 107. Factor r(n).
2*(n - 6)*(n - 1)*(n + 2)/5
Let r(p) be the first derivative of p**5/12 + 5*p**4/24 - 5*p**3 + 13*p**2/2 - 37. Let l(v) be the second derivative of r(v). Suppose l(q) = 0. Calculate q.
-3, 2
Let h(l) = 3*l**2 + 154*l - 116. Let y(m) = 2*m**2 + 103*m - 77. Let q(b) = 5*h(b) - 7*y(b). Let d(a) = -12*a + 10. Let u(x) = -9*d(x) - 2*q(x). Factor u(t).
-2*(t - 4)*(t - 1)
Let x(f) be the first derivative of -f**6/36 - f**5/5 - 13*f**4/24 - 2*f**3/3 - f**2/3 - 29. Factor x(n).
-n*(n + 1)**2*(n + 2)**2/6
Let j(p) = 246*p + 1722. Let x be j(-7). Factor 4/17*o**2 - 2/17*o - 2/17*o**3 + x.
-2*o*(o - 1)**2/17
Let k(u) be the second derivative of -1/84*u**4 + 3/14*u**2 + 1/21*u**3 + 3*u + 0. Factor k(x).
-(x - 3)*(x + 1)/7
Let r = -3 - -6. Factor -3*k**r - 2*k**3 + 3*k**3 - 3*k**3.
-5*k**3
Let c be ((-36)/(-16))/(3/20). Factor 35*m**2 + c*m**4 - 25*m**3 + 13*m**3 - 43*m**3 - 5*m**2.
5*m**2*(m - 3)*(3*m - 2)
Let n(g) be the third derivative of g**5/105 - 3*g**4/14 + 16*g**3/21 + g**2 - 58. Suppose n(c) = 0. What is c?
1, 8
Let p(c) be the third derivative of c**8/140 - c**7/56 + c**6/120 + 7*c**3/2 - 16*c**2. Let g(z) be the first derivative of p(z). Let g(i) = 0. Calculate i.
0, 1/4, 1
Suppose 182 = 5*g + d + 55, -3*g - 4*d + 83 = 0. Let w = g - 123/5. Find p such that -2/5*p - 2/5*p**4 + 2/5*p**3 + w*p**2 + 0 = 0.
-1, 0, 1
Factor 275*k + 47*k**3 - 65*k + 31*k**3 - 3*k**4 - 69 - 216*k**2.
-3*(k - 23)*(k - 1)**3
What is z in 3*z**5 + 108*z - 210*z**2 + 150*z**3 + 27*z - 371*z**4 - 22 + 326*z**4 - 11 = 0?
1, 11
Factor -122/3*n - 121/3 - 1/3*n**2.
-(n + 1)*(n + 121)/3
Let i(t) = -1406*t + 4218. Let j be i(3). Let c(s) = -2*s. Let k be c(-2). Factor j - 1/3*l**k + 1/3*l**5 + 0*l**2 + 0*l - 2/3*l**3.
l**3*(l - 2)*(l + 1)/3
Let 1621*p**4 + p**3 - 6*p**2 - 6*p**3 - 1622*p**4 = 0. What is p?
-3, -2, 0
Let t(h) be the second derivative of -h**4/72 - 19*h**3/9 - 37*h**2/3 - 4*h - 6. Find s such that t(s) = 0.
-74, -2
Factor -n + n**3 + 1/3*n**2 - 2/3 + 1/3*n**4.
(n - 1)*(n + 1)**2*(n + 2)/3
Let h(i) be the first derivative of 0*i**2 - 3/5*i**5 + 0*i - 1/3*i**3 + i**4 + 23. Factor h(b).
-b**2*(b - 1)*(3*b - 1)
Let o(a) be the first derivative of -5/3*a**3 - 5*a**2 + 6 - 5*a. Find p, given that o(p) = 0.
-1
Let b(o) be the third derivative of o**5/510 + 47*o**4/102 + 2209*o**3/51 + o**2 + 25. Factor b(v).
2*(v + 47)**2/17
Factor 0*d + 9/4*d**4 + 0 + 0*d**2 - 1/2*d**3.
d**3*(9*d - 2)/4
Suppose -3*p - 19 = -4*h, 0*h = h - 3*p - 7. Suppose -h*j - 8 = -2*c, 0*c - 2*j = 5*c - 44. Suppose -2*z - 4*z + c*z + 2*z**2 = 0. Calculate z.
-1, 0
Suppose u - 3*u = -4*s + 6, -32 = -3*s - 4*u. Solve -h**4 - 5 + s*h + 12*h**3 - 6*h**3 - 10*h**3 + 9 - 3*h**2 = 0.
-2, -1, 1
Let k(s) be the first derivative of -1/360*s**6 + 0*s**2 - 1/120*s**5 + 0*s**4 + 9 + 0*s + 3*s**3. Let a(g) be the third derivative of k(g). Factor a(v).
-v*(v + 1)
Suppose 4*r = -2 - 2. Let w be -2 + -1 + (5 - r). Factor 4*y - w*y - y**2 + 2*y**2 + 2*y**2.
y*(3*y + 1)
Let v(d) be the second derivative of 0*d**3 + 10*d + 0 - 5/6*d**4 + 3/4*d**5 + 0*d**2 - 1/6*d**6. Factor v(p).
-5*p**2*(p - 2)*(p - 1)
Suppose -3*d = -5*d + 10. Let s(r) = r - 1. Let v be s(d). Solve o**4 + o**4 - o**v = 0 for o.
0
Let w(f) = f**2 + 4*f - 11. Let r be w(6). Let h = r + -33. Factor -h*s**3 + 36*s + 36*s - 72*s - 12*s**2 - 4*s**4.
-4*s**2*(s + 1)*(s + 3)
Let r(t) be the first derivative of -4*t**3/3 + 18*t**2 - 56*t - 79. Factor r(g).
-4*(g - 7)*(g - 2)
Let t = -75 - -79. Find d, given that 0 + 0*d + 9/2*d**3 - 3*d**t - 3/2*d**2 = 0.
0, 1/2, 1
Let a(w) be the second derivative of w**4/21 - 32*w**3/21 + 86*w. Factor a(j).
4*j*(j - 16)/7
Suppose 2*v + 239 = 5*w + 236, 2*w = 5*v - 24. Factor 0 + 3/5*z - 3/5*z**w + 8/5*z**2.
-z*(z - 3)*(3*z + 1)/5
Let h be (-12)/(-20) - 1 - 132/(-80). Let a(l) = l**2 - 2*l - 1. Let q be a(-1). Find r, given that 0 - 9/4*r**3 - h*r**q + 5/4*r**4 + 1/2*r + 7/4*r**5 = 0.
-1, 0, 2/7, 1
Let u = 1332 - 3964/3. Let b(z) be the third derivative of u*z**4 + 0 - 128/3*z**3 + 2/15*z**6 + 0*z - 1/210*z**7 - 8/5*z**5 