
-7, -2, -1
Determine k, given that -25*k**5 + 69*k**4 - 17*k**3 - 134*k**4 + 5*k**2 - 28*k**3 + 10*k = 0.
-1, 0, 2/5
Let s(l) be the second derivative of -2/15*l**3 + 4/5*l**2 + 13*l + 1/25*l**5 - 2/15*l**4 + 0. Factor s(n).
4*(n - 2)*(n - 1)*(n + 1)/5
Let j(c) be the first derivative of 4 - 2*c + 1/6*c**4 + 1/3*c**3 - 2*c**2. Let s(w) be the first derivative of j(w). Determine z so that s(z) = 0.
-2, 1
Let v be ((-4)/(-10))/((-6)/150). Let t = v - -15. Factor -7 - u**t + 3*u**4 - u - 2*u**3 + 4*u + 6 - 2*u**2.
-(u - 1)**4*(u + 1)
Let t(j) be the third derivative of j**6/240 + j**5/32 + j**4/24 - j**3/16 - 2*j**2 - 48*j. Factor t(l).
(l + 1)*(l + 3)*(4*l - 1)/8
Suppose 3*d + 5 = -2*p, 4*d + 13 - 3 = -p. Factor 1/3*l**p - 2/3*l + 0.
l*(l - 2)/3
Let l = 9/262 - -1633/131. Let w(b) be the first derivative of 10*b**3 - 7*b**5 + 5/2*b**4 + 6 - l*b**2 + 5*b + 5/2*b**6. Factor w(f).
5*(f - 1)**3*(f + 1)*(3*f - 1)
Let r(p) be the third derivative of -3/40*p**5 + 1/80*p**6 + 1/140*p**7 - 10*p**2 - 5/16*p**4 + 0*p + 0 - 1/2*p**3. Factor r(z).
3*(z - 2)*(z + 1)**3/2
Suppose -3/2*q - q**2 + 0 + 2*q**3 + q**4 - 1/2*q**5 = 0. What is q?
-1, 0, 1, 3
Let k(i) be the first derivative of -i**3/6 + 3*i**2/2 + 8*i + 51. Factor k(m).
-(m - 8)*(m + 2)/2
Let h(w) = w**3 - 7*w**2 - 2*w + 11. Let t be h(7). Let c be 0*t*(-4)/(-24). Find l, given that 9/4*l**2 + c + 3/4*l + 9/4*l**3 + 3/4*l**4 = 0.
-1, 0
Let c(i) be the first derivative of -i**5/5 + 5*i**4/3 - 16*i**3/3 + 8*i**2 - 5*i - 9. Let y(v) be the first derivative of c(v). Factor y(a).
-4*(a - 2)**2*(a - 1)
Let z(q) be the second derivative of -q**9/3780 - q**8/840 + q**7/630 + q**6/90 - q**4/4 - 4*q. Let b(y) be the third derivative of z(y). What is a in b(a) = 0?
-2, -1, 0, 1
Let z = 553 + -553. Let r(v) be the first derivative of z*v + 3 - 2/21*v**3 + 1/14*v**4 - 2/7*v**2. Factor r(w).
2*w*(w - 2)*(w + 1)/7
Suppose -5*s + 23 - 6 = -3. Determine t, given that s*t**3 - 16*t - 16/3 + 4/3*t**2 = 0.
-2, -1/3, 2
Let b = -23/133 - -491/532. Factor 1 - 3/4*o**4 - 17/4*o**3 - 13/4*o**2 + 1/2*o**5 + b*o.
(o - 4)*(o + 1)**3*(2*o - 1)/4
Let n(d) be the third derivative of 0*d + 1/270*d**5 + 0 + 1/108*d**4 - 1/540*d**6 - 1/945*d**7 + 9*d**2 + 0*d**3. Factor n(l).
-2*l*(l - 1)*(l + 1)**2/9
Let h(c) be the first derivative of c**5/20 - c**3/4 + c**2/4 - 252. Determine w, given that h(w) = 0.
-2, 0, 1
Let h be (-27)/(-15) - 1/(-5). Let b be ((-5)/(-10)*0)/h. Factor 1/3*a - 2/3*a**2 + 1/3*a**3 + b.
a*(a - 1)**2/3
Let i be -4 + 3 + -4 + 11. Let y be (i/(-66))/(3/(-6)). Factor -y*v**2 - 8/11*v - 8/11.
-2*(v + 2)**2/11
Suppose -5*m + 0 = -20. Let y(q) = 20*q**2 + 54*q + 92. Let f(r) = 7*r**2 + 18*r + 31. Let k(z) = m*y(z) - 11*f(z). Factor k(x).
3*(x + 3)**2
Solve 41/4*h + 1/4*h**3 - 11/2*h**2 - 5 = 0 for h.
1, 20
Let q(s) be the first derivative of -s**6/15 - 6*s**5/5 - 23*s**4/3 - 20*s**3 - 25*s**2 - 15*s + 19. Let b(t) be the first derivative of q(t). Factor b(i).
-2*(i + 1)**2*(i + 5)**2
Let k = -34108/45 - -3792/5. Factor -28/9*n + 20/3*n**2 + 16/9*n**4 + k - 52/9*n**3.
4*(n - 1)**3*(4*n - 1)/9
Find r such that -69/2*r**4 + 93/2*r**2 + 33*r + 21/2*r**5 - 87/2*r**3 - 12 = 0.
-1, 2/7, 1, 4
Let f = 8 - -136. Factor -8*n**2 - 3*n**4 + 240*n + 40*n**3 - f - n**4 - 140*n**2.
-4*(n - 3)**2*(n - 2)**2
Let j(f) = -11*f**2 - 10*f - 5. Let h be 12 + -13 - 14/(-2). Let u(x) = -100*x**2 - 90*x - 45. Let m(c) = h*u(c) - 55*j(c). Factor m(b).
5*(b + 1)**2
Suppose 33 + 22 = 11*g. Solve 3 + 17 + 51*k + g*k**2 - 71*k = 0 for k.
2
Let k(u) be the second derivative of u**8/6720 - u**6/720 - 25*u**4/6 + 21*u. Let a(w) be the third derivative of k(w). Determine f, given that a(f) = 0.
-1, 0, 1
Suppose 0 = -v + 2*p + 9, 0 = 40*p - 35*p + 15. Let k(h) be the third derivative of 0*h + 0*h**4 + 0 + 4*h**2 + 1/12*h**5 - 5/6*h**v. Factor k(u).
5*(u - 1)*(u + 1)
Let x(n) be the third derivative of -n**5/180 + 47*n**4/72 + 350*n**2. Factor x(k).
-k*(k - 47)/3
Let o = -1 + -15. Let v be (2*(-4)/o)/(-2 - -4). Factor a - 1 - v*a**2.
-(a - 2)**2/4
Solve 39*g**3 + 50*g**3 + 8 + 37*g**2 - 38*g - 96*g**3 = 0.
2/7, 1, 4
Let n = 69248/3 - 23082. Determine d so that n*d**3 - 2/3*d**2 - 14/9*d + 4/3 + 2/9*d**4 = 0.
-3, -2, 1
Let n be -1 + 2 - (-50 + 11). Let k = 43 - n. Find g such that -8*g**2 + 2*g - 8*g**2 + 3 - 5*g**2 - 12*g**k - 8*g = 0.
-1, 1/4
Solve 25/3 - 25/6*d**2 + 115/6*d = 0 for d.
-2/5, 5
Suppose -36 - 18*n - 14*n - 3*n**2 + 5*n - 10*n + 16*n = 0. What is n?
-4, -3
Let i be 6*(-8)/(-36)*6/4. Let h(z) = -2*z - 5. Let v be h(-5). Factor 2*d**2 + 15*d + 1 + v*d**i + 8 + d**3.
(d + 1)*(d + 3)**2
Let c(p) be the second derivative of p**7/42 - 3*p**6/10 + 13*p**5/20 + 3*p**4/4 - 7*p**3/3 + 303*p. Find a, given that c(a) = 0.
-1, 0, 1, 2, 7
Solve -56*j + 44*j + 9 - 4 + 4 + 3*j**2 = 0 for j.
1, 3
Let z(s) = 15*s**3 - 595*s**2 + 1345*s - 800. Let q(l) = -l**3 + 35*l**2 - 79*l + 47. Let i(m) = -35*q(m) - 2*z(m). Let i(p) = 0. What is p?
1, 3
Let c be (-6)/6 + (-52)/(-12) + -3. Let z(v) be the third derivative of 1/24*v**4 + 0 + 1/60*v**5 + 0*v - c*v**3 - 2*v**2. Factor z(o).
(o - 1)*(o + 2)
Let i(j) = -3*j - 2. Let a be i(-2). Factor 9*b**3 + b**4 - 5*b + 6*b**3 + 9*b**a.
5*b*(b + 1)**2*(2*b - 1)
Let m(c) be the second derivative of c**4/16 - 21*c**3/4 + 123*c**2/8 - 3*c - 9. Find d such that m(d) = 0.
1, 41
Let q(b) be the second derivative of 13*b**4/54 - 28*b**3/27 + 4*b**2/9 + 2*b - 26. Factor q(k).
2*(k - 2)*(13*k - 2)/9
Let t = 991/2472 + -8/309. Factor 9/8*z**3 + 15/8*z**4 + 0 + 3/4*z**5 - t*z - 3/8*z**2.
3*z*(z + 1)**3*(2*z - 1)/8
Let q(h) be the first derivative of -h**6/18 - 7*h**5/5 - 33*h**4/4 + 121*h**3/9 - 208. Factor q(p).
-p**2*(p - 1)*(p + 11)**2/3
Let c be 0*(-2 - 30/(-12)). Let a(h) be the third derivative of c + h**2 - 1/27*h**3 + 0*h**6 - 1/945*h**7 + 0*h**4 + 1/135*h**5 + 0*h. Factor a(i).
-2*(i - 1)**2*(i + 1)**2/9
Let i = 4494/983 - 2/6881. Solve -40/7*b - 24/7*b**2 - 10/7*b**4 + 38/7*b**3 + i = 0.
-1, 4/5, 2
Let o(u) be the first derivative of -3*u**5/35 + 3*u**4/28 + 3*u**3/7 - 15*u**2/14 + 6*u/7 + 98. Factor o(r).
-3*(r - 1)**3*(r + 2)/7
Let i(h) be the first derivative of 147*h**5/5 + 315*h**4 + 571*h**3 + 342*h**2 + 84*h - 146. Factor i(k).
3*(k + 1)*(k + 7)*(7*k + 2)**2
Let a = -3621 - -18106/5. What is p in a*p**2 + 2/5*p - 3/5 = 0?
-3, 1
Let m be (-1)/4 + (1 - 105/(-20)). Let c be (5 - 21/m) + (-3)/(-6). Let -5/8*t - 1/8*t**c + 1/8*t**3 - 3/8 = 0. Calculate t.
-1, 3
Let l(c) be the first derivative of c**5 + 85*c**4/4 + 155*c**3 + 875*c**2/2 + 490*c - 418. Factor l(n).
5*(n + 1)*(n + 2)*(n + 7)**2
Let g(y) = y**2 + 7*y + 2. Suppose -2*s + 8 = -2*z, 0 = -0*s - 5*s - 5*z + 30. Let l(w) = -s + 4 + 2 - 3 - 6*w. Let q(h) = 4*g(h) + 5*l(h). Factor q(o).
2*(o - 1)*(2*o + 1)
Let c(u) = 4*u**2 - u. Let t(y) = -23*y**2 - 13*y + 18. Let k(n) = 6*c(n) + t(n). Solve k(v) = 0.
1, 18
Let b(g) = g**2 - 32*g - 140. Let i be b(-4). Let n(f) be the first derivative of -f**2 - 1/12*f**3 - 2 - i*f. Factor n(k).
-(k + 4)**2/4
Let z(y) be the first derivative of y**6/12 + y**5/10 - y**4/4 - y**3/3 + y**2/4 + y/2 - 38. Factor z(u).
(u - 1)**2*(u + 1)**3/2
Let z = 59 + -56. Factor 35*y**2 - 75*y + 45 - 11*y**3 - 4*y**z - 8*y**3 + 18*y**3.
-5*(y - 3)**2*(y - 1)
Let o be 23/(322/(-84)) - (-9 - -1). Let j(f) be the second derivative of 0*f**3 - 3*f + 0 + 1/4*f**4 - 3/2*f**o. Determine x, given that j(x) = 0.
-1, 1
Let r(v) be the first derivative of -v**2 + 1/42*v**4 - 1/7*v**3 - 2 + 1/210*v**5 + 0*v. Let a(u) be the second derivative of r(u). Solve a(z) = 0 for z.
-3, 1
Let n = -6 - -9. Factor -4*b**n + 87*b**2 - b**3 - 77*b**2.
-5*b**2*(b - 2)
Suppose -42 = 491*r - 505*r. Suppose -r + 3/8*m**4 - 9/8*m**3 - 3/4*m**2 + 9/2*m = 0. What is m?
-2, 1, 2
Let m = -12 + 14. Suppose 0 = 2*y + m*f - 12, -2*y = 3*f - 4 - 6. Suppose -8*h - h**2 - 3*h**4 - 11*h**2 + h**4 - y*h**3 - 2 + 0*h**2 = 0. What is h?
-1
Factor 36*a**3 - 4*a**4 - 7*a**2 - 73*a**2 + 5*a**3 - 41*a - 9*a - 3*a**3.
-2*a*(a - 5)**2*(2*a + 1)
Let q(a) be the third derivative of -a**7/42 + a**5/3 - 32*a**2 + 1. Determine l so that q(l) = 0.
-2, 0, 2
Let c(i) be the second derivative of -i**7/126 + 7*i**6/90 - 19*i**5/60 + 25*i**4/36 - 8*i**3/9 + 2*i**2/3 - 36*i - 2. Find l, given that c(l) = 0.
