 21)/3
Let x = -37 + 261/7. Let j be (-10)/5 + 16/7. Let x*k + 0 - j*k**2 = 0. What is k?
0, 1
Let m(x) be the third derivative of -x**8/40320 + x**7/1680 - x**6/180 + 7*x**5/20 - 28*x**2. Let r(a) be the third derivative of m(a). Factor r(f).
-(f - 4)*(f - 2)/2
Let w(k) be the second derivative of 3/10*k**2 + 12*k - 1/30*k**6 + 0 + 1/30*k**4 + 3/50*k**5 + 1/210*k**7 - 7/30*k**3. Factor w(z).
(z - 3)*(z - 1)**3*(z + 1)/5
Let p = -12 - -14. Factor -p*m**4 + 5*m + 0*m**2 - 6*m**2 - 8*m**3 - 5*m.
-2*m**2*(m + 1)*(m + 3)
Let i(a) be the first derivative of 10 + 2*a**3 - 8*a + 0*a**2 + 1/2*a**4. Find q such that i(q) = 0.
-2, 1
Suppose 3*b - o - 10 = -5*o, 0 = -3*b + 4*o + 2. Find i, given that 39*i - 3*i**2 + 174 - 180 + 45*i**3 - 75*i**b = 0.
1/3, 2/5, 1
Let t(w) be the second derivative of w**5/100 + 2*w**4/15 + 13*w**3/30 + 3*w**2/5 + 64*w + 3. Solve t(n) = 0.
-6, -1
Let o(a) be the third derivative of -a**6/120 + 11*a**5/60 - 19*a**4/12 + 20*a**3/3 - 180*a**2. Factor o(z).
-(z - 5)*(z - 4)*(z - 2)
Let z be (78/(-260))/(2 + (364/20)/(-7)). Find x such that 4 - 3*x + z*x**2 = 0.
2, 4
Let u = -36 + 36. Let r(f) be the third derivative of 0 + u*f + 1/75*f**5 - 1/60*f**4 - 1/300*f**6 + 0*f**3 - 5*f**2. What is d in r(d) = 0?
0, 1
Let a(r) = 7*r**3 + 2*r**2 - 7*r + 4. Let n(g) = -19*g**3 - 5*g**2 + 20*g - 12. Let b(h) = -8*a(h) - 3*n(h). Let b(d) = 0. Calculate d.
-2, 1, 2
Let o = 13 - 26. Let g = o + 16. Solve k**3 - 2*k**2 - 4*k**3 + 5*k**g - 2*k + 2 = 0.
-1, 1
Let z be 6/(-20)*25/(-10)*24/15. Factor 6/5 - 18/5*q**3 - z*q**2 + 18/5*q.
-6*(q - 1)*(q + 1)*(3*q + 1)/5
Let r(b) be the first derivative of b**7/105 - b**5/15 + b**3/3 + 21*b**2/2 - 22. Let w(f) be the second derivative of r(f). Let w(h) = 0. What is h?
-1, 1
Suppose -50 = -5*o + 5*c, 3*o + 2*c = -o + 34. Factor -14*f**3 + 16*f**2 + 2*f**5 - 3*f**5 + 9*f**4 - 3*f**4 + 1 + 1 - o*f.
-(f - 2)*(f - 1)**4
Factor -12*k - 6*k - 30*k**3 + 20*k**2 + 64*k**3 - 36*k**3.
-2*k*(k - 9)*(k - 1)
Let 1/5*o**5 - 4/5*o**3 + 3/5*o + 0 + 2/5*o**2 - 2/5*o**4 = 0. What is o?
-1, 0, 1, 3
Let s be ((-6)/(-10))/(5 - 24/5). Factor 8*i**2 + 8*i + 2*i**s - i**2 + 5*i**2 - 4*i**2.
2*i*(i + 2)**2
Let a = -21 - -26. Factor 6 - a*x - 20*x + 9 + 5*x**2 + 5.
5*(x - 4)*(x - 1)
Suppose 39 = 4*x + 19. Let u(r) = -4*r**2 + r. Let i(q) = -q**2. Let f(t) = x*i(t) - u(t). Find h, given that f(h) = 0.
-1, 0
Let j(o) be the second derivative of o**6/15 + o**5/2 - o**4 - o - 8. Factor j(i).
2*i**2*(i - 1)*(i + 6)
Let s(o) be the first derivative of o**6/3 - 3*o**4 - 16*o**3/3 - 3*o**2 - 598. Factor s(t).
2*t*(t - 3)*(t + 1)**3
Let m = 42 + -40. Let r be 14*4/(-40) + m. Determine d so that 0 + r*d**2 - 6/5*d + 3/5*d**3 = 0.
-2, 0, 1
Let o(f) be the second derivative of 32/15*f**3 - 1 + 0*f**2 + 8/5*f**4 + 1/25*f**5 - f - 4/25*f**6 + 2/105*f**7. Solve o(w) = 0.
-1, 0, 4
Suppose 7758 = 70*k + 7618. Determine o so that -24/7*o - 48/7 - 3/7*o**k = 0.
-4
Let s(j) be the first derivative of -2*j**6/3 + 37*j**5/5 - 101*j**4/4 + 35*j**3/3 + 141*j**2/2 - 36*j - 94. Find v such that s(v) = 0.
-1, 1/4, 3, 4
Let m = 104 - 106. Let f(c) = c**4 + 6*c**2 + c. Let q(p) = p**3 - p**2. Let s(i) = m*f(i) - 6*q(i). Factor s(v).
-2*v*(v + 1)**3
Let p = -32999/110 - -300. Let q(a) be the third derivative of 1/66*a**4 + 0 + 0*a**3 - 4*a**2 - p*a**5 + 0*a + 1/660*a**6. Determine w, given that q(w) = 0.
0, 1, 2
Let w(m) be the second derivative of m**7/42 - 4*m**6/15 + 13*m**5/20 + 13*m**4/6 - 32*m**3/3 + 16*m**2 - 4*m - 19. Let w(h) = 0. What is h?
-2, 1, 4
Let t = 780/1171 + 2/3513. Let 2/3*x**3 - 2/3*x - 2/3 + t*x**2 = 0. Calculate x.
-1, 1
Solve -2 - 10 + 6*o**3 - 4*o**2 - 6*o**3 + 20*o - 4*o**3 = 0.
-3, 1
Let u(o) be the second derivative of o**6/135 + 113*o**5/90 - 115*o**4/18 + 347*o**3/27 - 116*o**2/9 + 333*o. Factor u(z).
2*(z - 1)**3*(z + 116)/9
Let h(w) = -w**3 + 16*w**2 + 4. Let i be h(16). Factor 3*y + 3*y**2 - i*y**2 + 9*y + 2*y**2 + 36.
(y + 6)**2
Let y = 1187 + -71237/60. Let k = 1/20 - y. Factor 1/3*v**2 + k - 2/3*v.
(v - 1)**2/3
Let d(g) = 23*g**2 - 25*g - 16*g**3 + 1 - 1. Let i(o) = -4*o**3 + 6*o**2 - 6*o. Let w(k) = -2*d(k) + 9*i(k). Find z, given that w(z) = 0.
0, 1
Let d(s) be the third derivative of s**8/5040 + s**7/420 + s**6/90 - 3*s**5/20 - 16*s**2. Let y(k) be the third derivative of d(k). Factor y(u).
4*(u + 1)*(u + 2)
Let u(s) be the second derivative of s**5/60 - s**4/12 + s**3/6 - 22*s**2 + 35*s. Let v(r) be the first derivative of u(r). Factor v(q).
(q - 1)**2
Let k(i) = -5*i**3 - 85*i**2 - 2. Let v(q) = 9*q**3 + 84*q**2 + 3. Let b(w) = -3*k(w) - 2*v(w). Let b(h) = 0. What is h?
0, 29
Let y(q) = -5*q**2 + 16*q + 21. Let w(b) = 230 + 20*b - 70*b**2 + 209*b + 15*b**2 - 54*b. Let u(p) = 4*w(p) - 45*y(p). Determine h, given that u(h) = 0.
-1, 5
Let t(q) be the first derivative of q**4/12 + q**3/9 - 85*q**2/6 + 275*q/3 - 656. Solve t(c) = 0.
-11, 5
Let b = 76 + -70. Solve b*v - 4 - 4 + 19*v**2 - 17*v**2 = 0.
-4, 1
Suppose 0 = 3*r + 5*q - 5, r + 5*q + 3 = -2. Determine f, given that -4*f**3 + f**4 - r*f**2 + 0 + 11*f**2 + 3*f + 1 - 7*f = 0.
1
Let z(x) be the first derivative of -x**8/1512 - x**7/315 - x**6/270 - x**2 - 10. Let m(p) be the second derivative of z(p). Suppose m(k) = 0. Calculate k.
-2, -1, 0
Let y(s) be the first derivative of 170*s**3/3 + 15*s**2/2 + 985. Suppose y(q) = 0. Calculate q.
-3/34, 0
Let c = -524 + 524. Let v(q) be the third derivative of 1/68*q**4 - 1/510*q**5 - 9*q**2 + c*q + 0*q**3 + 0. Factor v(h).
-2*h*(h - 3)/17
Let n(v) be the second derivative of v**7/42 + v**6/6 + 3*v**5/10 + 96*v. Solve n(c) = 0.
-3, -2, 0
Solve 1/5*r**3 + 12/5*r + 0 - 8/5*r**2 = 0.
0, 2, 6
Let j(v) be the first derivative of 0*v + 3/2*v**2 + v**3 - 39. Factor j(a).
3*a*(a + 1)
Let j(h) be the second derivative of -3/20*h**5 + 0*h**2 + 14*h + 0 + 1/4*h**4 - 1/10*h**6 + 1/2*h**3. Factor j(v).
-3*v*(v - 1)*(v + 1)**2
Suppose 0 = -m + 4*r - 12, 4*m - 4*r - 6 = -54. Let s be 8*(-4)/m*(-6)/(-10). Factor -2/5*b**3 - 2*b + 4/5 + s*b**2.
-2*(b - 2)*(b - 1)**2/5
Let h = 1846 + -1842. Solve 0 + 0*n + 2*n**3 + 8/11*n**h - 6/11*n**2 = 0.
-3, 0, 1/4
Let i = -4427/56 + 681/8. Let w = i + -39/7. Factor 0 + 0*u**2 - 1/4*u + w*u**3 + 0*u**4 - 1/4*u**5.
-u*(u - 1)**2*(u + 1)**2/4
Suppose 3*m + 4*v = 20, 4*m + 5*v - 17 - 8 = 0. Let f(q) be the first derivative of m*q + 0*q**3 - q**2 + 1/2*q**4 - 4. Factor f(k).
2*k*(k - 1)*(k + 1)
Let j(q) be the third derivative of q**7/105 + 7*q**6/60 - q**5 + 136*q**2. Factor j(b).
2*b**2*(b - 3)*(b + 10)
Let h(d) be the third derivative of -d**6/30 + 2*d**5/3 + d**4/6 - 20*d**3/3 + 432*d**2 + 2. Factor h(a).
-4*(a - 10)*(a - 1)*(a + 1)
Suppose -32*y + 19*y - 8*y = -84. Suppose -12/7*j + 9*j**3 - 3*j**5 + 24/7*j**2 + 6/7*j**y + 0 = 0. What is j?
-1, 0, 2/7, 2
Let m(b) be the first derivative of 2/63*b**3 + 3 + 0*b - 2/21*b**2. Suppose m(d) = 0. What is d?
0, 2
Let v(r) be the first derivative of 2*r**6/21 - 8*r**5/35 - 12*r**4/7 + 160*r**3/21 - 64*r**2/7 - 33. Factor v(j).
4*j*(j - 2)**3*(j + 4)/7
Let j = 160/319 - 4/29. Factor 0*x**4 - j*x**2 + 2/11*x**5 - 6/11*x**3 + 0 + 0*x.
2*x**2*(x - 2)*(x + 1)**2/11
Let l(o) = -5*o**2 - 58*o + 51. Let i(r) be the first derivative of -5*r**3/3 - 28*r**2 + 52*r + 32. Let q(n) = -4*i(n) + 3*l(n). Suppose q(j) = 0. What is j?
-11, 1
Let a be 4/14 - (-4015)/35. Suppose 3*x + a = 8*x. Find u such that -23 - 3*u**3 + x + 3*u**5 = 0.
-1, 0, 1
Let g = 113/590 + 1/118. Let s be ((-272)/20)/(-4) + (1 + -1 - 3). Factor g*y**2 - 1/5*y**3 + 0 + s*y.
-y*(y - 2)*(y + 1)/5
Suppose 4*n + 34 = -3*g, -2*g - n - 4 = 12. Let j be (1/(-2))/(1/g). Factor -k + 2 + 3*k + 4*k + 2*k**j + 6*k**2.
2*(k + 1)**3
Let f(l) be the first derivative of 2*l**3/3 + 258*l**2 + 33282*l - 505. Factor f(t).
2*(t + 129)**2
Let z(u) be the second derivative of u**6/30 + 11*u**5/20 + 35*u**4/12 + 25*u**3/6 + 3*u + 3. Solve z(m) = 0 for m.
-5, -1, 0
Let j(k) = k**3 + 7*k - 17. Let f be j(2). Suppose 5 = -5*i, -2*q + q = i - 2. Factor f*l**4 + 4*l - 4*l**5 - 10*l**4 - q*l**4 + 8*l**2.
-4*l*(l - 1)*(l + 1)**3
Let b be (-30)/(15/(-3)) - -4. Suppose 5*a - 30 + b = 0. Factor -2/5*u**5 + 0*u + 0*u**a + 2/5*u**3 + 0 + 0*u**2.
-2*u**3*(u - 1)*(u + 1)/5
Let w(h) be the third derivative of -h**8/84 + 2*h**7/21 - 7*h**6/30 -