/3
Let g = 5686/7 - 812. Factor 6/7*c**2 + 0*c + 2/7*c**4 + g*c**5 - 10/7*c**3 + 0.
2*c**2*(c - 1)**2*(c + 3)/7
Factor -5/2*r**2 + 0*r + 1/4*r**3 + 0.
r**2*(r - 10)/4
Let -448 + 16*w - 1/7*w**2 = 0. Calculate w.
56
Let o be -4 - (70*-1 + -3). Let n = o + -66. Suppose 1/2*t**n + 0 - t + 1/2*t**2 = 0. What is t?
-2, 0, 1
Let d(k) = k**4 - k**2 + k. Let r be (-276)/9 - 2/(-3). Let f(s) = -45*s**4 - 115*s**3 - 125*s**2 - 55*s + 30. Let o(y) = r*d(y) - f(y). Solve o(i) = 0 for i.
-6, -1, 1/3
Let p be (-3)/2*(-48)/36. Factor 12*j - 159 + 153 - 3*j - 3*j**p.
-3*(j - 2)*(j - 1)
Suppose 30*k = 35*k - 75. Factor -52*w**3 + 0*w**5 - 33*w**2 + 0*w**5 - 24*w**4 - 16*w - k*w**2 - 4*w**5.
-4*w*(w + 1)**2*(w + 2)**2
Factor 4*r**2 - 2/5*r**3 + 0 + 48/5*r.
-2*r*(r - 12)*(r + 2)/5
Let a(i) be the first derivative of -1764*i**5/5 - 84*i**4 - 16*i**3/3 + 239. Let a(f) = 0. Calculate f.
-2/21, 0
Suppose 138*r = 362 - 86. Factor -1/3*v**r - 1/3*v + 2.
-(v - 2)*(v + 3)/3
Suppose -8*y = -4*y + 8. Let u = 3 - y. Solve -3*z**u + z**2 - 11*z**2 + 6*z**4 + 3*z + 4*z**2 = 0.
-1, 0, 1
Suppose 356*i - 364*i + 16 = 0. Let c(x) be the second derivative of 0 + 2/9*x**3 + 0*x**i + 1/18*x**4 + 4*x. What is b in c(b) = 0?
-2, 0
Let w(a) be the second derivative of -a**6/120 + a**5/40 + 5*a**4/16 - 4*a**3/3 + 2*a**2 - 2*a. Factor w(d).
-(d - 4)*(d - 1)**2*(d + 4)/4
Let k = -39 - -39. Let 2*o**3 - 3*o**3 + 4*o**3 - 9 + 9*o**2 + k*o - 3*o = 0. Calculate o.
-3, -1, 1
Let v(c) be the first derivative of -c**4/4 - 5*c**3/2 + 9*c**2 - 23*c + 7. Let r(b) be the first derivative of v(b). Factor r(y).
-3*(y - 1)*(y + 6)
Let j(o) = -12*o**2 + 28*o + 64. Let b(s) = 4*s**2 - 9*s - 19. Let m(d) = -8*b(d) - 3*j(d). Suppose m(q) = 0. What is q?
-2, 5
Let j(q) be the third derivative of q**6/60 - q**5/30 - q**4/12 + q**3/3 - 73*q**2. Suppose j(n) = 0. Calculate n.
-1, 1
Let o(m) = 25*m**2 + 13*m. Let g be o(6). Find i, given that -g*i + 20*i**2 - 5*i**3 + 978*i = 0.
0, 4
Let z(r) = r**2 + 6. Let j(w) = 5*w**2 + 212*w - 5576. Let k(v) = -2*j(v) + 14*z(v). Factor k(u).
4*(u - 53)**2
Let a(n) be the third derivative of -n**7/1050 - 7*n**6/600 + 17*n**5/300 - 3*n**4/40 + 192*n**2. What is q in a(q) = 0?
-9, 0, 1
Let k(x) = 2*x**5 + x**2 - x + 1. Let p(y) = -15*y**5 + 420*y**4 - 9*y**2 + 9*y - 9. Let c(n) = -9*k(n) - p(n). Factor c(l).
-3*l**4*(l + 140)
Let r(d) be the second derivative of 31*d - 1/48*d**4 + 1/24*d**3 + 0 + 0*d**2. Factor r(b).
-b*(b - 1)/4
Determine o, given that 14*o**3 - 4*o**4 - 4 + 18*o + o**4 + 4 + 5*o**4 + 30*o**2 = 0.
-3, -1, 0
Let b = 83/6 + -69/5. Let v(i) be the second derivative of 0*i**3 + 0*i**4 - 2/63*i**7 + 0 + 3*i + b*i**5 + 0*i**2 + 1/45*i**6. Suppose v(p) = 0. What is p?
-1/2, 0, 1
Let z(c) = -c**3 - c**2 - c - 1. Let d(p) = -p**4 + 8*p**3 + 10*p**2 - 16*p - 17. Let t(o) = -d(o) + 4*z(o). Determine a so that t(a) = 0.
-1, 1, 13
Determine v, given that 11/8*v**2 + 1/8*v**5 + 13/8*v**4 + 0*v + 23/8*v**3 + 0 = 0.
-11, -1, 0
Let q(x) be the second derivative of x**9/9072 - x**7/840 - x**6/540 + 5*x**3/3 + 6*x. Let d(c) be the second derivative of q(c). Suppose d(k) = 0. What is k?
-1, 0, 2
Let p(x) be the third derivative of x**6/480 - x**4/32 + x**3/12 + 46*x**2. Solve p(w) = 0 for w.
-2, 1
Let h(b) be the third derivative of b**7/2240 - 7*b**6/1920 + b**5/160 + 55*b**4/24 + b**2 + 21. Let l(n) be the second derivative of h(n). Factor l(r).
3*(r - 2)*(3*r - 1)/8
Let s(y) be the first derivative of y**3 + 3*y**2 + 3*y - 1. Let a(k) = 5*k**2 + 12*k + 5. Let m(g) = 6*a(g) - 11*s(g). Factor m(x).
-3*(x - 1)**2
Let m(l) be the third derivative of 0 + 0*l**4 + 7*l**2 + 0*l + 1/2*l**3 - 1/20*l**5. Factor m(s).
-3*(s - 1)*(s + 1)
Let f(m) be the third derivative of -5*m**8/336 - 9*m**7/14 - 95*m**6/12 - 7*m**5/2 + 3835*m**4/24 - 845*m**3/2 - 333*m**2. Suppose f(j) = 0. What is j?
-13, -3, 1
Let v(u) be the first derivative of -3*u**5/25 + 9*u**4/10 - 7*u**3/5 - 9*u**2/5 + 24*u/5 - 612. Suppose v(g) = 0. What is g?
-1, 1, 2, 4
Let n(q) be the second derivative of q**9/5040 + 3*q**8/2240 + q**7/420 - 2*q**4 + 9*q. Let t(f) be the third derivative of n(f). Factor t(c).
3*c**2*(c + 1)*(c + 2)
Let o(h) be the second derivative of -27*h**6/5 + 18*h**5/5 - 2*h**4/3 + 22*h. Suppose o(y) = 0. Calculate y.
0, 2/9
Let q(k) be the third derivative of -2*k**7/175 - k**6/200 + 3*k**5/25 - k**4/8 - k**3/5 + 77*k**2. Solve q(b) = 0 for b.
-2, -1/4, 1
Let x(w) be the third derivative of -w**8/336 + 13*w**7/210 - 41*w**6/120 + 47*w**5/60 - 3*w**4/4 - 96*w**2 - 5*w. Factor x(p).
-p*(p - 9)*(p - 2)*(p - 1)**2
Let x = 93 - 91. Solve 0*r**3 - 4*r + 5*r**x + 9 - 11*r + 3*r**3 - 2*r**2 = 0.
-3, 1
Let s(l) = l**3 - 2*l**2 + 2*l - 1. Let p(d) = 79*d**3 - 306*d**2 - 58*d + 33. Let c(a) = -p(a) - s(a). Factor c(i).
-4*(i - 4)*(4*i - 1)*(5*i + 2)
Suppose 4*k - 16 = -6*t + 2*t, 3*t + 20 = k. Factor 8*i - k*i + 9*i**2 - 3*i**3 + 0*i.
-3*i**2*(i - 3)
Let l = -5 - 2. Let x(p) = p**3 + 8*p**2 + 7*p + 4. Let i be x(l). Factor 0*v**4 - 9*v**2 + 3*v**3 - 3 + 0*v + 3*v**i - 3 - 15*v.
3*(v - 2)*(v + 1)**3
Let s(q) be the third derivative of q**9/7560 - q**7/1260 - q**4/4 + 6*q**2. Let y(t) be the second derivative of s(t). Suppose y(r) = 0. Calculate r.
-1, 0, 1
Let l(n) = -5*n - 37. Let g(c) = -c**2 - 13*c - 30. Let v be g(-11). Let o be l(v). Factor u**o + 0 + 2/3*u**4 + 1/3*u**2 + 0*u.
u**2*(u + 1)*(2*u + 1)/3
Let h(c) be the first derivative of c**4 - 44*c**3 - 68*c**2 - 298. Factor h(q).
4*q*(q - 34)*(q + 1)
Suppose -4/3*o + 0*o**4 + 0*o**2 + 0 + 8/3*o**3 - 4/3*o**5 = 0. What is o?
-1, 0, 1
Let d(u) be the second derivative of -6*u**2 - 4/3*u**3 + 0 + 1/3*u**4 + 8*u. Factor d(t).
4*(t - 3)*(t + 1)
Let x(y) be the second derivative of -5*y + 0 + 0*y**5 + 0*y**3 - 2*y**4 + 1/10*y**6 + 24*y**2. Find t such that x(t) = 0.
-2, 2
Factor 1/5*s**2 + 2/5 - 3/5*s.
(s - 2)*(s - 1)/5
Let n(u) = -18*u + 1818. Let x be n(101). Determine r so that x + 2*r**3 + 0*r + 1/2*r**4 + 3/2*r**2 = 0.
-3, -1, 0
Let v(o) = -o**3 + 9*o**2 - o + 9. Let k(y) = y**2 + 6*y + 9. Let u be k(-6). Let z be v(u). Find b such that 2/11*b**3 + z + 2/11*b**2 - 4/11*b = 0.
-2, 0, 1
Suppose 4*a = 3*g - 7, g + a + 8 = 3*g. Let u be g + -2 - (3 + -2). Factor 7*q**u + 0 - 1 - 6*q**2.
(q - 1)*(q + 1)
Suppose 5*i - 5*q - 45 = 0, 12*i - 4*q - 20 = 16*i. Suppose -10/9*l + 8/9*l**i + 2/9*l**3 + 0 = 0. Calculate l.
-5, 0, 1
Let n(t) be the first derivative of -t**4/18 - 14*t**3/27 - 16*t**2/9 - 8*t/3 + 5. Factor n(y).
-2*(y + 2)**2*(y + 3)/9
Let a = 596/895 - -2/2685. Suppose -2/3*u + 0 + 4/3*u**3 - a*u**2 = 0. What is u?
-1/2, 0, 1
Let b be 3*(31 + 2 + 1). Let f = b + -102. Solve 0*w + f - 2/3*w**2 = 0 for w.
0
Let x be (-3)/2*72/(-1134). Let t(c) be the first derivative of -5 + 0*c**2 - 1/14*c**4 + x*c**3 + 0*c. Factor t(u).
-2*u**2*(u - 1)/7
Let x = 79/119 - 4/17. Factor 3/7*q + 0 + x*q**2.
3*q*(q + 1)/7
Let h(u) = u**4 - u**3 + 2*u. Let g(n) = n**4 - 21*n**3 + 20*n**2 - 2*n. Let s(f) = -g(f) - h(f). Let s(i) = 0. What is i?
0, 1, 10
Let r(i) be the third derivative of 6*i**2 + 0 + 0*i**4 + 0*i + 0*i**3 + 1/300*i**5. Factor r(m).
m**2/5
Let z be 24/20*(-45)/(-6). Let z*f**3 - f**4 + 12*f - 2*f**4 - 18*f**3 = 0. Calculate f.
-2, 0, 1
Let f(g) = 30*g**2 - 195*g - 65. Let k(o) = -o**2 + o - 1. Let t(x) = -f(x) + 5*k(x). Factor t(n).
-5*(n - 6)*(7*n + 2)
Let b be 1 + -3 + 4 + -263. Let r be b/(-18) + 1/2. Factor s**3 + 0 + 4 + r*s**2 - 7*s - 13*s**2.
(s - 1)**2*(s + 4)
Let a(m) = -2. Let l = 100 + -102. Let z(t) = -t**3 - 9. Let g be -1 + (22 - 2)/2. Let d(n) = g*a(n) + l*z(n). Solve d(j) = 0.
0
Let m(h) be the third derivative of -8/3*h**3 - 3/2*h**4 + 0*h - 2/5*h**5 - 1/30*h**6 - 7*h**2 + 0. Let m(v) = 0. Calculate v.
-4, -1
Let o(f) = -f**3 - f**2 - f + 2. Let p(s) = 28*s**4 - 23*s**3 - 123*s**2 + 77*s + 38. Let l(x) = -3*o(x) + p(x). Let l(n) = 0. Calculate n.
-2, -2/7, 1, 2
Let c be (-10)/1 - (-10234)/1020. Let b(g) be the second derivative of -c*g**6 + 0*g**4 + 0*g**3 - 1/20*g**5 + 0 + 0*g**2 + 6*g. Factor b(m).
-m**3*(m + 1)
Suppose -9 + 15 = 3*k. Let o(m) be the first derivative of -1/25*m**5 + 1/5*m - 1/5*m**k + 0*m**3 + 7 + 1/10*m**4. What is f in o(f) = 0?
-1, 1
What is n in -6/7*n**3 + 2/7*n**4 - 2/7*n**2 + 2/7*n**5 + 0 + 4/7*n = 0?
-2, -1, 0, 1