t i(o) be the first derivative of 4*o**3/3 - 8*o**2/3 + 4*o/3 - 2. Solve i(n) = 0 for n.
1/3, 1
Factor 51*i**4 + 323*i - 330*i + 375 - 968*i + 870*i**2 - 3*i**5 - 318*i**3.
-3*(i - 5)**3*(i - 1)**2
Let v be (-2)/3 - (-10)/9. Suppose 3*o + 5 = 5*y - 6, 3*y = 3*o + 3. What is r in -2/9*r**o - v*r**2 + 0 - 2/9*r = 0?
-1, 0
Let c(k) be the first derivative of 1/720*k**5 - 4/3*k**3 - 3 + 0*k + 0*k**2 + 1/72*k**4 - 1/2160*k**6. Let g(b) be the third derivative of c(b). Factor g(q).
-(q - 2)*(q + 1)/6
Let h(j) = j**2 - 12*j + 5. Let m(f) = 6*f - 3. Let x be 141/27 + 6/(-27). Let i(l) = x*m(l) + 3*h(l). Let i(c) = 0. Calculate c.
0, 2
Suppose -j + 0*j - 4*y = 31, -y = 3*j + 49. Let w be (24/(-30))/(18/j). Factor 4*p**4 - w*p**5 - 28/3*p**3 + 32/3*p**2 - 6*p + 4/3.
-2*(p - 2)*(p - 1)**4/3
Let w be (-43)/129 - (-22)/30. Factor 0 - 6/5*s**3 - 2/5*s + w*s**4 + 6/5*s**2.
2*s*(s - 1)**3/5
Let g(f) be the first derivative of -18/5*f - 21/10*f**6 - 164/5*f**3 - 321/10*f**4 - 159/10*f**2 - 1 - 354/25*f**5. What is b in g(b) = 0?
-3, -1, -1/3, -2/7
Let i(s) be the second derivative of -s**7/84 + s**6/30 + 3*s**5/40 - s**4/3 + s**3/3 - 9*s. Determine y so that i(y) = 0.
-2, 0, 1, 2
Let t = 10 + -6. Let p be (t/2*1)/7. Factor 2/7*z + 2/7 - 2/7*z**3 - p*z**2.
-2*(z - 1)*(z + 1)**2/7
Suppose 0 = o + 3*o + 4. Let i = 1 + o. Factor i + 2/5*g**3 + 2/5*g**2 + 0*g.
2*g**2*(g + 1)/5
Let k(p) = -87*p**2 + 144*p - 67. Let y(n) = -89*n**2 + 144*n - 68. Let z(l) = 4*k(l) - 3*y(l). Let z(d) = 0. Calculate d.
8/9
Let l = -10 - -13. Factor 2/3*a**l + a**2 + 0 - 2/3*a.
a*(a + 2)*(2*a - 1)/3
Solve -1/4*a**4 - 1/2*a**2 - a**3 + 3/4 + a = 0 for a.
-3, -1, 1
Let l(x) be the second derivative of -x**7/5040 - x**6/240 - 3*x**5/80 - 3*x**4/16 + x**3/2 + 9*x. Let b(r) be the second derivative of l(r). Factor b(y).
-(y + 3)**3/6
Let g = 9 - 7. Let s(z) be the second derivative of g*z + 1/10*z**6 + 0 - 1/6*z**4 - 1/42*z**7 + 1/2*z**3 - 1/10*z**5 - 1/2*z**2. Solve s(t) = 0 for t.
-1, 1
Let r = -190 - -381/2. Factor -1/4*p**2 - r*p + 0.
-p*(p + 2)/4
Let h be -3 + 6 + (-2 - 3) + 2. Factor 2/9*w**3 + 4/9*w**2 + h + 2/9*w.
2*w*(w + 1)**2/9
Suppose 0 + 1/4*m**3 + 1/4*m + 1/2*m**2 = 0. What is m?
-1, 0
Let g(q) = 8*q**2 + 2. Let m(c) = -6*c**2 - 2. Let u(w) = 4*g(w) + 5*m(w). Factor u(a).
2*(a - 1)*(a + 1)
Let i(h) be the third derivative of -2/15*h**3 + 0*h - 1/20*h**4 - 1/150*h**5 + h**2 + 0. Determine n, given that i(n) = 0.
-2, -1
Let a = -303 - -2123/7. Factor -2/7 + 2/7*x**3 + 2/7*x**2 - a*x.
2*(x - 1)*(x + 1)**2/7
Suppose -3*t - 5*l + 5 = -t, -5*l + 5 = 0. Factor 0 + 0*w - w**5 + t*w**3 + 0*w**2 - 2/5*w**4.
-w**4*(5*w + 2)/5
Let v(c) be the third derivative of -c**7/945 - c**6/135 - c**5/45 - c**4/27 - c**3/27 - 10*c**2. What is b in v(b) = 0?
-1
Let a(r) = 39*r**3 - 12*r**2 - 105*r. Let o(b) = b**2 - 3*b**3 - 1 + 8*b + 2 - 1. Let v(q) = -2*a(q) - 27*o(q). What is z in v(z) = 0?
-1, 0, 2
Let g(d) be the first derivative of d**5/210 - d**4/84 - 4*d**2 + 6. Let x(y) be the second derivative of g(y). Factor x(b).
2*b*(b - 1)/7
Factor -4/3*g**3 + 2/9*g**4 + 8/9 + 26/9*g**2 - 8/3*g.
2*(g - 2)**2*(g - 1)**2/9
Suppose i = -5*d - 13, -4 = 3*i + 4*d + 2. Suppose 5*z = i*z. What is m in 2*m + z*m**2 - m**2 + 0*m = 0?
0, 2
Let n(a) be the first derivative of 1 + 2*a**4 + 16/5*a**5 - 5/3*a**6 - 20/3*a**3 + a**2 + 4*a. Solve n(f) = 0 for f.
-1, -2/5, 1
Let u = 3 + -4. Let w = u - -4. Factor w + 0*z - 2*z**2 - 7 + 6*z.
-2*(z - 2)*(z - 1)
Let p(h) be the first derivative of 2*h**3/15 + 3*h**2/5 - 8*h/5 + 19. Factor p(v).
2*(v - 1)*(v + 4)/5
Solve -5/7*g**5 + 3/7*g**3 - g**4 + g**2 + 0 + 2/7*g = 0 for g.
-1, -2/5, 0, 1
Find d, given that 3/2*d**2 + 1/2 + 3/2*d + 1/2*d**3 = 0.
-1
Let h(q) be the third derivative of -q**8/112 + q**7/70 + 3*q**6/40 - q**5/4 + q**4/4 + 35*q**2. Factor h(c).
-3*c*(c - 1)**3*(c + 2)
Determine g so that 2/9*g**4 - 2/9*g - 2/3*g**3 + 2/3*g**2 + 0 = 0.
0, 1
Let o be 1/(-45) - 24/(-108). Let -1/5*w**3 + 1/5*w + 1/5*w**2 - o*w**4 + 0 = 0. Calculate w.
-1, 0, 1
Suppose 0*u**3 + 2/17*u**4 + 2/17*u**5 + 0*u + 0*u**2 + 0 = 0. What is u?
-1, 0
Suppose 0 = -t + 4 + 2. Let g = -4 + 7. Solve 32*u + 79*u**2 - 25*u**2 + 4 - t*u + 14*u**4 + 76*u**g - 30*u**3 = 0.
-1, -2/7
Factor 2/13*p**2 - 4/13*p + 2/13.
2*(p - 1)**2/13
Let f(o) be the first derivative of -o**3/3 + o - 1. Find n, given that f(n) = 0.
-1, 1
Let y(f) be the third derivative of -f**5/12 - 25*f**4/24 - 10*f**3/3 + 9*f**2. Find q, given that y(q) = 0.
-4, -1
Suppose 0 = -2*c + 3*p - p + 8, -3*c - 2*p = -2. Let d be c - 0/(1 + 1). Let 0 + 0*l**d + 2/9*l**3 + 0*l - 2/9*l**4 = 0. What is l?
0, 1
Let h be ((-9)/15)/(39/(-90)). Factor 8/13 - 40/13*z + h*z**2.
2*(z - 2)*(9*z - 2)/13
Find y, given that -2/13*y**2 + 28/13*y - 98/13 = 0.
7
Suppose -29 = -5*w - 9. What is u in 2 - 3 - 5*u + 0 - 3*u**3 - 5*u**w - u**5 - 10*u**2 - 7*u**3 = 0?
-1
Let u(j) = -j**2 - j + 5. Suppose 0 = -3*a + 2*a. Let q be u(a). Suppose -4 + 2*m**2 + q*m + 0*m - 3*m = 0. What is m?
-2, 1
Let f(c) = 4*c**3 + 4*c**2 - 4*c + 6. Let u(y) = 3*y**3 + 3*y**2 - 3*y + 5. Let z(w) = 4*f(w) - 5*u(w). Factor z(j).
(j - 1)*(j + 1)**2
Suppose 5/11 - 6/11*r + 1/11*r**2 = 0. What is r?
1, 5
Let z(b) = 4*b - 5. Let w be z(3). Factor -6*j**2 - w*j + j - 2*j**4 - 6*j**3 + 4*j.
-2*j*(j + 1)**3
Let -3*y**2 + 2*y - 2 + 0*y**2 - 5*y + 8 = 0. What is y?
-2, 1
Factor 1/2*h**3 - 1/6*h**4 - 1/6*h**2 + 1/3 - 1/2*h.
-(h - 2)*(h - 1)**2*(h + 1)/6
Let h(j) = -4*j**3 - 6*j**2 - 5. Let u = 2 + 1. Let i(g) = 2*g**u + 4 + 3*g**2 + 2 + 4*g**2 + 2*g**3. Let w(n) = 6*h(n) + 5*i(n). Factor w(q).
-q**2*(4*q + 1)
Let s(u) be the second derivative of -u**5/240 + u**3/24 - u**2 + 2*u. Let b(x) be the first derivative of s(x). Factor b(t).
-(t - 1)*(t + 1)/4
Let l(n) be the first derivative of 3*n**4/2 + 3*n**3 + 2*n**2 + n + 1. Let u(i) be the first derivative of l(i). Factor u(g).
2*(3*g + 1)*(3*g + 2)
Let a(i) be the first derivative of 2*i**5/105 - i**4/14 + 4*i**3/63 + 13. Factor a(u).
2*u**2*(u - 2)*(u - 1)/21
Let a(c) be the second derivative of c**7/14 + 3*c**6/10 + 9*c**5/20 + c**4/4 - 5*c. Suppose a(p) = 0. What is p?
-1, 0
Let t(a) = a**2 - 11*a - 9. Let w be t(12). Suppose w*z = 2 + 4. Factor -2*u**4 + u - z*u**2 - 4*u + 3*u + 4*u**3.
-2*u**2*(u - 1)**2
Determine p so that 2*p**2 - 8*p**2 - 3*p**3 + 8*p + 0*p**2 + p = 0.
-3, 0, 1
Let z(v) be the second derivative of v**4/4 - 3*v**3 + 15*v**2/2 + 33*v. Factor z(u).
3*(u - 5)*(u - 1)
Let v(i) be the first derivative of -105*i**6/2 - 94*i**5 - 15*i**4/4 + 40*i**3 - 10*i**2 + 45. Let v(t) = 0. What is t?
-1, 0, 2/9, 2/7
Let x(v) = -4*v**2 - 9*v + 2. Let j be x(-3). Let w be (7 + j)*(-1)/4. Suppose w*a + 1/4*a**4 + 1/4*a**2 + 0 + 1/2*a**3 = 0. Calculate a.
-1, 0
Suppose -8*n = -4*n - 5*i - 46, i + 29 = 3*n. Suppose 0 = -n*u + 11*u. Suppose -8/7*x**2 + 6/7*x**3 + 2/7*x**5 + u + 8/7*x**4 - 8/7*x = 0. What is x?
-2, -1, 0, 1
Let t(i) = -8*i + 34. Let j be t(4). Factor -1/2*l**j + 1/2*l + 0.
-l*(l - 1)/2
Let d(a) be the first derivative of -a**5/270 - a**4/36 + 7*a**2/2 - 2. Let p(i) be the second derivative of d(i). Factor p(b).
-2*b*(b + 3)/9
Let i = -2172/5 + 436. Factor -2/5*b**2 - 8/5 + i*b.
-2*(b - 2)**2/5
Suppose 9 - 1 = 2*v. Suppose v*f - s = 19, -f + 4 = 4*s - 5. Factor -21/2*y**4 - 3/2*y - 1/2 + 3*y**2 + f*y**3 + 9/2*y**5.
(y - 1)**3*(3*y + 1)**2/2
Let r(i) be the second derivative of 0*i**6 + 1/50*i**5 + 0*i**4 - 1/105*i**7 + 0*i**3 + 0*i**2 + 0 - 8*i. Factor r(w).
-2*w**3*(w - 1)*(w + 1)/5
Let h = 8 + -6. Factor h - 6*u + 24*u**3 + 8*u**2 - 2*u**2 - 26*u**3.
-2*(u - 1)**3
Let d be (22/(-4) - -2)/(-7). Factor -1/2 - n**3 - 1/2*n**4 + 1/2*n**5 + d*n + n**2.
(n - 1)**3*(n + 1)**2/2
Let c(q) = -2. Let n(w) be the second derivative of -1/12*w**4 + 0 - 1/6*w**3 + 2*w + 1/2*w**2. Let l(t) = c(t) + 2*n(t). Factor l(x).
-2*x*(x + 1)
Let s(o) be the third derivative of 1/54*o**4 - 1/540*o**6 - o**2 + 0 + 0*o**3 + 0*o - 1/270*o**5. Factor s(x).
-2*x*(x - 1)*(x + 2)/9
Suppose 3*v = k - 5, -v + 4 = 5. Let p(c) = 2*c - 4. Let d be p(3). Suppose 2 + 3*j**2 - j**k - 4*j**d = 0. Calculate j.
-1, 1
Solve 3/7*q**2 + 6/7 + 9/7*q = 0 for q.
-2, -1
Let v(q) be the third derivative of -q**7/10080 + q**6/2880 + q**4/24 + q**2. Let w(d) be the second derivati