21*i**3 + i**2 + i - 1. Let w be o(1). Let d = w + -16. Factor 0 + 24*b + d + 3 - 1 + 18*b**2.
2*(3*b + 2)**2
Let s(j) = -j**2 + 5*j - 2. Let l be s(3). Factor -28*r**3 - 3*r**5 + 9*r - 32*r**2 - 12*r**4 - 18*r + r**5 - l - 9*r.
-2*(r + 1)**4*(r + 2)
Let g(v) be the second derivative of -v**5/24 + 5*v**4/72 + 3*v. Solve g(b) = 0 for b.
0, 1
Let v(b) be the third derivative of b**7/840 - b**6/480 - b**5/240 + b**4/96 + 5*b**2. Factor v(d).
d*(d - 1)**2*(d + 1)/4
Let g(r) be the second derivative of -r**6/900 + r**5/50 - 3*r**4/20 - r**3/3 + r. Let o(x) be the second derivative of g(x). Factor o(z).
-2*(z - 3)**2/5
Let 2*t**4 + 72/7*t**2 + 16/7*t + 60/7*t**3 + 0 = 0. Calculate t.
-2, -2/7, 0
Factor -r**4 - 124*r**2 - 124*r**2 + 9*r + 7*r**3 + 233*r**2.
-r*(r - 3)**2*(r - 1)
Let t = -2/77 - -46/77. Factor -t*y - 2/7 - 2/7*y**2.
-2*(y + 1)**2/7
Let m(u) be the third derivative of u**8/80640 + u**7/20160 - u**6/1440 - u**5/60 - 2*u**2. Let g(w) be the third derivative of m(w). Factor g(l).
(l - 1)*(l + 2)/4
Suppose k - 5*z - 496 = 0, -5*z - 1162 = -4*k + 837. Let l = k + -4501/9. Find n, given that 0 + l*n**3 + 4/9*n**5 + 0*n + 2/9*n**2 + 10/9*n**4 = 0.
-1, -1/2, 0
Let n = 4 - 2. Suppose 20 = u - 4*t, -2*t - 9 = -u + 5. Factor u*q - n - 6*q + 3 + 2*q**2 - 5.
2*(q - 1)*(q + 2)
Let b(d) be the second derivative of -5/48*d**3 + 1/8*d**2 + 0 - 1/240*d**6 + 1/160*d**5 - 6*d + 1/32*d**4. Factor b(o).
-(o - 1)**3*(o + 2)/8
Let l(k) be the second derivative of k**4/48 - 5*k**3/12 + 25*k**2/8 - 13*k. Factor l(t).
(t - 5)**2/4
Factor 64/3*y**3 + 16/3*y + 32/3*y**4 + 2/3 + 16*y**2.
2*(2*y + 1)**4/3
Let o(l) be the third derivative of 0 + 0*l - 11/30*l**5 - 7/20*l**6 - 5/168*l**8 + 0*l**3 - 1/6*l**4 + l**2 - 17/105*l**7. What is g in o(g) = 0?
-1, -2/5, 0
Let j(q) be the third derivative of q**6/24 - q**5/3 - 25*q**4/24 + 14*q**2. Suppose j(y) = 0. Calculate y.
-1, 0, 5
Let i be (-8)/30 + (-6)/(-10). Factor 4/3 + 4/3*c + i*c**2.
(c + 2)**2/3
Suppose 6 = y + y. Let r be (y/7)/((-6)/(-4)). Factor -6/7*m + 4/7 + r*m**2.
2*(m - 2)*(m - 1)/7
Determine w, given that 736*w**2 - 411 + 512*w**5 - 126*w - 431*w**4 + 419 - 1856*w**3 + 1967*w**4 = 0.
-4, 1/4
Suppose -q = -2*s - 1, -6*s = -s + 3*q - 25. Determine c, given that -2*c**3 + 0 - 2/3*c + 2/3*c**4 + 2*c**s = 0.
0, 1
Let v(z) be the first derivative of 2*z**3/21 + 3*z**2/7 + 4*z/7 + 5. Suppose v(a) = 0. What is a?
-2, -1
Let a(s) = -s**3 + s**2 + s - 1. Let r(d) = 5*d**3 + 5*d**2 + 7*d + 7. Suppose -4*n + 5*n = -1. Let m(q) = n*r(q) - 3*a(q). Factor m(z).
-2*(z + 1)**2*(z + 2)
Let k(s) = -2*s**3 - 3*s**2 + 5*s. Let p(y) = 3*y**3 + 7*y**2 - 10*y. Let w(g) = -7*k(g) - 3*p(g). What is i in w(i) = 0?
-1, 0, 1
Let u(b) be the third derivative of b**9/120960 - b**8/8064 + b**7/3360 + b**6/160 + b**5/20 + 4*b**2. Let m(r) be the third derivative of u(r). Factor m(v).
(v - 3)**2*(v + 1)/2
Let -2*a**3 + 4*a + a**4 + 16 + 1/4*a**5 - 8*a**2 = 0. Calculate a.
-4, -2, 2
Let p(a) be the first derivative of a**4/22 - 4*a**3/33 - a**2/11 + 4*a/11 - 4. Solve p(d) = 0 for d.
-1, 1, 2
Suppose -5*m = -49 + 39. Factor -49/4*f**5 - 109/4*f**3 - f + 0 + 63/2*f**4 + 9*f**m.
-f*(f - 1)**2*(7*f - 2)**2/4
Let u(o) be the first derivative of 11*o**4/18 + 136*o**3/27 + 37*o**2/3 + 4*o - 30. Suppose u(a) = 0. Calculate a.
-3, -2/11
Let m be (-30)/(-3)*(-12)/(-20). Let u = m + -6. Factor -15/4*p**3 + 3/2*p**2 + 0*p + 9/4*p**4 + u.
3*p**2*(p - 1)*(3*p - 2)/4
Let v(l) = l**3 - l + 1. Let z(n) = n**5 - 2*n**4 + 4*n**2 - n. Let p(r) = -10*v(r) + 5*z(r). Let p(h) = 0. What is h?
-1, 1, 2
Let v(t) be the second derivative of -t**7/336 + t**6/60 - 3*t**5/160 - 2*t. Suppose v(l) = 0. What is l?
0, 1, 3
Suppose -4*d + 0*d = -12. Factor -3*h**3 + 2*h + 6*h**3 - 2*h**d - 3*h**2.
h*(h - 2)*(h - 1)
Let m(g) be the first derivative of g**6/120 - g**5/56 - g**4/28 + 10*g**3/3 - 3. Let p(t) be the third derivative of m(t). Factor p(i).
3*(i - 1)*(7*i + 2)/7
Let i(z) be the first derivative of 2/9*z**3 + 0*z + 0*z**2 + 1/6*z**4 - 6. Factor i(v).
2*v**2*(v + 1)/3
Let l be 0 - (12/(-2) + 3). Determine b, given that 5*b**4 - 13*b**3 - l*b + 0 + 9*b**2 - 2 + 4*b = 0.
-2/5, 1
Let i = 379/260 - 3/52. Let a(d) be the second derivative of 2*d + 0 - 8/3*d**4 + i*d**5 + 1/21*d**7 - 2*d**2 - 2/5*d**6 + 3*d**3. Factor a(p).
2*(p - 2)*(p - 1)**4
Suppose -2*f = -3*t, -3*t + 0*f - 2*f + 12 = 0. Factor -2*w**3 - t + w + 1 + 3 + w - 2*w**2.
-2*(w - 1)*(w + 1)**2
Determine m, given that -9*m**2 - 3/2*m + 0 = 0.
-1/6, 0
Let g be 1/(5 - (3 - 1)). Let q(z) = -z**3 + 2*z + 1. Let n be q(-1). Solve 1/3*f + n + g*f**2 = 0.
-1, 0
Determine y, given that -2*y**2 + 18/5 - 2/5*y**3 - 6/5*y = 0.
-3, 1
Let l(a) = a**3 - a**2. Let k(o) = 4*o**3 - 4*o**2 + 2*o - 2. Let m(f) = -k(f) + 6*l(f). Factor m(v).
2*(v - 1)**2*(v + 1)
Let t(d) = d**3 + d**2. Let i be t(-2). Let w = i + 6. Determine u so that -w*u + 6 + 4*u**4 - 6 + 6*u**3 = 0.
-1, 0, 1/2
Suppose 1 = n - 4. Let k = n - 0. Find d such that 1/3 + 2/3*d**3 - 5/3*d + 2*d**2 - 7/3*d**4 + d**k = 0.
-1, 1/3, 1
Let i(z) be the first derivative of -5 + 0*z - 2/55*z**5 + 4/11*z**2 - 3/22*z**4 + 0*z**3. Factor i(f).
-2*f*(f - 1)*(f + 2)**2/11
Let d(n) be the first derivative of 5*n**6/9 - 4*n**5/15 - 5*n**4/3 + 8*n**3/9 + 5*n**2/3 - 4*n/3 + 4. Suppose d(c) = 0. What is c?
-1, 2/5, 1
Let n(m) = 4*m**4 + 8*m**3 + 16*m**2 + 8*m - 4. Let c(l) = 8*l**4 + 15*l**3 + 33*l**2 + 17*l - 9. Let k(a) = -4*c(a) + 9*n(a). Determine z, given that k(z) = 0.
-1, 0
Let g(h) be the first derivative of h**4/2 + 2*h**3/3 - h**2 - 10*h - 1. Let y(s) = -s**2 + s + 1. Let r(d) = g(d) + 8*y(d). Factor r(b).
2*(b - 1)**3
Factor 16/3 + 56/3*k + 16/3*k**4 + 50/3*k**3 + 2/3*k**5 + 76/3*k**2.
2*(k + 1)**2*(k + 2)**3/3
Let x be (-2)/4*2*-29. Let u = 88/3 - x. Determine j so that 1/3*j**2 + 0 + u*j = 0.
-1, 0
Let z(l) = l + 15. Let h be z(-13). Let g(k) be the second derivative of 0*k**3 + 2*k + 0 + 9/70*k**5 - 1/21*k**4 + 0*k**h - 1/15*k**6. Let g(t) = 0. What is t?
0, 2/7, 1
Let c be (-2)/(-8) - 30/(-8). Suppose 3*q + 0 = -3, -2*r = c*q - 2. Let -5/2*i**r + 0*i + 0 + 2*i**4 + i**2 - 1/2*i**5 = 0. Calculate i.
0, 1, 2
Let x = -1865/2104 - -3/263. Let t = x + 11/8. Determine p, given that t*p**2 + 0 + 1/2*p - 1/2*p**3 - 1/2*p**4 = 0.
-1, 0, 1
Let y(a) = 6*a**5 - 4*a**4 - 4*a**3 + 4*a**2 + 6*a. Let j(u) = -11*u**5 + 7*u**4 + 8*u**3 - 7*u**2 - 11*u. Let d(l) = -4*j(l) - 7*y(l). Factor d(g).
2*g*(g - 1)**2*(g + 1)**2
Let z(i) be the second derivative of i**6/420 + i**5/210 - i**4/84 - i**3/21 + i**2/2 - 3*i. Let s(g) be the first derivative of z(g). Factor s(o).
2*(o - 1)*(o + 1)**2/7
Let n(r) be the second derivative of 2*r - 3/4*r**3 - 1/8*r**4 + 0 - 3/2*r**2. Factor n(a).
-3*(a + 1)*(a + 2)/2
Let g(v) = 10*v**5 - 2*v**4 + 4*v**2. Let d(b) = 29*b**5 - 6*b**4 - b**3 + 11*b**2. Let i(m) = 4*d(m) - 11*g(m). Determine w, given that i(w) = 0.
-2/3, 0, 1
Let s(y) be the second derivative of 0 + 3/5*y**5 - 3/2*y**3 - 3*y**2 - 1/14*y**7 - 5*y + 1/2*y**4 + 0*y**6. Let s(r) = 0. What is r?
-1, 1, 2
Let i(w) be the first derivative of 0*w**3 + 0*w + 0*w**4 + 1/10*w**5 + 0*w**2 - 3. Suppose i(c) = 0. What is c?
0
Suppose 0 = 37*x - 3*x. Solve -2/7*f + 10/7*f**3 + 2/7*f**2 + x + 6/7*f**4 = 0 for f.
-1, 0, 1/3
Let f be 4 - 7 - (-118)/34. Let p = f - -62/85. Factor 0 + p*c**3 + 2/5*c**5 + 0*c + 2/5*c**2 + 6/5*c**4.
2*c**2*(c + 1)**3/5
Suppose a + 4*m = -1 + 9, -3*a + 9 = -3*m. Suppose 0 = a*r + r. Factor -1/3*j**2 + r - 2/3*j.
-j*(j + 2)/3
Let m(o) be the second derivative of 0*o**2 + 2*o + 3/5*o**5 + 4/3*o**3 - 5/3*o**4 + 0. Determine j, given that m(j) = 0.
0, 2/3, 1
Let d be (-1)/((-5)/8) - 0. Let k = 111 + -108. Find m, given that -2/5 - 2/5*m**4 - 12/5*m**2 + d*m + 8/5*m**k = 0.
1
Let c = 11/14 - -5/7. Determine j so that 0 - 9/2*j**3 - c*j + 9/2*j**2 + 3/2*j**4 = 0.
0, 1
Let n(t) = 45*t**4 - 70*t**3 - 55*t**2 + 80. Let u(z) = 5*z**4 - 8*z**3 - 6*z**2 + 9. Let l(r) = -4*n(r) + 35*u(r). What is b in l(b) = 0?
-1, 1
Let v = -1 + 1. Suppose 5*o + 16 - 1 = 5*w, -o + 3*w - 13 = v. Suppose -h**2 + 2*h + 0*h**2 + 2 - 2*h**3 - h**o = 0. Calculate h.
-1, 1
Suppose 3*z - 8 - 30 = 5*q, -3*q - 6 = z. Suppose -4*j = -z*j. What is g in j + 1/4*g**2 - 1/4*g = 0?
0, 1
Let x(r) be the first derivative 