m**6/480 - 11*m**5/80 - m**4/3 + m**3/2 - m**2 - m - 39. Let i(d) be the second derivative of x(d). Factor i(p).
-(p + 2)*(p + 3)*(7*p - 2)/4
Suppose -11 + 1 = -10*d. Let g be 33/12 - d - 6/(-24). Factor 1/2*h**g + 0*h + 1/2*h**4 + 0 - h**3.
h**2*(h - 1)**2/2
Let i(r) = r**2 - 3*r - 28. Let u be i(7). Suppose u = 5*k - 36 + 6. Suppose 3/2*s**3 + 5/2*s**4 + 0 + 2*s - k*s**2 = 0. Calculate s.
-2, 0, 2/5, 1
Let v(b) = -7*b + 1. Let h be v(1). Let j = h - -9. Factor 12*d**2 - 8*d - 7*d + 2 - 3*d**j + 4.
-3*(d - 2)*(d - 1)**2
Solve -2*d + d**3 + 0 + 7/3*d**2 = 0.
-3, 0, 2/3
Factor 1154/3*r + 332929/6*r**2 + 2/3.
(577*r + 2)**2/6
Let s = -79 + 87. Suppose 20*b - 8 = -s. Factor b - 3/2*q**2 + 0*q.
-3*q**2/2
Let g(d) = -d**2 - 575*d + 3486. Let i be g(6). Factor 0 + 0*b**3 + 1/4*b**2 - 1/4*b**4 + i*b.
-b**2*(b - 1)*(b + 1)/4
Let s(v) be the first derivative of 1/44*v**4 + 2/33*v**3 + 0*v**2 + 0*v - 12. Factor s(p).
p**2*(p + 2)/11
Suppose 0 = 17*g + 30*g - 20*g - 81. Factor 63/2*q - 3*q**4 - 183/4*q**2 + 21*q**g - 27/4.
-3*(q - 3)**2*(2*q - 1)**2/4
Let -3/2*h**5 + 6*h**3 + 0*h + 24 + 9/2*h**4 - 24*h**2 = 0. What is h?
-2, -1, 2
Suppose -183*n - 42 = -190*n. Let c(x) be the first derivative of 0*x + 2 + 0*x**3 + 1/6*x**2 + 0*x**5 + 1/18*x**n - 1/6*x**4. Let c(z) = 0. Calculate z.
-1, 0, 1
Let z = 20686 - 20686. Let 1/3*m**2 + 0*m + z - 1/6*m**3 - 1/6*m**4 = 0. What is m?
-2, 0, 1
Factor -6*o - 10*o**5 + 8*o**2 - 79*o**4 + 2*o + 14*o**5 + 71*o**4.
4*o*(o - 1)**3*(o + 1)
Suppose -5*d**3 - 2*d + 187*d**2 - 139*d**2 + 2*d + 4*d**3 = 0. Calculate d.
0, 48
Let g(v) be the third derivative of v**8/30240 + v**7/7560 - v**5/15 - 6*v**2. Let a(x) be the third derivative of g(x). Factor a(r).
2*r*(r + 1)/3
Let k(p) be the third derivative of -p**6/40 - 9*p**5/20 - 3*p**4 - 10*p**3 - p**2 + 82*p. Determine l, given that k(l) = 0.
-5, -2
Let i be 4*(-63)/(-12) + (-6)/2. Let g(t) be the first derivative of -2 - 2/3*t**3 + 6*t**2 - i*t. Factor g(r).
-2*(r - 3)**2
Suppose -55*i + 61*i - 150 = 0. Factor i*h**2 + 44*h + 38*h - 67*h - 10*h**3.
-5*h*(h - 3)*(2*h + 1)
Let z = 4/19713 + 19705/39426. Find c, given that -3 + 5/2*c + z*c**2 = 0.
-6, 1
Factor -146/7*a**3 + 2/7*a**4 + 0*a**2 + 0*a + 0.
2*a**3*(a - 73)/7
Let n(l) be the third derivative of -3*l**6/160 - l**5/8 + 23*l**4/32 - 5*l**3/4 - 106*l**2. Factor n(z).
-3*(z - 1)*(z + 5)*(3*z - 2)/4
Let w(o) = 5*o**2. Let n be w(-1). Suppose 4*j = -3*h + 3*j + 7, 0 = 3*h + n*j + 1. Factor h*u**2 + 53*u**4 - 35*u**4 - 42*u**3 - 7*u**2 - 30*u**2 - 6*u.
2*u*(u - 3)*(3*u + 1)**2
Factor 29*c**3 - 21*c**3 + 5*c**4 + 97*c**3 - 135*c**2 + 15*c**4 - 1000*c - 240.
5*(c - 3)*(c + 4)**2*(4*c + 1)
Solve 2/3*d**5 - d**4 - 4*d**3 + 6*d + 3 + 2/3*d**2 = 0 for d.
-1, 3/2, 3
Suppose 5*l = 33 - 23. Suppose -2*q = -0*q. Determine b, given that 2 - b**3 + q*b**3 - 9*b - 9*b**2 - l*b**3 - 5 = 0.
-1
Let a = 204 - 208. Let r be 217/70 + a + 1. Suppose r*n**2 + 9/10 - 3/5*n = 0. Calculate n.
3
Let i = -7 - -6. Let m be -3 - (-12)/3 - i. Suppose 7*h**5 - 2*h**2 - 2*h + h + m*h**4 - 6*h**5 = 0. What is h?
-1, 0, 1
Suppose -158*f + 164*f = 36. Let a(m) be the first derivative of -1/20*m**4 + 0*m**3 + f + 3/10*m**2 - 2/5*m. Factor a(p).
-(p - 1)**2*(p + 2)/5
Let r(v) = -v**2 - v. Let n(g) = -g**3 + 8*g**2 - 4*g + 3. Suppose 4*u - 10 = -u. Suppose u*t - 19 = -7. Let y(j) = t*r(j) + 2*n(j). Factor y(a).
-2*(a - 3)*(a - 1)**2
Let p = 17231/14 + -1218. Let t = p + -86/7. Find y, given that -t*y**4 - 8 + 4*y**3 - 12*y**2 + 16*y = 0.
2
Suppose 0 = z - 5*b + 5, z - 3*z + 4 = -3*b. Suppose -4*p = -2*m - 2, 10 - 1 = -3*p + z*m. Suppose 5/2*k**2 + 0 + 1/2*k + 4*k**3 + p*k**4 = 0. Calculate k.
-1, -1/2, 0
Let b(u) = -4*u. Let c be b(-2). Let a be (-2)/10*-17 - (9 - c). Find p such that -63/5*p**3 + 12/5*p**4 + a - 72/5*p + 111/5*p**2 = 0.
1/4, 1, 2
Let w(g) be the third derivative of 38*g**2 - 1/315*g**7 - 1/90*g**5 + 0*g**4 + 0 - 1/90*g**6 + 0*g + 0*g**3. Determine s, given that w(s) = 0.
-1, 0
Let p(w) = 3*w**3 - 15*w**2 + 12. Let d(m) = -m**3 + m**2 + m - 1. Let o(j) = -24*d(j) - 3*p(j). Factor o(q).
3*(q - 1)*(q + 2)*(5*q + 2)
Suppose -1 = 2*r - 5. Factor -5 + 2 + 1 + 2*z**r + z - z**3.
-(z - 2)*(z - 1)*(z + 1)
Let a be 3 + 1 - 6/3. What is s in -7*s + 4*s**3 + 0*s**a + 3*s + 12 - 12*s**2 = 0?
-1, 1, 3
Let d = 30 + -9. Suppose 0 = 16*q - d*q + 20. Solve -3*b + 0 - 9/2*b**3 + 15/2*b**2 - 3/2*b**q + 3/2*b**5 = 0 for b.
-2, 0, 1
Let y be 10 + -8 + -1 + -1. Suppose y*w = 3*w - 15. Factor -2*n**4 - w*n**2 - n**2 + 0*n + 6*n**3 + n + n.
-2*n*(n - 1)**3
Let v(d) be the second derivative of -1/12*d**3 + 37*d + 0 + 0*d**2 - 1/48*d**4. Let v(y) = 0. Calculate y.
-2, 0
Let i = 48 - 45. Factor -3*z**i + 0*z**4 + 3*z - 2*z**4 + 3*z**4 - 2*z**4 + z**2.
-z*(z - 1)*(z + 1)*(z + 3)
Let r(w) be the first derivative of -3*w**5/20 - 5*w**4/8 + w**3 - 3*w**2 - 5. Let a(c) be the second derivative of r(c). Factor a(p).
-3*(p + 2)*(3*p - 1)
Let j(q) be the second derivative of -q**5/80 + q**4/4 - 15*q**3/8 + 25*q**2/4 + q + 18. Suppose j(k) = 0. What is k?
2, 5
Let o(i) be the third derivative of -i**5/40 + 143*i**4/8 - 20449*i**3/4 - 2*i**2 + 2*i. Determine a, given that o(a) = 0.
143
Suppose 2*a - 14 = 3*s, -5*a + 25 = -5*s - 5. Let u(n) = n - 1. Let r(p) = p**2 - 4*p + 3. Let m(w) = a*u(w) - 4*r(w). Factor m(q).
-4*(q - 4)*(q - 1)
Let l = 20132/9 - 2234. Let h = -892/9 + 100. Factor -8/3*x - l*x**2 - h - 4/3*x**3 - 2/9*x**4.
-2*(x + 1)**2*(x + 2)**2/9
Let o be ((-2)/(-2) + 0)*-1*0. Let m be o - 3 - -9 - 2. Determine l, given that 3/5*l**3 + 3/5*l**2 + 1/5*l**m + 1/5*l + 0 = 0.
-1, 0
Let p(m) = -m**3 - 3*m**2 + 5*m + 7. Let q be p(-4). Determine j so that 35*j**2 - 4*j**q + 3*j**3 + j**4 - 35*j**2 = 0.
0, 1
Let u(b) be the second derivative of b**6/180 - b**5/15 - 4*b**3/3 - 13*b. Let i(x) be the second derivative of u(x). Factor i(c).
2*c*(c - 4)
Suppose -2*t + 3*x = 2*t - 14, 2 = 4*t + 3*x. Let o = 49 + -40. Let o*p - 4 + 3*p + 7*p**2 - 13*p**3 + p**3 - 3*p**t = 0. What is p?
-1, 1/3, 1
Let k(x) be the second derivative of x**6/660 + x**5/110 - 4*x**3/33 - 11*x**2/2 - 25*x. Let g(z) be the first derivative of k(z). Suppose g(s) = 0. What is s?
-2, 1
Solve -560*i**2 + 31 + 3 + 32*i + 558*i**2 = 0.
-1, 17
Let j(u) = -141 + 119 + 3*u - u. Let t be j(11). What is i in t - 1/3*i - 1/3*i**4 - i**2 - i**3 = 0?
-1, 0
Suppose 0 = 4*b + 20, -3*m - 3*b - b = 11. Let x be m/(-1 - -1 - -1). Factor -2*f**4 + 3*f**2 + 4*f**3 - x*f**2 - 2*f**2 + 0*f**2.
-2*f**2*(f - 1)**2
Factor -2*f**3 - f - 1/2 + 7/2*f**2.
-(f - 1)**2*(4*f + 1)/2
Factor 7/9*b**2 + 11/9*b + 5/9 + 1/9*b**3.
(b + 1)**2*(b + 5)/9
Let w(d) = -7*d**5 + 13*d**4 - 12*d**3 + 2. Let n(j) = -9*j**5 + 15 + 11*j**5 - 85*j**3 + 90*j**4 - 52*j**5. Let v(t) = 2*n(t) - 15*w(t). What is k in v(k) = 0?
0, 1, 2
Factor 155/6*n**2 + 10 + 100/3*n + 35/6*n**3.
5*(n + 2)**2*(7*n + 3)/6
Let g(n) be the second derivative of -n**5/60 - 11*n**4/36 + 28*n**3/9 - 10*n**2 - 131*n. Let g(q) = 0. What is q?
-15, 2
Factor -9/7*r + 3*r**3 + 39/7*r**2 - 54/7 + 3/7*r**4.
3*(r - 1)*(r + 2)*(r + 3)**2/7
Let w(l) be the third derivative of -l**6/8 + 13*l**5/5 - 17*l**4/8 - 15*l**3 + 68*l**2 - l. Determine d, given that w(d) = 0.
-3/5, 1, 10
Let v be (-2098)/10 - (-7)/(1 - 36). Let z be (-8)/(-30)*v/(-126). Factor -2/9*f**2 - 2/9*f + z.
-2*(f - 1)*(f + 2)/9
Factor -7/4*j + 3 + 1/4*j**2.
(j - 4)*(j - 3)/4
Suppose 2*q - 1 - 15 = -4*d, 0 = -4*q - 4*d + 24. Let l be ((-2)/(-12)*4)/(1/3). What is m in 2*m**l + m**3 - q*m**3 - 13*m - 8*m**2 + 10*m = 0?
-1, 0
Suppose 3*p + 2 = -o, 0 = -5*o - 7 - 3. Suppose 4*c - 6 = 26. Factor c - 8*v + p*v**2 + 4*v**2 + 0*v**2 - 2*v**2.
2*(v - 2)**2
Suppose 6*x - 3*x - 2*h - 198 = 0, -4*x + 3*h = -265. Factor -47*n**2 + 6*n - 49*n**2 - 12*n - 8 + 66*n - x*n**3.
-4*(n + 2)*(4*n - 1)**2
Let o(r) be the third derivative of -3*r**6/20 - 11*r**5/30 - r**4/6 - 152*r**2. Find p, given that o(p) = 0.
-1, -2/9, 0
Suppose 38/3*s + 4/3*s**4 - 7*s**2 - 13/3*s**3 - 8/3 = 0. Calculate s.
-2, 1/4, 1, 4
Let y(h) = 7*h**2 - 47*h + 484. Let p(c) = 2*c**2 - c. Let n(r) = 6*p(r) - 2*y(r). Let n(i) = 0. What is i?
22
Let x(p) = -9*p**3 + 32*p**2 - 2*p + 2. Let z(b) = 38*b**3 - 129*b**2 + 9*b - 9. Let q(w) = 9*x(w) + 2*z(w). Factor q(k).
-5*k**2*(k - 6)
L