1. Let a(y) = 22. Let l(q) = 2. Let n(x) = -2*a(x) + 20*l(x). Let w(u) = -4*g(u) - n(u). Suppose w(s) = 0. Calculate s.
-1, 0, 1
Solve -1/2*y**3 + 0 + 3/2*y - y**2 = 0 for y.
-3, 0, 1
Let g(u) = -2*u**4 - 4*u**3 + 4*u**2 + 4*u - 2. Let t be 24/42*7/(-2). Let o(l) = -4*l**4 - 9*l**3 + 9*l**2 + 9*l - 5. Let k(n) = t*o(n) + 5*g(n). Factor k(h).
-2*h*(h - 1)*(h + 1)**2
Suppose 3*s + p - 3472 = 0, -4 = p + 1. Factor -s - 793*r - 846 - 182 - 3*r**3 + 64*r - 81*r**2.
-3*(r + 9)**3
Suppose -4*c = -5*s + 7, -4*c = -s + 1 - 6. Let u(k) be the third derivative of -3*k**2 + 0 + 0*k**s - 1/48*k**4 + 0*k - 1/240*k**5. Factor u(p).
-p*(p + 2)/4
Let a be ((-249)/(-126) - 3)*-8. Let t = 1532/105 - a. Factor -t + 16/5*u - 2/5*u**2.
-2*(u - 4)**2/5
Suppose 2*b + 6 = 3*q, 18*b - 23*b + 31 = 4*q. Suppose -2/9*p**2 + 2/9*p + 2/9 - 2/9*p**b = 0. Calculate p.
-1, 1
Let g be (2 - 21)/(6/24). Let v = -76 - g. Factor v - 1/6*q**2 + 0*q - 1/6*q**4 - 1/3*q**3.
-q**2*(q + 1)**2/6
Let m(f) be the first derivative of -f**6/4 + 12*f**5/5 - 33*f**4/4 + 12*f**3 - 27*f**2/4 - 102. Determine j, given that m(j) = 0.
0, 1, 3
Suppose 0 = -20*m + 16*m - g + 24, 4*m - 5*g = 24. Suppose -5*j - 4 = -m*j. Factor 0 + 0*k - 2/9*k**5 + 2/9*k**2 - 2/9*k**j + 2/9*k**3.
-2*k**2*(k - 1)*(k + 1)**2/9
Let u = 2/13 + 31/52. Factor -3/4*j**3 - u*j**5 + 0*j - 3/2*j**4 + 0*j**2 + 0.
-3*j**3*(j + 1)**2/4
Suppose 1040*s + 106 = 1093*s. Factor 1/7*u - 1/7*u**3 + 5/7 - 5/7*u**s.
-(u - 1)*(u + 1)*(u + 5)/7
Let r(x) = 4*x**3 - 17*x**2 + 7*x + 1. Let v(j) = 13*j**2 + 3*j**2 + 4*j**3 - 6*j - 8*j**3 - 2*j. Let k(q) = 4*r(q) + 5*v(q). Factor k(z).
-4*(z - 1)**3
Let c(s) be the first derivative of s**5/35 + 5*s**4/28 + s**3/3 + 3*s**2/14 - 347. Let c(a) = 0. What is a?
-3, -1, 0
Let i be 30/4*(-12)/(-15). Let j be (2/(-15))/(2/((-440)/i)). Factor 10/9*a**2 - j*a + 16/9.
2*(a - 4)*(5*a - 2)/9
Let a be (-12)/30 + 34/10. Suppose 0 = -2*l - a*c - 7, 5*l - 2*l - 3*c - 27 = 0. Factor -1 - 12*t + 6*t**4 + 2*t**2 - 3 + 11*t**3 + t**5 - l.
(t - 1)*(t + 1)*(t + 2)**3
Let o(s) = s**3 + 25*s**2 - 61*s + 33. Let z be o(-29). Let c = 10952/7 + z. Factor 12/7*y + c + 2/7*y**2.
2*(y + 3)**2/7
Let z(u) = -75*u - 15. Let n be z(1). Let r be (-27)/(-6)*-5*3/n. Factor -3/4 - 9/4*c**2 + r*c**3 + 9/4*c.
3*(c - 1)**3/4
Find b such that 392*b**3 - 60*b - 205*b**3 - 267*b**3 - 132*b**2 - 8 = 0.
-1, -2/5, -1/4
Let j(x) be the second derivative of -x**7/315 - x**6/360 + x**5/90 + x**4/72 - x**2/2 + 4*x. Let r(q) be the first derivative of j(q). Factor r(z).
-z*(z - 1)*(z + 1)*(2*z + 1)/3
Let v(b) be the first derivative of 5 + 2*b**2 - 2*b**4 + 0*b + 4/3*b**3. Factor v(r).
-4*r*(r - 1)*(2*r + 1)
Let a(d) be the first derivative of -d**6/480 - d**5/10 - 2*d**4 + 5*d**3 + 22. Let q(u) be the third derivative of a(u). Factor q(b).
-3*(b + 8)**2/4
Suppose -9 = -2*p - 1. Let h(m) = 55*m**2 - 210*m. Let f(o) = 5*o**2 - 19*o. Let z(c) = p*h(c) - 45*f(c). Factor z(b).
-5*b*(b - 3)
Let p(m) = 24*m**4 + 48*m**3 - 60*m**2 - 164*m + 20. Let b(i) = -i**4 + i**3 - i**2 + i - 1. Let q(n) = -20*b(n) - p(n). Solve q(h) = 0.
-18, -1, 0, 2
Suppose -14*s + 36 = 4*s. Factor -8*q**s - 469*q**4 + 236*q**4 + 2*q**2 + 4*q + 235*q**4.
2*q*(q - 1)**2*(q + 2)
Suppose 377 = -7*c + 3730. Factor c*x**2 + 96*x**3 + 9/2*x**4 + 121/2 - 352*x.
(x + 11)**2*(3*x - 1)**2/2
Let c(l) = -2*l**3 + 5*l**2 - 4. Let w be c(4). Let v = w - -54. Suppose -2/9*b**v + 2/9 + 0*b = 0. Calculate b.
-1, 1
Let r be (-14)/(-4) - 2/(-4). Let x(b) = 4*b**2 - 13*b - 10. Let n be x(5). Suppose -21*a**2 + n*a**3 - 9*a**r + 8 + 3*a - 2 - 4 = 0. Calculate a.
-2/9, 1
Let n be 32435/18962 - (-4)/(-19). Solve 9/4 - 3/4*v**2 + n*v = 0.
-1, 3
Let h(m) = 253*m**3 + 125*m**2 - 118*m + 10. Let q(c) = 4047*c**3 + 2001*c**2 - 1887*c + 159. Let j(u) = -33*h(u) + 2*q(u). Suppose j(s) = 0. What is s?
-1, 2/17, 2/5
Let t(b) be the third derivative of 17*b**6/280 + b**5/2 + 59*b**4/56 + 3*b**3/7 + 6*b**2. Factor t(z).
3*(z + 1)*(z + 3)*(17*z + 2)/7
Let z be 8 + (-4499)/616 - 3/24. Factor 2/7*b**2 + 2/7 - z*b.
2*(b - 1)**2/7
Let z(q) = q**2 - 60*q - 607. Let j be z(69). Let n(b) be the first derivative of 0*b - 1/2*b**2 - j - 1/6*b**3. Factor n(c).
-c*(c + 2)/2
Let n = 2467 - 707. Factor -410*l**3 + 802 - n*l - 35*l**4 + 54 - 1560*l**2 - 216.
-5*(l + 4)**3*(7*l - 2)
Let q(v) be the second derivative of v**4/48 + 59*v**3/12 + 449*v. Solve q(o) = 0 for o.
-118, 0
Solve -104 + 202 - 5*v**2 - 98 = 0.
0
Let o(z) be the second derivative of z**4/48 - z**3/8 - 5*z**2/4 + 31*z + 3. Factor o(q).
(q - 5)*(q + 2)/4
Factor -9 - 3/2*w**3 + 6*w**2 - 3/2*w.
-3*(w - 3)*(w - 2)*(w + 1)/2
Let x be (-108)/(-51) - (-2)/(-17). Factor 11*k + x - 2*k - 12*k**2 + 3*k**2 + 3*k**3 - 5.
3*(k - 1)**3
Let y(j) be the first derivative of -7*j**6/5 - 16*j**5/25 + 2*j**4/5 - 73. Factor y(d).
-2*d**3*(3*d + 2)*(7*d - 2)/5
Let q(n) = -7*n**5 - 16*n**4 + 95*n**3 + 16*n**2 - 96*n + 4. Let h(k) = 2*k**5 - k**4 + k**3 + k**2 - k - 1. Let u(b) = -4*h(b) - q(b). Factor u(y).
-y*(y - 10)**2*(y - 1)*(y + 1)
Let p(h) = 30*h**3 - 53*h**2 + 6*h - 17. Let k(i) = -5*i**3 + 9*i**2 - i + 3. Let s(o) = 34*k(o) + 6*p(o). Factor s(n).
2*n*(n - 1)*(5*n - 1)
Suppose -4*c + 0*c = q - 22, -c + 10 = -2*q. What is t in 15 + 18*t - 6*t - c*t + 5*t**2 + 14*t = 0?
-3, -1
Let f = 83 + -81. Factor -2*z + 8*z**3 - f*z - 11*z**3 + 2*z**2 + 5*z**3.
2*z*(z - 1)*(z + 2)
Let d(z) be the second derivative of -12*z - 2/5*z**5 + 1/15*z**6 + 0 + 0*z**2 + 5/6*z**4 - 2/3*z**3. Let d(y) = 0. What is y?
0, 1, 2
Let a(n) be the first derivative of -n**4 + 68*n**3/3 - 32*n**2 + 36. Factor a(b).
-4*b*(b - 16)*(b - 1)
Let z = 18/35 + -13/28. Let j(c) be the third derivative of -1/20*c**6 + 0*c + 0*c**4 - z*c**5 - 1/70*c**7 + 0*c**3 - 5*c**2 + 0. Solve j(u) = 0 for u.
-1, 0
Let s(y) be the second derivative of 0 + 0*y**3 - 1/4*y**4 - 6*y + 3/20*y**5 + 1/8*y**6 - 3/2*y**2. Let m(k) be the first derivative of s(k). Factor m(g).
3*g*(g + 1)*(5*g - 2)
Let l(j) be the first derivative of j**3 + 39*j**2 + 507*j + 652. Factor l(g).
3*(g + 13)**2
Factor 0*k**2 - 1/3*k**5 + 0 - 5/3*k**4 + 0*k - 4/3*k**3.
-k**3*(k + 1)*(k + 4)/3
Determine f so that -2/7*f**3 + 6/7*f + 4/7 + 0*f**2 = 0.
-1, 2
Let l = -1 - 2. Let n(v) = 3*v. Let b(x) = -2*x. Let c(y) = 4*b(y) + 3*n(y). Let f(t) = -3*t**2 - 12*t - 12. Let a(i) = l*c(i) + f(i). Factor a(w).
-3*(w + 1)*(w + 4)
Factor -26/11*n**2 + 2/11*n**4 + 0 - 4/11*n**3 - 20/11*n.
2*n*(n - 5)*(n + 1)*(n + 2)/11
Let g(z) be the first derivative of -6*z + 15/2*z**2 + z**3 - 2 - 21/4*z**4 + z**6 + 3/5*z**5. Determine l so that g(l) = 0.
-2, -1, 1/2, 1
Factor -363/4 - 99/2*x - 27/4*x**2.
-3*(3*x + 11)**2/4
Let j(l) = -35*l**3 - 75*l**2 - 60*l - 20. Let f(z) = 9*z**3 + 19*z**2 + 15*z + 5. Let i(r) = 15*f(r) + 4*j(r). Factor i(k).
-5*(k + 1)**3
Let g(r) be the third derivative of r**6/45 + 7*r**5/135 + r**4/54 - 215*r**2. Let g(z) = 0. What is z?
-1, -1/6, 0
Let k be 5/35 - 40/(-14). Let v(m) = m**3 + 6*m**2 + 5*m. Let p be v(-5). Factor p*y - 9/5*y**5 - 3/5*y**4 - 1/5*y**2 + y**k + 0.
-y**2*(y + 1)*(3*y - 1)**2/5
Let d(o) be the second derivative of -1/12*o**4 - 46*o + 0 + 1/2*o**2 + 1/6*o**3 - 1/20*o**5. Factor d(m).
-(m - 1)*(m + 1)**2
Let m(a) = 41*a**2 + 2*a + 1. Let l be m(-1). Find r, given that 20*r**3 + 12*r**2 - 20*r + 20*r**4 + 3*r**2 + 5 - l*r**4 = 0.
-1, 1/2, 1
Factor 14*o**3 - 2/3*o**5 - 8/3*o**4 + 0 + 0*o**2 + 0*o.
-2*o**3*(o - 3)*(o + 7)/3
Let w(n) be the first derivative of 0*n - 1/8*n**2 + 1/12*n**3 + 1. Suppose w(x) = 0. Calculate x.
0, 1
Let c(x) be the first derivative of x**5/300 - x**4/30 + x**3/10 - 5*x**2/2 - 20. Let g(s) be the second derivative of c(s). Suppose g(n) = 0. What is n?
1, 3
Let u(k) = -4*k - 62. Let p be u(-13). Let o be (-2)/5 + (-34)/p. Let -6/5*j**2 + 3/5*j - 6/5*j**o + 3/5*j**4 + 3/5 + 3/5*j**5 = 0. Calculate j.
-1, 1
Let t(v) be the first derivative of 0*v + 38 + 6/5*v**2 + 3/20*v**4 - v**3. Solve t(b) = 0.
0, 1, 4
Let s(z) be the third derivative of -z**7/70 + z**6/20 - 112*z**2. Suppose s(t) = 0. What is t?
0, 2
Let j be 27/(-15) + (-456)/(-95). Let q(o) be the first derivative of 2/5*o**2 - 5 - 2/15*o**j + 2/25*o**5 + 0*o - 1/5*o**4. Factor q(z).
2*z*(z - 2)*(z - 1)*(z + 1)/5
Let u(l) be the second derivative of 0*l**2 - 1/180*