2, -1
Let p(s) = -8*s + 8*s - 14*s + 20*s**2 - 15*s + 9. Let t(q) = -4*q**2 + 6*q - 2. Let a(i) = 2*p(i) + 11*t(i). Solve a(y) = 0 for y.
1
Let h be (-4)/(-8)*(-5 + 11). Suppose -8*m = h*m + 6*m. Solve -2/5*a**5 + m + 0*a**2 + 0*a**3 + 2/5*a**4 + 0*a = 0 for a.
0, 1
Let k(x) = 20*x**5 + 31*x**4 + 13*x**3 - 2*x**2 + x + 5. Let i(r) = -62*r**5 - 94*r**4 - 38*r**3 + 6*r**2 - 4*r - 16. Let v(l) = -5*i(l) - 16*k(l). Factor v(z).
-2*z*(z + 1)**3*(5*z - 2)
Let y(w) be the first derivative of -2*w**3/3 - 33*w**2 + 509. Factor y(q).
-2*q*(q + 33)
Suppose 57 - 30 = 9*r. Suppose 3*s - 15 = -2*b, -3*s + 2*s + 4*b = -5. Solve 6*z**4 + 2*z - 7*z**4 + 2*z**3 + z**s - 5*z**r + z**2 = 0 for z.
-1, 0, 1, 2
Let y(a) be the first derivative of -169*a**3/9 - 104*a**2/3 - 64*a/3 + 133. Factor y(x).
-(13*x + 8)**2/3
Let m be (-5 + 2 + -5)*(-15)/420. Factor 0 - 9/7*p**3 - p**2 + m*p.
-p*(p + 1)*(9*p - 2)/7
Let l(b) be the third derivative of -b**8/33600 - b**7/3150 - b**6/720 - b**5/300 + 3*b**4/8 - 12*b**2. Let f(a) be the second derivative of l(a). Factor f(x).
-(x + 1)**2*(x + 2)/5
Let l(k) be the second derivative of -k**5/60 + 7*k**4/48 - k**3/4 + 11*k**2/2 - 13*k. Let r(w) be the first derivative of l(w). Factor r(s).
-(s - 3)*(2*s - 1)/2
Let h = 6889 - 6887. Let o = -2 - -5. Find l, given that l + 1/3 + 1/3*l**o + l**h = 0.
-1
Let u(p) be the second derivative of -p**8/1008 - p**7/210 + p**5/45 - 17*p**2/2 + 30*p. Let s(l) be the first derivative of u(l). Let s(y) = 0. What is y?
-2, 0, 1
Let n(z) be the first derivative of -z**3/3 + 7*z**2/2 + 2*z - 1. Let h be n(7). Find q, given that -6*q**h + 3*q - 6*q**2 + 9*q**2 = 0.
0, 1
Let w = -40 - -37. Let r(n) = n**4 + 15*n**3 + 16*n**2 + 3*n + 1. Let b(t) = -4*t**4 - 45*t**3 - 48*t**2 - 9*t - 2. Let j(f) = w*b(f) - 8*r(f). Factor j(z).
(z + 1)**2*(z + 2)*(4*z - 1)
Let f(j) = 4*j**4 - 5*j**3 - 21*j**2 - 4*j + 17. Let v(o) = -o**4 + o**3 + 5*o**2 + o - 4. Suppose 36 = -p - 3*p. Let u(w) = p*v(w) - 2*f(w). Solve u(c) = 0.
-2, -1, 1
Let m(s) = -s**2 - 15*s - 11. Let y be m(-15). Let a = -8 - y. Determine x, given that 6 + 2*x**2 + 3*x**a - 9*x + 0 - 2*x**2 = 0.
-2, 1
Let f(r) be the second derivative of 3/95*r**5 - 8*r + 1/285*r**6 + 4/19*r**3 + 0 + 4/19*r**2 + 13/114*r**4. Factor f(j).
2*(j + 1)**2*(j + 2)**2/19
Let m(q) be the second derivative of q**5/30 - 3*q**3 + 18*q**2 - 9*q. What is u in m(u) = 0?
-6, 3
Let f(y) be the third derivative of 13*y**2 + 1/24*y**4 + 1/60*y**5 + 0*y + 0 - 1/3*y**3. Find n, given that f(n) = 0.
-2, 1
Let p(n) be the first derivative of n**4/6 + 4*n**3/3 + 5*n**2/3 - 8*n + 132. Suppose p(y) = 0. Calculate y.
-4, -3, 1
Let o(c) = -9*c**2 - 146*c + 179. Let f(l) = 3*l**2 + 48*l - 60. Let w(h) = 8*f(h) + 3*o(h). Factor w(m).
-3*(m - 1)*(m + 19)
Let w(n) be the third derivative of 1/4*n**4 + 0 + 0*n + 5*n**2 + 0*n**3 - 1/20*n**5. Factor w(g).
-3*g*(g - 2)
Let t be 206/12*-10 - 2/(-3). Let l = t - -171. Factor l*g + 1/2*g**3 + 0 - g**2 + 3/2*g**4.
g**2*(g + 1)*(3*g - 2)/2
Let n(r) = -15*r**2 + 15. Let m(i) = -7*i**2 + 7. Let p be 12/2 - (4 + -2). Suppose 0*u - 36 = p*u. Let g(q) = u*m(q) + 4*n(q). Factor g(x).
3*(x - 1)*(x + 1)
Let w(m) be the second derivative of m**6/10 - 57*m**5/20 + 39*m**4/2 + 70*m**3 - 300*m**2 - 53*m. Factor w(s).
3*(s - 10)**2*(s - 1)*(s + 2)
Factor 6/7*j**2 - 3/7*j**4 + 3/7*j - 6/7*j**3 - 3/7 + 3/7*j**5.
3*(j - 1)**3*(j + 1)**2/7
Let u = 707 + -704. Factor 0 - 4/5*r**2 + 0*r - 4/5*r**u.
-4*r**2*(r + 1)/5
Let a(l) be the second derivative of -l**3 + 1/36*l**4 + 27/2*l**2 + 42*l + 0. Find i such that a(i) = 0.
9
Let g be (-1)/(-4)*(-96)/(-36). Factor 2/3*a**3 - g - 7/3*a**2 + 7/3*a.
(a - 2)*(a - 1)*(2*a - 1)/3
Suppose u = 8*j - 3*j - 70, -3*j + 20 = -5*u. Let g be (2/9)/(j/(270/12)). Suppose 0 + b + g*b**2 = 0. Calculate b.
-3, 0
Determine v, given that 96 + 138*v**3 + 130*v + 420*v - 122*v**4 + 264*v**2 + 442*v**2 - 6*v**5 - 2*v**5 = 0.
-16, -1, -1/4, 3
Let h(n) be the third derivative of -1/36*n**4 + 1/90*n**6 - 2/45*n**5 + 2/9*n**3 - 1/504*n**8 + 0 + 2*n**2 + 0*n + 2/315*n**7. Suppose h(c) = 0. Calculate c.
-1, 1, 2
Let q(l) = l**3 - 14*l**2 + 12*l + 18. Let s be q(13). Suppose 11*h**5 - 9*h**s + 1 - 8 + 10*h**4 - 2*h**2 - 16*h + 14*h**3 - 1 = 0. Calculate h.
-2, -1, 1
Let 1/3*r**2 + 2*r + 0 = 0. Calculate r.
-6, 0
Suppose 128/5*p + 2/5*p**3 - 38/5*p**2 - 24 = 0. What is p?
2, 15
Suppose 0 = q - 11 + 1. Let l be (-12)/(-10)*q/4. Find a, given that -a**3 + 9*a - 2*a**3 + 0*a**l - 6 = 0.
-2, 1
Let c(l) be the first derivative of -l**8/1470 + l**7/420 + l**6/630 + 13*l**3/3 + 7. Let a(b) be the third derivative of c(b). What is m in a(m) = 0?
-1/4, 0, 2
Suppose 4*f + 4*w - 68 = 0, 4*w = -4*f - w + 65. Suppose 0 = -4*l - f, 2*o + 9 = -2*l - 1. Let o*u + 0 + 2*u**3 - 4/5*u**2 + 14/5*u**4 = 0. What is u?
-1, 0, 2/7
Let h be 507/90 + -2 + 42/(-140). Solve h*y - 4*y**2 + 2*y**3 - 1/3*y**4 - 1 = 0 for y.
1, 3
Let o(d) be the second derivative of d**4 - 16*d**3/3 + 10*d**2 + 2*d + 145. Factor o(l).
4*(l - 1)*(3*l - 5)
Let m(b) = -4*b + 7*b**5 + 0*b**2 + 0 - 2 - 5*b**4 + 5 + 8*b**2. Let w(g) = -8*g**5 + 4*g**4 - 8*g**2 + 4*g - 4. Let j(s) = 4*m(s) + 3*w(s). Factor j(z).
4*z*(z - 1)**3*(z + 1)
Let g(v) be the first derivative of 1 + 0*v**2 + 2*v**3 + 0*v - 21/4*v**4. Factor g(i).
-3*i**2*(7*i - 2)
Let c(b) = 3*b**4 - 3*b**3 + 9*b**2 + 15*b. Let f(t) = -t**4 - t**3 - t**2 - t. Let a(x) = c(x) + 6*f(x). Suppose a(n) = 0. What is n?
-3, -1, 0, 1
Suppose -2*g = 7*g - 27. Let u(i) be the third derivative of -1/27*i**3 - 1/540*i**6 + 0 - 1/36*i**4 - g*i**2 + 0*i - 1/90*i**5. Factor u(v).
-2*(v + 1)**3/9
Let w(d) be the second derivative of 11*d + 1/3*d**3 + 0 - 1/3*d**2 + 2/9*d**4. Find f, given that w(f) = 0.
-1, 1/4
Solve -44/9*p**2 + 46/9 + 16/3*p - 16/3*p**3 - 2/9*p**4 = 0.
-23, -1, 1
Let f = -3 + 0. Let z be ((-3 + f)/(-3))/1. Suppose -3*i**2 + 2 - i**2 + i**z + i**2 = 0. Calculate i.
-1, 1
Let v(f) be the third derivative of f**6/180 + 7*f**5/90 + 7*f**4/36 - 5*f**3/3 - f**2 + 60*f. Factor v(w).
2*(w - 1)*(w + 3)*(w + 5)/3
Factor -1/2*b**2 + 0 + 1/4*b + 1/4*b**3.
b*(b - 1)**2/4
Let d be ((-29)/1131)/((-4)/52). Let c be 2/(8 - 0)*2. Factor 1/3*q**2 - 1/2*q - c*q**4 + 1/6*q**5 + d*q**3 + 1/6.
(q - 1)**4*(q + 1)/6
Factor 0 - 66/5*t + 1/5*t**2.
t*(t - 66)/5
Let y(h) be the first derivative of 4*h**3/3 + 6*h**2 - 39. Factor y(g).
4*g*(g + 3)
Let w(x) be the second derivative of 0*x**3 + 0*x**2 + 5*x + 0 - 2*x**5 - 1/6*x**6 - 20/3*x**4. Factor w(g).
-5*g**2*(g + 4)**2
Suppose -25 = -5*y - 0*y. Let k = y + -2. Factor -4*j**2 - j**k + 0 - j + 2 - 4*j - 4.
-(j + 1)**2*(j + 2)
Let z = -28 + 31. Factor 40*x - 6*x**z + 27 + 9*x**3 + 2*x**3 + 25*x**2 - 7.
5*(x + 1)*(x + 2)**2
Let h(b) be the third derivative of 0 + 13/210*b**5 - 2*b**2 + 1/70*b**6 - 30*b + 4/21*b**3 + 1/735*b**7 + 1/7*b**4. Determine c so that h(c) = 0.
-2, -1
Let g = -34 - -37. Factor 19845*k**3 + 16911*k**3 - 7500*k**2 - 5506*k**g + 600*k - 16.
2*(25*k - 2)**3
Suppose 2*b = -m + 162 + 216, 0 = -4*m + 4*b + 1512. Let s be 516/m + (2/9)/(-1). Let 2/7*x**2 + 8/7 - s*x = 0. Calculate x.
2
Determine g so that g**2 + 40 - 4*g**3 + 11*g - g**3 - 5*g**2 - 6*g**2 + 9*g = 0.
-2, 2
Let n be 1*(-3)/12*(-2 + -6). Suppose -3*k + 3 = -d - n*k, 5*d = -4*k + 30. Let 21/4*j**5 + 33/4*j**3 + 0 - 3/2*j**d - 12*j**4 + 0*j = 0. Calculate j.
0, 2/7, 1
Let h(w) be the third derivative of -w**6/168 - w**5/105 + 61*w**4/168 - 2*w**3/7 - 417*w**2. What is t in h(t) = 0?
-4, 1/5, 3
Let d(y) be the second derivative of -5*y**4/12 + 65*y**3/3 - 120*y**2 - 679*y. Factor d(o).
-5*(o - 24)*(o - 2)
Let q(k) = -48*k**3 + 74*k**2 - 29*k. Let c be (13 - -1)*25/(-50). Let u(t) = 144*t**3 - 223*t**2 + 88*t. Let z(f) = c*q(f) - 2*u(f). Factor z(n).
3*n*(4*n - 3)**2
Let q(y) be the third derivative of -y**5/60 - 11*y**4/24 + 2*y**3 - 39*y**2. Find m such that q(m) = 0.
-12, 1
Find j, given that 1/3*j**5 + 2/3*j**4 + 5/3*j - 8/3*j**2 + 2 - 2*j**3 = 0.
-3, -1, 1, 2
Let w be 3/(-15) - 1409/455. Let u = w + 54/13. Factor 4/7*a**3 + 0*a**2 + 0 + 0*a - u*a**4 + 2/7*a**5.
2*a**3*(a - 2)*(a - 1)/7
Determine d so that 52/3 - 64*d**2 + 14/3*d**3 + 42*d = 0.
-2/7, 1, 13
Let q = 29 - 24. Determine z so that -19*z - 392*z**2 - 65*z**5 + 25*z**4 + 504*z**3 + 135*z - 43