o - 4*p, 5*o + 2*p = a*p + 29. Suppose -5*t**3 + 26*t**4 - 7*t**5 + 4*t - 7*t**3 - 6*t**2 - o*t**5 = 0. What is t?
-1/2, 0, 2/3, 1
Let x(o) be the first derivative of 289*o**4/8 + 34*o**3/3 + o**2 + 6. Find w such that x(w) = 0.
-2/17, 0
Let q(j) be the third derivative of 1/30*j**5 + 0 + 5/12*j**4 + 2*j**3 - 17*j**2 + 0*j. Solve q(f) = 0 for f.
-3, -2
Let k = -71 - -68. Let n be (-1 + k)/(5/(25/(-10))). Determine w, given that 0*w + 3/5*w**n - 1/5*w**3 - 4/5 = 0.
-1, 2
Let d be (-13 - -7) + 3*(0 - 1). Let l(c) = 10*c**3 + 69*c**2 - 9*c + 9. Let i(o) = 5*o**3 + 34*o**2 - 4*o + 4. Let h(b) = d*i(b) + 4*l(b). Factor h(n).
-5*n**2*(n + 6)
Solve -837/2*r + 27 - 9317/2*r**5 + 9801*r**4 - 7271*r**3 + 2520*r**2 = 0 for r.
3/11, 2/7, 1
Suppose 0*x + 10 = 5*x - 2*z, -10 = -5*x - 2*z. Determine k, given that -x*k + 12/7 - 6/7*k**2 = 0.
-3, 2/3
Let d be 7*-1 - ((-198)/27 - 135/81). Factor 1/4*r**4 + 1/4*r**5 - 1/4*r**d + 0 - 1/4*r**3 + 0*r.
r**2*(r - 1)*(r + 1)**2/4
Let u be (-24)/(-16) + 35/(-30). Factor -u - 2/3*k - 1/3*k**2.
-(k + 1)**2/3
Let a = -10 + 12. Factor 5 - a*o**2 + 14*o**2 - 11*o**2 - 6*o**2.
-5*(o - 1)*(o + 1)
Let z(q) = -4*q - 88. Let h be z(-22). Let f(b) be the first derivative of h*b**2 - 3 + 4/3*b**3 - 4*b. Determine w, given that f(w) = 0.
-1, 1
Suppose -13*m - 28*m**4 + 27*m**4 + 3*m**2 + 18*m - m**3 + 2 = 0. What is m?
-1, 2
Let p = -387 - -2323/6. Let n(y) be the first derivative of -p*y**6 - 2/5*y**5 + 1/4*y**4 + 0*y - 3 + 2/3*y**3 + 0*y**2. Factor n(q).
-q**2*(q - 1)*(q + 1)*(q + 2)
Let o = -9 + 9. Let v be ((-8)/(-20) + o)*10. Factor -6*h - h**3 + 3*h**2 + 0*h**3 + v*h**3.
3*h*(h - 1)*(h + 2)
Let i(t) be the second derivative of 0 - 3/2*t**2 - 1/4*t**4 - t**3 - 12*t. Factor i(a).
-3*(a + 1)**2
Let j(c) = 11*c**3 + 3 + 3*c - 9*c**3 + 4*c + 15*c**2. Let i(w) = 7*w**3 + 45*w**2 + 22*w + 8. Let n(q) = 3*i(q) - 8*j(q). Factor n(v).
5*v*(v + 1)*(v + 2)
Let m(k) be the first derivative of 5/2*k**2 + 5/3*k**3 + 12 + 0*k. Factor m(p).
5*p*(p + 1)
Let z(k) = -k**2 + 6*k + 23. Let s be z(8). Let d(l) = -l**4 - 11*l**2 - 19*l + 7. Let r(o) = 4*o**2 + 6*o - 2. Let q(y) = s*r(y) + 2*d(y). Factor q(h).
-2*h*(h - 2)*(h + 1)**2
Let f(x) = 20*x**2 + 4*x - 3. Let t be f(1). Let l be (0/t)/(-2*1). Suppose l + 2/9*o**5 - 2/9*o**2 + 4/9*o + 2/9*o**4 - 2/3*o**3 = 0. Calculate o.
-2, -1, 0, 1
Let v(n) be the third derivative of 1/140*n**7 + 1/448*n**8 + 1/160*n**6 + 0*n**4 + 0*n**3 + 0*n + 0 + 0*n**5 + 3*n**2. Factor v(q).
3*q**3*(q + 1)**2/4
Suppose 0 = -2*v - 2*p - 12, -6*v + 2*p + 9 = -5*v. Let m = 1 - v. Suppose -18*a**m + 53*a + 8 - 37*a**3 + 108*a**2 + 3*a - 19*a**3 - 98*a**4 = 0. Calculate a.
-1, -2/7, 1
Suppose 66*t - 53*t = 0. Let n(o) be the third derivative of t - 1/270*o**5 - 11*o**2 - 2/27*o**3 + 1/36*o**4 + 0*o. Factor n(l).
-2*(l - 2)*(l - 1)/9
Let q(u) = u**2 + 3*u + 4. Let h be q(-3). Let c be 3 + (-4)/h - 0. Suppose -3*a**2 + a**2 + 12 + a**2 + 4*a**c + 12*a = 0. What is a?
-2
Let w(s) be the third derivative of s**5/20 + 3*s**4/4 - 7*s**3/2 + 41*s**2 - 2*s. Determine a so that w(a) = 0.
-7, 1
Let j(r) be the second derivative of -r**6/285 + r**5/95 + r**4/38 + 2*r - 127. Suppose j(l) = 0. What is l?
-1, 0, 3
Let y = 4201/16756 + -3/4189. Factor 3/4*j + 0 + j**2 + y*j**3.
j*(j + 1)*(j + 3)/4
Suppose -5*l + 13 + 7 = 0. Suppose z**l - 2*z**3 + 2*z**4 - 7*z**4 - z**2 + 3*z**4 = 0. What is z?
-1, 0
Solve 21/2 + 2*z + 1/8*z**3 - 11/8*z**2 = 0 for z.
-2, 6, 7
Let i be (-4)/18 - (-1786)/6768. Let y(k) be the second derivative of k + 0 + 0*k**2 + i*k**3 + 1/15*k**6 + 1/40*k**5 - 5/48*k**4. Solve y(l) = 0.
-1, 0, 1/4, 1/2
Suppose 2*o = 5*n, -5*n + 2*o + 15 = 3*o. Suppose 9 = k - n*q, -3*q - 6 = -2*k + 3*k. Factor -4/13 - 34/13*i**k - 22/13*i - 10/13*i**4 - 42/13*i**2.
-2*(i + 1)**3*(5*i + 2)/13
Let n(y) be the first derivative of y**6/72 + y**5/24 + 22*y**3/3 - 20. Let m(t) be the third derivative of n(t). Factor m(c).
5*c*(c + 1)
Let n(p) be the second derivative of 22*p - 1/30*p**6 + 1/12*p**4 + 0*p**3 + 0*p**2 + 1/42*p**7 + 0 - 1/20*p**5. Determine a, given that n(a) = 0.
-1, 0, 1
Let t(g) be the third derivative of g**6/300 - g**5/75 - g**4/20 - 3*g**2 + 47. Suppose t(z) = 0. Calculate z.
-1, 0, 3
Let r(x) be the second derivative of -13 + 0*x**2 - 1/24*x**4 - x - 1/3*x**3. Solve r(l) = 0 for l.
-4, 0
Let l be ((-2)/(-1))/(171/24 + -7). Suppose -3*b + 2*i = -8, 4*b + 0*i - 3*i - 11 = 0. Factor -8*y - 4*y**b - l + y**2 - y**2 - 12*y.
-4*(y + 1)*(y + 4)
Let n = -9673/5 - -1935. Solve 2/5*a**2 + 0*a - n = 0 for a.
-1, 1
Let j be (2/6)/((-1)/(-12)). Factor 5 + 4 - 9 + 12*d**3 - 3*d**j - 9*d**2.
-3*d**2*(d - 3)*(d - 1)
Let n(l) be the second derivative of 4*l**7/21 - l**6/3 - 3*l**5/10 + 5*l**4/6 - l**3/3 + 8*l + 3. What is q in n(q) = 0?
-1, 0, 1/4, 1
Let h(c) = -c**2 - c. Let t(i) = -2*i**2 - 12*i - 18. Let p(m) = -4*h(m) + 4*t(m). Suppose p(g) = 0. What is g?
-9, -2
Suppose 13*n - 8*n + l - 16733 = 0, -2*n + 6704 = 4*l. Let d = -13259/4 + n. Factor -d - 5/4*x**2 - 25/2*x.
-5*(x + 5)**2/4
Let v(z) = 34*z - 17. Let n be v(3). Let f = n + -85. Factor -2/5*o**3 + f*o**2 + 6/5*o + 4/5.
-2*(o - 2)*(o + 1)**2/5
Let k(a) be the third derivative of -a**6/540 + 8*a**5/135 - 13*a**4/108 - 10*a**3/9 + 351*a**2. Factor k(b).
-2*(b - 15)*(b - 2)*(b + 1)/9
Let o(m) = 3*m**5 + 8*m**4 + 11*m**3 - 12*m - 6. Let x(z) = z**5 + z**4 - z**2 + 1. Let g(h) = 2*o(h) - 4*x(h). Find a, given that g(a) = 0.
-2, -1, 1
Let w(p) be the second derivative of 1/9*p**3 - 1/36*p**4 - 1/60*p**5 + 0 + 23*p + 0*p**2. Factor w(i).
-i*(i - 1)*(i + 2)/3
Factor 0*h + 0 + 1/4*h**4 - 15/4*h**2 + 1/2*h**3.
h**2*(h - 3)*(h + 5)/4
Let t(z) = 2*z**5 - z**3 - z**2 + z. Let y(d) = -7*d**5 + 25*d**4 + 56*d**3 + 56*d**2 + 19*d + 5. Let x(o) = -6*t(o) - y(o). Factor x(g).
-5*(g + 1)**5
Suppose 9*d = -6*d + 25*d - 17*d. Factor d - 1/7*u**2 + 1/7*u.
-u*(u - 1)/7
Factor -2/5*s + 43/5*s**2 + 0.
s*(43*s - 2)/5
Let d(p) be the first derivative of -p**6/36 + 2*p**5/15 + p**4/8 - 17*p**3/9 + 13*p**2/3 - 4*p + 7. Factor d(w).
-(w - 2)**3*(w - 1)*(w + 3)/6
Let u = -4293 + 4295. Suppose 0*z**u + 0*z + 0 + 1/2*z**4 - 2*z**3 = 0. What is z?
0, 4
Factor -4000 - 27*c**3 + 2800*c + 20*c**3 + 284*c**4 - 280*c**4 + 123*c**3 + 1080*c**2.
4*(c - 1)*(c + 10)**3
Let n(f) be the first derivative of -f**6/15 + 4*f**5/25 - 4*f**3/15 + f**2/5 + 378. Factor n(a).
-2*a*(a - 1)**3*(a + 1)/5
Let y be 7*(-26)/637 - 11/(-14). Let 0*t**2 + t**3 + 0 + 0*t**4 - 1/2*t**5 - y*t = 0. Calculate t.
-1, 0, 1
Let s(c) be the second derivative of -1/30*c**5 + 1/6*c**4 + 1/3*c**2 + 0 - 1/3*c**3 + 23*c. Factor s(i).
-2*(i - 1)**3/3
Let x(u) = u**3 - 5*u**2 - 5*u. Let r be x(5). Let a = r - -27. Factor -8*n**2 + a*n**5 + 2*n - 14*n**4 + 0*n**5 + 12*n**3 + 6*n**4.
2*n*(n - 1)**4
Let z(p) be the first derivative of -p**6/360 - p**5/60 + p**4/8 + 25*p**3/3 - 7. Let l(y) be the third derivative of z(y). Factor l(i).
-(i - 1)*(i + 3)
Let p(w) be the first derivative of -w**7/2940 + w**6/840 - w**4/168 + 4*w**3 + 17. Let x(v) be the third derivative of p(v). Factor x(y).
-(y - 1)**2*(2*y + 1)/7
Let a(i) = 5*i**2 - 9*i. Let b(h) = -4*h**2 + 10*h. Let j(s) = 4*a(s) + 6*b(s). Let j(w) = 0. Calculate w.
0, 6
Let g(t) be the second derivative of 5/6*t**3 + 0*t**5 + 0*t**2 - 1/1800*t**6 + 0 - 10*t + 1/30*t**4. Let k(h) be the second derivative of g(h). Factor k(c).
-(c - 2)*(c + 2)/5
Suppose -3/2*g**3 - 3 + 9/2*g + 0*g**2 = 0. Calculate g.
-2, 1
Let n = -11 - -16. Let d(q) = 7*q**3 - 7*q**2 - 4*q - 5. Let l(w) = 1886 + 4*w**3 - 3*w**2 - 2*w - w**3 - 1888. Let u(t) = n*l(t) - 2*d(t). Factor u(f).
f*(f - 2)*(f + 1)
Suppose 7*a - 11 = 3. Factor -20*f**3 - 28*f**2 - a + 39*f - 2*f - 5*f + 18.
-4*(f - 1)*(f + 2)*(5*f + 2)
Let q(l) = l**4 + l**3 - 1. Let o(j) be the first derivative of 3/4*j**4 + 9 - 4*j + 2/5*j**5 + 0*j**2 + 2/3*j**3. Let z(f) = -2*o(f) + 6*q(f). Factor z(u).
2*(u - 1)**2*(u + 1)**2
Factor -6/5 + 2/5*y**2 - 4/5*y.
2*(y - 3)*(y + 1)/5
Let f be 96/252*6 - (-2 + 4). Factor 0*p + 0 - f*p**2 - 2/7*p**3.
-2*p**2*(p + 1)/7
Let g(r) be the third derivative of r**8/110880 - r**7/6930 + r**6/990 - r**5/10 + 46*r**2. Let o(h) be the third derivative of g(h). Factor o(s).
2*(s - 2)**2/11
Let p be -3*(2/1)/(-2). Let g = -112 + 115. Find x such th