1547. Let v = 878/663 + x. Find i such that -v*i**2 + 0*i + 2/3*i**4 + 0*i**3 + 2/3 = 0.
-1, 1
Let f(r) = -r**3 + 6*r**2 + 2*r + 3. Let q be f(6). Suppose 2 - 11 = -5*z + 3*l, -4*z + q = -5*l. Factor z*w - 4*w**2 - w + 4*w + 1.
-(w - 1)*(4*w + 1)
Let a = -12 - -8. Let z be (-18)/a - (-3)/6. Factor -4/7*x**3 + 2/7*x + 0*x**2 + 0 + 2/7*x**z + 0*x**4.
2*x*(x - 1)**2*(x + 1)**2/7
Let u(g) be the first derivative of g**5/15 - g**4/2 + 13*g**3/9 - 2*g**2 + 4*g/3 - 26. Factor u(q).
(q - 2)**2*(q - 1)**2/3
Let z(o) be the third derivative of -o**8/168 + o**7/105 + o**6/10 + o**5/15 - 5*o**4/12 - o**3 - 43*o**2. Find a such that z(a) = 0.
-1, 1, 3
Suppose 4*t = 2*t. Suppose 2*a = -2*a + 24. Find i, given that -2 + 5*i + t + a*i - 9*i**2 = 0.
2/9, 1
Let w(m) be the second derivative of -m**6/360 + m**4/24 + m**3/9 + 3*m**2/2 - m. Let h(r) be the first derivative of w(r). Factor h(a).
-(a - 2)*(a + 1)**2/3
Suppose -3*t = -2*f + 38, -3*t = -3*f + 2*f + 13. Factor -19*s + 3 + 1 - s + f*s**2.
(5*s - 2)**2
Let u(w) be the third derivative of 1/90*w**6 - 1/504*w**8 + 0 - 2/315*w**7 - 3*w**2 + 0*w + 2/9*w**3 + 7/36*w**4 + 4/45*w**5. Determine j so that u(j) = 0.
-1, 2
Let c(v) = -v**3 + 1. Let k(n) = -n**2 + n. Let f(m) = -c(m) - k(m). Find q such that f(q) = 0.
-1, 1
Let h(d) be the first derivative of -d**5 - 1/2*d**4 - 1/4*d**6 + 4/3*d**3 + 0*d + 0*d**2 - 1. What is a in h(a) = 0?
-2, 0, 2/3
Suppose 0 = 2*y - 5*y - 3, 11 = 4*z + 5*y. Suppose 3*m = -z*a + 21, -3 = 4*m - 5*a - 0. Factor -1/3 + 1/3*p**2 + 1/3*p - 1/3*p**m.
-(p - 1)**2*(p + 1)/3
Let d(p) = p**3 - 4*p**2 - 5*p + 3. Let n(t) = -3*t - t**3 + 4 - 4*t**2 + t**3 - 3*t + 2*t**3. Let o(c) = -4*d(c) + 3*n(c). Suppose o(g) = 0. What is g?
-1, 0
Determine z, given that 0 - 5/3*z**2 + 4/3*z**3 + 2/3*z - 1/3*z**4 = 0.
0, 1, 2
Suppose 3*j - 2*j = 1. Let q(s) = -4*s**2 + 6*s**2 + s**2 - 4*s**2. Let y(a) = 2*a**2. Let p(t) = j*y(t) + 3*q(t). Factor p(k).
-k**2
Factor 0*l + 0 - 4/9*l**5 + 0*l**2 - 4/9*l**4 + 0*l**3.
-4*l**4*(l + 1)/9
Let s(p) = 8*p**4 - 8*p**3 + 4*p**2 - 4*p + 4. Let k(v) = v**4 + v**3 - v**2 - v + 1. Let x(q) = -4*k(q) + s(q). Determine z, given that x(z) = 0.
0, 1, 2
Let b(d) be the first derivative of -3*d**4/4 - 3*d**3 - 9*d**2/2 - 3*d - 3. Suppose b(f) = 0. Calculate f.
-1
Let w(p) be the third derivative of -1/300*p**6 + 0 + 0*p**4 + 0*p + 0*p**3 + 1/150*p**5 - 5*p**2. Factor w(z).
-2*z**2*(z - 1)/5
Let 8/13*a**3 + 2/13 - 8/13*a - 2/13*a**2 = 0. Calculate a.
-1, 1/4, 1
Let n(u) = -3*u**4 + 3*u**2 + 6*u - 6. Let m(h) = -7*h**4 + h**3 + 7*h**2 + 12*h - 13. Let g(v) = 6*m(v) - 13*n(v). Factor g(t).
-3*t*(t - 2)*(t - 1)*(t + 1)
Let k = -27 - -44. Let h = k + -17. Suppose 0*f**2 + 4/7*f**4 + 0*f + 2/7*f**3 + 2/7*f**5 + h = 0. Calculate f.
-1, 0
Determine f, given that 2/13*f + 0 + 2/13*f**2 - 2/13*f**4 - 2/13*f**3 = 0.
-1, 0, 1
Let u(s) be the third derivative of s**5/72 - s**4/72 + 3*s**2. Let u(d) = 0. Calculate d.
0, 2/5
Let v(s) = s**2 - s. Let n(g) = -g**3 - 2*g**2 + g + 2. Let c(f) = n(f) + 6*v(f). Find t such that c(t) = 0.
1, 2
Suppose -2*d - 12 = -b, 0*b + 2*d = 4*b - 24. Factor -k**3 - 1/3*k**5 + k**b + 0 + 1/3*k**2 + 0*k.
-k**2*(k - 1)**3/3
Let p(z) = 10*z**3 + 12*z**2 - 4*z - 6. Let v(h) = -9*h**3 - 12*h**2 + 4*h + 7. Let i(a) = 5*p(a) + 6*v(a). Suppose i(m) = 0. What is m?
-3, -1, 1
Let t = -994 + 994. Find m such that 2/7*m**4 - 2/7*m**2 + t*m + 0 + 0*m**3 = 0.
-1, 0, 1
Factor 0*h**3 - 1/6*h + 1/6*h**5 + 0 + 1/3*h**4 - 1/3*h**2.
h*(h - 1)*(h + 1)**3/6
Let w = -263 - -265. Find y, given that -2/5 + 1/5*y + 1/5*y**w = 0.
-2, 1
Let s(x) = -x**2 - x - 1. Let r(p) = -3*p**5 - 12*p**4 - 12*p**3 + 18*p**2 + 27*p + 18. Let o(j) = r(j) + 12*s(j). Solve o(u) = 0 for u.
-2, -1, 1
Let b(t) be the third derivative of -6*t**2 + 1/20*t**6 + 0*t**3 + 0 - 1/8*t**5 + 1/8*t**4 + 0*t - 1/140*t**7. Factor b(y).
-3*y*(y - 2)*(y - 1)**2/2
Let y be 3/1 + 323/(-119). Factor y*x**2 + 0 + 0*x.
2*x**2/7
Let t(d) be the second derivative of 2*d**2 + 2/3*d**4 - d - 1/10*d**5 - 5/3*d**3 + 0. Solve t(y) = 0.
1, 2
Let m(f) be the third derivative of -f**5/12 + 35*f**4/12 - 245*f**3/6 - 21*f**2. Determine k so that m(k) = 0.
7
Let y(p) be the first derivative of -1/6*p**3 - 1/12*p**4 + 7/240*p**5 - 1/2*p**2 + 2 + 0*p + 1/96*p**6. Let w(r) be the second derivative of y(r). Factor w(g).
(g - 1)*(g + 2)*(5*g + 2)/4
Let h(p) be the third derivative of p**6/30 - p**5/5 - p**4/6 + 2*p**3 + 2*p**2 - 33. Suppose h(d) = 0. What is d?
-1, 1, 3
Let i(r) be the third derivative of 0 + 2*r**2 + 0*r**6 + 0*r**3 - 1/30*r**5 + 1/105*r**7 + 0*r + 0*r**4. Determine x, given that i(x) = 0.
-1, 0, 1
Solve 6*h**3 + 3 - 6*h + 4*h**4 - 5*h**4 - 2*h**4 = 0.
-1, 1
Let c(b) = b**2 + 14*b - 26. Let t be c(-16). Factor -t*v**3 + 8/3*v + 0*v**2 + 0.
-2*v*(3*v - 2)*(3*v + 2)/3
Let a be 5/((-315)/(-32)) + 4/(-18). Let w(k) = -k**3 + 7*k**2 - 6*k + 3. Let q be w(6). Factor -2/7*p**q + 0*p**2 + 0 + a*p.
-2*p*(p - 1)*(p + 1)/7
Factor -2*a**2 + a - 2 + 3*a - a + a.
-2*(a - 1)**2
Let y(u) be the third derivative of u**5/20 - u**3/2 - 4*u**2. Solve y(r) = 0.
-1, 1
Let a(k) = k - 11. Let q be a(13). Suppose -q*n + 0*n + 8 = 0. Let 2/7*f**n + 0 - 2/7*f**3 + 2/7*f - 2/7*f**2 = 0. What is f?
-1, 0, 1
Let o(i) = -i + 1. Let g(u) = 7*u**2 - 3*u + 5. Let x(m) = -4*m**3 - 1. Suppose -7 = -q - 8. Let c be x(q). Let h(n) = c*g(n) - 15*o(n). Factor h(l).
3*l*(7*l + 2)
Find w such that 7/3*w**2 - w**3 + 0 + 5/3*w**5 - 2/3*w - 7/3*w**4 = 0.
-1, 0, 2/5, 1
Suppose -2*r - 3*r = -50. Suppose -2 + 154*b**3 + 224*b**3 - 84*b - 243*b**4 - 39*b**2 - r = 0. What is b?
-2/9, 1
Suppose -12 = -5*r + 2*r. Let h(m) be the second derivative of 1/8*m**r + 0 - 1/40*m**5 + 0*m**2 + m - 1/20*m**6 + 1/12*m**3. Find d such that h(d) = 0.
-1, -1/3, 0, 1
Find l, given that -l**2 - 1/4*l**3 - 1/2 - 5/4*l = 0.
-2, -1
Let u(k) be the first derivative of -3/7*k**2 - 2/7*k - 4/21*k**3 + 1/21*k**6 + 1 + 6/35*k**5 + 1/7*k**4. Let u(p) = 0. Calculate p.
-1, 1
Let a(d) be the second derivative of 0 + 1/20*d**5 + 0*d**2 - 1/4*d**4 - 1/3*d**3 + 1/10*d**6 + 1/42*d**7 - 3*d. Factor a(c).
c*(c - 1)*(c + 1)**2*(c + 2)
Let j(g) be the first derivative of -3*g**5/5 - 9*g**4/2 + 8*g**3 + 9*g**2 - 21*g - 15. Factor j(u).
-3*(u - 1)**2*(u + 1)*(u + 7)
Let x(m) be the second derivative of -m**4/6 + 2*m**3/3 + 8*m**2 - 18*m. Solve x(s) = 0.
-2, 4
Find k such that 0 + 0*k**2 - 3*k - 3/2*k**4 + 27/4*k**3 - 9/4*k**5 = 0.
-2, -2/3, 0, 1
Suppose -13*m = -0*m. Factor -8/5*q + m - 2/5*q**3 + 8/5*q**2.
-2*q*(q - 2)**2/5
Let f(p) = p**2 + 7*p + 10. Let v = -21 - -15. Let y be f(v). Factor 1/2*j**y - 1/2*j**3 - 1/2*j**2 + 1/2*j + 0.
j*(j - 1)**2*(j + 1)/2
Solve 1/4*l**4 + 3*l**2 + 3/4 + 3/2*l**3 + 5/2*l = 0.
-3, -1
Let c(k) be the second derivative of -k**6/60 + k**5/20 + 27*k. Solve c(d) = 0 for d.
0, 2
Suppose 3*i + 34 = 34. Let u(h) be the third derivative of 3*h**2 + 0*h**5 + 0*h**4 + 0 + i*h**3 + 0*h + 1/105*h**7 + 0*h**6. Factor u(j).
2*j**4
Let n(v) be the first derivative of -2*v**3/21 + 2*v**2/7 + 6*v/7 + 19. Suppose n(u) = 0. Calculate u.
-1, 3
Let p(i) be the first derivative of -1 + 1/4*i**3 + 1/4*i + 3/8*i**2 + 1/16*i**4. Factor p(k).
(k + 1)**3/4
Suppose 4*w - 5 = 3. Factor -2/9*j**w + 0 + 4/9*j.
-2*j*(j - 2)/9
Suppose -2*m - 9 = 19. Let x(n) = -4*n**4 + 3*n**3 - 3*n - 3. Let c(l) = -9*l**4 + 7*l**3 - 7*l - 7. Let j(z) = m*x(z) + 6*c(z). Factor j(i).
2*i**4
Let f(a) be the second derivative of -a**10/166320 - a**9/83160 + a**4/6 - 2*a. Let h(p) be the third derivative of f(p). Factor h(g).
-2*g**4*(g + 1)/11
Let y(z) be the first derivative of -z**4/12 + 5*z**3/3 - 25*z**2/2 + 125*z/3 - 13. Solve y(m) = 0 for m.
5
Let c(t) = 16*t**3 + 20*t**2 - 16*t - 12. Let o(b) = 15*b**3 + 19*b**2 - 17*b - 11. Let d(w) = -3*c(w) + 4*o(w). Let d(r) = 0. What is r?
-2, -1/3, 1
Let l(b) = 2*b**2 - b**2 + 0*b**2 + 2 - 3*b. Let t be l(2). Factor 2/11*y**4 + 0*y**3 + t*y - 2/11*y**2 + 0.
2*y**2*(y - 1)*(y + 1)/11
Suppose -z - 3*t + 17 = 0, -4*z = t - 25 + 1. Let 16*q**2 - 2*q - 4*q**z + 2 + 3*q**5 + 6*q**4 - 7*q - 14*q**3 = 0. What is q?
1, 2
Let q(a) = 23*a**4 + 577*a**3 + 7597*a**2 + 32947*a + 8. Let g(f) = 15*f**4 + 385*f**3 + 5065*f**2 + 21965*f + 5. Let i(d) = 8*g(d) - 5*q(d). Factor i(n).
5*n*(n + 13)**3
Let h(