Let r(o) = o**2 - o - 1. Let g be r(-2). Let f(w) = -4*w**2 + 11*w - 2. Let z(x) = 2*x**2 - 6*x + 1. Let u(a) = g*z(a) + 3*f(a). Find i such that u(i) = 0.
1/2, 1
Let a(i) be the first derivative of 1/20*i**5 + 0*i**4 - i - 1/84*i**7 + 0*i**3 + 1 + 0*i**2 + 1/60*i**6. Let p(m) be the first derivative of a(m). Factor p(n).
-n**3*(n - 2)*(n + 1)/2
Factor -2/9*y**2 + 2/9*y - 2/9*y**3 + 2/9*y**4 + 0.
2*y*(y - 1)**2*(y + 1)/9
Suppose 6*o = 3*o + 3. Let -f**2 - o - f + 4*f + 2*f**2 - 3*f**3 + 0*f**3 = 0. Calculate f.
-1, 1/3, 1
Let d(c) be the second derivative of 1/15*c**3 - 7*c - 3/20*c**4 + 0*c**2 + 0 + 3/25*c**5 - 1/30*c**6. Factor d(v).
-v*(v - 1)**2*(5*v - 2)/5
Let x(b) = b**2 - b - 4. Let d be x(3). Suppose -8*c + d + 9 - 3 + 2*c**2 = 0. Calculate c.
2
Factor 24/5*f + 3*f**2 - 12/5.
3*(f + 2)*(5*f - 2)/5
Suppose -89*u = -84*u. Factor 4/3*n**2 + 2/3*n**4 + 0 + u*n + 2*n**3.
2*n**2*(n + 1)*(n + 2)/3
Factor -8*q + 44*q**2 - 39*q**3 + 11*q**4 + 14*q**4 - 31*q**3.
q*(q - 2)*(5*q - 2)**2
Factor 4/5*z**4 + 8/5*z**3 + 0*z + 0*z**2 + 0.
4*z**3*(z + 2)/5
Let m(f) be the first derivative of -f**4/20 + f**2/10 - 4. Let m(j) = 0. Calculate j.
-1, 0, 1
Determine m so that -4/7*m**2 - 24/7 - 20/7*m = 0.
-3, -2
Let b = 3 - 1. Solve -5*y**2 + 2*y**2 + 4*y**b + y = 0 for y.
-1, 0
Factor 2/11*n**4 + 6/11*n**2 - 6/11*n**3 - 2/11*n + 0.
2*n*(n - 1)**3/11
Let o = -89/4 - -23. Let w(v) be the first derivative of -7/15*v**5 + 0*v**2 + 0*v + 1 + o*v**4 - 2/9*v**3. Find s such that w(s) = 0.
0, 2/7, 1
Let r(y) = -5*y**4 - 17*y**3 - 31*y**2 - 19*y. Let h(n) = 11*n**4 + 35*n**3 + 63*n**2 + 39*n. Let g(i) = 6*h(i) + 14*r(i). Let g(a) = 0. What is a?
-4, -2, -1, 0
Let d(t) be the second derivative of -t**6/240 + t**5/40 - t**3/3 - 3*t**2/2 - t. Let s(q) be the first derivative of d(q). Suppose s(h) = 0. What is h?
-1, 2
Suppose -35 - 7*m**3 + 0*m**3 + 38 + 3*m + 4*m**3 - 3*m**2 = 0. What is m?
-1, 1
Let c(f) be the second derivative of -f**4/3 - 14*f**3/3 + 16*f**2 + 2*f + 18. Factor c(v).
-4*(v - 1)*(v + 8)
Let v be (-10)/(-15) + 28/(-33). Let m = 8/77 - v. Factor -m*p**3 + 0*p**2 + 0 + 0*p + 2/7*p**4.
2*p**3*(p - 1)/7
Let q(d) be the second derivative of 0 - 1/60*d**5 + 0*d**3 + 1/48*d**4 + 1/240*d**6 - 3*d + 1/2*d**2. Let z(j) be the first derivative of q(j). Factor z(u).
u*(u - 1)**2/2
Let m = -3 + 14. Suppose -2*b = m - 1, -13 = s + 3*b. Factor 0*z**3 + 0*z**s + 0*z**4 + 2/5*z**5 + 0 + 0*z.
2*z**5/5
Let z(f) be the second derivative of f**5/40 - f**4/12 - 2*f**3/3 + 36*f. Suppose z(d) = 0. What is d?
-2, 0, 4
Let h(i) be the third derivative of -1/15*i**6 + 0*i + 0 + 0*i**4 - 1/60*i**5 + 2*i**2 + 0*i**3 - 8/105*i**7. Let h(q) = 0. What is q?
-1/4, 0
Suppose 0 = -2*m + 5*f - 14, 0 = -2*m - 2*f + 1 + 13. Suppose -13 = -4*x + 3. Factor -6*a**4 + 2*a**4 + 5*a**x - a**m.
a**3*(a - 1)
Let q(t) be the second derivative of -3*t**5/140 - 5*t**4/28 - t**3/2 - 9*t**2/14 - 11*t. Factor q(u).
-3*(u + 1)**2*(u + 3)/7
Factor 0*c - 20/7*c**2 - 2/7*c**3 + 0.
-2*c**2*(c + 10)/7
Let n(q) be the first derivative of q**4/3 + 4*q**3/9 - 4*q**2/3 - 6. Factor n(u).
4*u*(u - 1)*(u + 2)/3
Let d(y) = -y**3 - 20*y**2 - 19*y + 2. Let m be d(-19). Factor -2/3 + 0*p + 2/3*p**m.
2*(p - 1)*(p + 1)/3
Suppose 2*o + 5 - 11 = 0. Determine c, given that -o*c**2 + 4*c**2 - 5 + 2*c + 4 + 2 = 0.
-1
Let y = -172 - -175. Let t(v) be the second derivative of -2/3*v**y + 0 + 5/48*v**4 + 2*v + 7/80*v**5 + 1/2*v**2. Determine m, given that t(m) = 0.
-2, 2/7, 1
Let v + 3*v**2 + 0*v + v - v**2 = 0. What is v?
-1, 0
Factor 3/4*d**3 + 3/4*d**2 - 3/4*d + 0 - 3/4*d**4.
-3*d*(d - 1)**2*(d + 1)/4
Factor 0*w + 0 - 3/2*w**2.
-3*w**2/2
Let k = 2477/4 + -617. Factor -3/4*j + k*j**2 + 0.
3*j*(3*j - 1)/4
Let n(s) be the third derivative of -s**5/270 + 4*s**3/27 - 5*s**2. Factor n(r).
-2*(r - 2)*(r + 2)/9
Let w be ((-6)/10)/((-5)/((-25)/(-2))). Factor -1/4*a**5 - 13/4*a**3 + 0 + 3*a**2 - a + w*a**4.
-a*(a - 2)**2*(a - 1)**2/4
Let u be (-2)/8 - 45/(-20). Determine l, given that -27*l**u + 12 + 4*l + 23*l**2 + 4*l = 0.
-1, 3
Suppose -3*s + d + 0 = -2, -d - 6 = -5*s. Suppose 2/5*h**s + 2/5*h - 2/5 - 2/5*h**3 = 0. Calculate h.
-1, 1
Let l be ((-171)/36 + 4)/((-6)/16). Factor -l*q - 2/3*q**3 + 2*q**2 + 2/3.
-2*(q - 1)**3/3
Let b(s) be the third derivative of -s**8/336 + s**7/70 + s**6/120 - 7*s**5/60 + 2*s**3/3 - 34*s**2. Factor b(a).
-(a - 2)**2*(a - 1)*(a + 1)**2
Let x be (2/6)/((-1)/9). Let i be x - (0 - 11/3). What is z in 1/3*z - i*z**3 + 1/3*z**5 + 1/3 - 2/3*z**2 + 1/3*z**4 = 0?
-1, 1
Let v(k) be the second derivative of -1/48*k**4 + 0 + 0*k**5 + 0*k**3 + 1/120*k**6 + 0*k**2 + 4*k. Let v(t) = 0. Calculate t.
-1, 0, 1
Let f(v) be the first derivative of -v**6/10 - 12*v**5/25 - 3*v**4/4 - 2*v**3/5 - 12. Factor f(x).
-3*x**2*(x + 1)**2*(x + 2)/5
Let w(f) = f**4 - f**3 - f**2 - f - 1. Let u(b) = 64*b**4 - 60*b**3 - 68*b**2 + 52*b. Let t(o) = u(o) - 4*w(o). Suppose t(g) = 0. What is g?
-1, -1/15, 1
Let z(g) be the second derivative of -1/12*g**4 + 4*g + 1/9*g**3 + 1/6*g**2 + 0. Factor z(q).
-(q - 1)*(3*q + 1)/3
Let r be 4/22 - 1145/6600. Let i(b) be the third derivative of 1/24*b**4 + 0 + b**2 + r*b**5 + 1/12*b**3 + 0*b. Find c, given that i(c) = 0.
-1
Let z(f) be the first derivative of f**6/6 - 2*f**5/5 - 11*f**4/16 + 13*f**3/12 + 2*f**2 + f + 4. Let z(p) = 0. Calculate p.
-1, -1/2, 2
Let m(z) = z**5 + 2*z**4 + z**3 - z**2 + 1. Let i(u) = u**4 + u**3 - u**2 + 1. Let c(t) = 4*i(t) - 4*m(t). Factor c(d).
-4*d**4*(d + 1)
Let x(d) be the first derivative of 32/5*d - 7 + 8/5*d**2 + 2/15*d**3. Factor x(n).
2*(n + 4)**2/5
Let k(l) = -2*l - 10. Let p be k(-5). Let o(f) be the first derivative of -f**2 - 8/3*f**3 - 8/5*f**5 - 1/3*f**6 - 3*f**4 - 2 + p*f. Factor o(r).
-2*r*(r + 1)**4
Determine p, given that -10/17*p**2 - 6/17*p**3 + 8/17*p + 8/17 = 0.
-2, -2/3, 1
Let d(g) be the second derivative of -g**4/60 + 16*g. Find t, given that d(t) = 0.
0
Let d(v) be the first derivative of -v**5/5 + v**3/3 + 9. Let d(q) = 0. What is q?
-1, 0, 1
Suppose -1/2*j**2 - 8 + 4*j = 0. Calculate j.
4
Suppose 0*o + 20/9*o**2 + 0*o**3 - 4/9*o**4 - 16/9 = 0. Calculate o.
-2, -1, 1, 2
Let b be ((1 + -1)/1)/(-2). Suppose p + h + 3 - 6 = b, -4*p - 5*h + 13 = 0. Solve 0*n**2 - n**2 + n**p + 3*n**2 + 3*n = 0.
-1, 0
Let y(j) = 12*j**2 + 9*j - 21. Let n(x) = 3*x**2 + 2*x - 5. Let c be (-6)/(-4)*(2 - 16). Let t(p) = c*n(p) + 5*y(p). Factor t(z).
-3*z*(z - 1)
Solve c - 5 + 10 + c**2 - 7 = 0.
-2, 1
Let u(a) be the second derivative of 5*a**7/42 + a**6/2 + a**5/4 - 5*a**4/4 - 5*a**3/3 + 4*a. Find q, given that u(q) = 0.
-2, -1, 0, 1
Let g(z) be the third derivative of -1/16*z**4 + 2*z**2 - 1/240*z**6 + 0*z + 0 - 1/40*z**5 - 1/12*z**3. Determine s so that g(s) = 0.
-1
Let g(u) be the third derivative of -u**8/392 + 2*u**7/735 + 3*u**6/140 - u**4/21 + 5*u**2. Solve g(l) = 0.
-1, 0, 2/3, 2
Let d(b) be the third derivative of -2*b**7/735 + 3*b**5/35 - 2*b**4/21 - 8*b**3/7 - 2*b**2. Determine y, given that d(y) = 0.
-3, -1, 2
Solve -12 - 11 - 3*k**2 - 3 + 56*k - 10 = 0 for k.
2/3, 18
Suppose -39 = -j - 36. Let 1/6*o**j + 1/6*o - 1/3*o**2 + 0 = 0. What is o?
0, 1
Suppose -k + 1 = -2*v - 2*v, 3*k + v - 3 = 0. Let n(h) be the first derivative of 2/9*h**3 + 1/6*h**4 + 0*h - 2/3*h**2 + k. Let n(m) = 0. Calculate m.
-2, 0, 1
Let t(g) = -3*g**2 - 16*g - 62. Let k(l) = -16*l**2 - 80*l - 309. Let i(u) = -6*k(u) + 33*t(u). Solve i(v) = 0 for v.
-8
Let n(g) be the third derivative of 0*g + 0*g**3 + 0 + 4*g**2 + 0*g**5 + 0*g**4 + 1/180*g**6. Solve n(d) = 0.
0
Factor -1/3*s**4 + 2/3*s**2 + 2/3*s**3 - 1/3 - 1/3*s**5 - 1/3*s.
-(s - 1)**2*(s + 1)**3/3
Let z be 3 - (-20 + (-8)/4). Factor 27*b**2 + 2*b + b - b - z*b**2.
2*b*(b + 1)
Let i(p) = p**2 - 8*p - 16. Let x(d) = d**2. Let k(a) = 3*i(a) - 6*x(a). Factor k(s).
-3*(s + 4)**2
Let v(m) = -9*m + 94. Let k be v(10). Factor -2/3*z**3 + 0*z - 1/3*z**2 + 0 - 1/3*z**k.
-z**2*(z + 1)**2/3
Suppose m = 4*j - 5*j + 13, -4*j - 5*m = -55. Let o be 1 - (-14)/j - 2. Factor -o*l**5 + 0*l**3 + 0 + 4/5*l**4 + 2/5*l - 4/5*l**2.
-2*l*(l - 1)**3*(l + 1)/5
Factor -5*r**2 - 4*r - 3*r**5 + 8*r**4 + 7*r**5 - 3*r**2.
4*r*(r - 1)*(r + 1)**3
Let w be 2*2 - (5 - 4). Determine k so that -2*k**3 - k**5 + 3*k**5 + 0*k**w = 0.
-1, 0, 1
Let b(g) be the third derivati