1, 0, 1
Let l(i) be the second derivative of -i**7/189 - 4*i**6/135 - 2*i**5/45 + 38*i. Determine m, given that l(m) = 0.
-2, 0
Let v = -1 + 5/3. Factor 0 + v*x**4 + 0*x + 4/3*x**3 + 2/3*x**2.
2*x**2*(x + 1)**2/3
Factor 1772 + 10*w**2 + 2*w**4 - 4*w - 8*w**3 - 1772.
2*w*(w - 2)*(w - 1)**2
Let u(r) be the second derivative of -2*r**6/15 + 3*r**5/5 - 2*r**4/3 - 33*r. Factor u(l).
-4*l**2*(l - 2)*(l - 1)
Let b(k) = 25*k**2 + 720*k + 2160. Let j(v) = -2*v**2 - 60*v - 180. Let f(u) = 3*b(u) + 35*j(u). Factor f(x).
5*(x + 6)**2
Suppose -3*o + 2*a + 9 = 5*a, -a - 17 = -4*o. Factor -1/2*b**3 + 1/2*b + 0 - 1/4*b**2 + 1/4*b**o.
b*(b - 2)*(b - 1)*(b + 1)/4
Let l = 638/7 - 90. Suppose 0 - 2/7*m**3 + 2/7*m - 8/7*m**2 + l*m**4 = 0. What is m?
-1, 0, 1/4, 1
Let u(h) = -9*h**2 + 4*h. Let s be -1*3*-1 + 1. Suppose -j + s*j = -4*k - 26, -15 = j - 5*k. Let c(g) = -5*g**2 + 2*g. Let a(v) = j*c(v) + 4*u(v). Factor a(t).
2*t*(7*t - 2)
Let x(o) be the second derivative of -o**5/270 + o**4/36 - 2*o**3/27 - 3*o**2/2 - 2*o. Let u(w) be the first derivative of x(w). Find z, given that u(z) = 0.
1, 2
Solve -64/5 + 0*v + 12/5*v**2 + 2/5*v**3 = 0 for v.
-4, 2
Let m(a) be the second derivative of a**8/6720 - a**6/720 - a**4/12 - 3*a. Let s(x) be the third derivative of m(x). Factor s(i).
i*(i - 1)*(i + 1)
Let r be (-4 + 2)*(10 - 12). Find p such that -8/11 - 14/11*p**r - 16/11*p - 4/11*p**3 + 42/11*p**2 = 0.
-2, -2/7, 1
Let q(a) be the second derivative of 0 + a**2 - 2/3*a**3 + a + 1/6*a**4. What is w in q(w) = 0?
1
Let g = 4 - 3. Let a be ((-8)/(-1))/2*g. Factor -10*f**2 - 2*f - 2*f + 15*f**a - 5*f**4 + 4*f**3.
2*f*(f - 1)*(f + 1)*(5*f + 2)
Let r(d) = 18*d - 2. Let l be r(1). Let a = 16 - l. Suppose -2/3*i**5 + 0 + a*i**3 - 4/3*i**2 + 2/3*i + 4/3*i**4 = 0. What is i?
-1, 0, 1
Let z(v) be the second derivative of -1/20*v**5 + 6*v + 3/20*v**6 + 0 + 0*v**3 + 0*v**4 + 0*v**2 - 3/28*v**7. Determine u, given that z(u) = 0.
0, 1/3, 2/3
Let t(p) be the first derivative of p**6/33 + 2*p**5/55 - 3*p**4/22 - 10*p**3/33 - 2*p**2/11 + 19. Solve t(r) = 0 for r.
-1, 0, 2
Let f = 17 + -17. Let c(w) be the second derivative of 0*w**3 + 1/20*w**5 - 2*w - 1/12*w**4 + f + 0*w**2. Factor c(b).
b**2*(b - 1)
Let t(m) be the first derivative of 3/80*m**5 - 5/48*m**4 - 2 + 1/30*m**6 - 1/8*m**3 + 3*m + 1/8*m**2. Let a(s) be the first derivative of t(s). Factor a(w).
(w - 1)*(w + 1)**2*(4*w - 1)/4
Let n be -3*3*1/(-3). Factor 0*w**n + w**3 - 3*w**3 + 2*w.
-2*w*(w - 1)*(w + 1)
Suppose 0 = -10*u + 6*u + 8. Let a be (-2)/(-12) - 1*-1. Factor u*z**2 - a*z**3 - 1/2*z - 1/3.
-(z - 1)**2*(7*z + 2)/6
Let v be (-5)/(-3) + (-4)/6. Let h be v + (-5 + 4)/(-1). Find q, given that 0 - 1/6*q + 1/6*q**h = 0.
0, 1
Factor 2/7 + 1/7*c**2 - 3/7*c.
(c - 2)*(c - 1)/7
Determine g, given that -2/5*g**5 + 6/5 + 6/5*g**4 - 12/5*g**2 - 2/5*g + 4/5*g**3 = 0.
-1, 1, 3
Solve 3/4*a**5 + 9/4*a + 3/2*a**2 - 3*a**3 + 0*a**4 - 3/2 = 0 for a.
-2, -1, 1
Suppose 3*y - 9*j - 15 = -6*j, -5*j + 5 = y. Factor 0*f + 7/3*f**3 - 8/3*f**4 - 2/3*f**2 + f**y + 0.
f**2*(f - 1)**2*(3*f - 2)/3
Determine p, given that 0 + 10/11*p**2 - 4/11*p = 0.
0, 2/5
Let v(b) be the second derivative of -b**6/45 + b**5/10 - 4*b**3/9 + 14*b. Determine g, given that v(g) = 0.
-1, 0, 2
Let f(g) be the first derivative of -1/4*g**2 - 1/3*g**3 - 1/12*g**6 - 6 + 1/4*g**4 + 1/10*g**5 + 1/2*g. Factor f(u).
-(u - 1)**3*(u + 1)**2/2
Let y be 3/18 + 1/2. Let j be ((-3)/(-18)*1)/(1/8). Factor -y - 5/3*x - 1/3*x**3 - j*x**2.
-(x + 1)**2*(x + 2)/3
Let o(y) be the second derivative of y**3/6 - 5*y**2/2 + y. Let w be o(8). Factor -2*g**2 - 4*g + 2 + w*g + g**2.
-(g - 1)*(g + 2)
Factor 1/9*d**2 - 2/9*d + 0.
d*(d - 2)/9
Let p(l) = 2*l**3 - 8*l**2 - 11*l + 5. Let a be p(5). Let -1/3*y**4 + a*y + 0 + 2/3*y**3 - 1/3*y**2 = 0. What is y?
0, 1
Suppose -r - 3*r - 5*i - 10 = 0, -r = -2*i - 4. Suppose q = -r*q. What is d in 0 - 1/4*d**4 + 1/2*d**3 - 1/4*d**2 + q*d = 0?
0, 1
Factor -11*i - 6*i**2 - i + 2*i**3 + 4*i + 0*i.
2*i*(i - 4)*(i + 1)
Let j(z) be the first derivative of 3*z - 1/3*z**3 + 1 - z**2. Find o such that j(o) = 0.
-3, 1
Let c = 15 + -9. Let w = 10 - c. Suppose -l + 0*l - 6*l**2 - l**4 - 3*l - w*l**3 - 1 = 0. What is l?
-1
Let y(a) be the third derivative of 3/4*a**5 - a**2 + 2/35*a**7 + 13/40*a**6 + 7/8*a**4 + 0 + 0*a + 1/2*a**3. Suppose y(z) = 0. What is z?
-1, -1/4
Let v(y) be the third derivative of y**7/735 + y**6/84 + 4*y**5/105 + y**4/21 + 9*y**2. Factor v(d).
2*d*(d + 1)*(d + 2)**2/7
Let n(d) = d**3 - 3*d**2 + 2*d - 4. Let w be n(3). Factor -10*b**4 + 10*b**4 - 2*b**4 + 4*b + 6*b**w.
-2*b*(b - 2)*(b + 1)**2
Let t(y) = -y**3 + 2*y**2 + 2*y - 2. Let j be t(2). Factor j*x**2 - 2*x**2 - x**2.
-x**2
Suppose 0 - 6 = -3*l. Factor 2 + 9*b + l + 6*b + 3*b**3 + 12*b**2 + 2.
3*(b + 1)**2*(b + 2)
Suppose 2*d - 3*t = d + 246, -258 = -d - 3*t. Let l be d/117 + (-4)/26. Let -2/3*s + s**l + 0 - 1/3*s**3 = 0. Calculate s.
0, 1, 2
Solve 18/17 + 2/17*b**3 + 30/17*b + 14/17*b**2 = 0 for b.
-3, -1
Let t**3 - 25*t + 0 + 6*t**2 + 2 + 31*t + t**3 = 0. Calculate t.
-1
Let q(g) = g**3 - 4*g**2 - 3*g + 5. Let h be q(4). Let z = -3 - h. Factor z*w + 0*w**2 - 2*w**2 - 2*w + 4.
-2*(w - 2)*(w + 1)
Let y(m) = -1. Let j(z) = 3*z**3 - 9*z**2 + 9*z - 5. Let v(a) = j(a) - 2*y(a). Factor v(f).
3*(f - 1)**3
Suppose 0 = -4*j + h + 6, j + 4*h - 8 = h. Let 6*g**3 + 0*g**2 - 2*g**j - 8*g**3 = 0. What is g?
-1, 0
Find f, given that -4*f**4 + 2*f**5 + 2 - f**4 - 4*f**2 - 2*f + 7*f**4 + 4*f**3 - 4*f**5 = 0.
-1, 1
Let a(o) be the second derivative of -o**4/60 - o**3/10 - o**2/5 + 7*o. Factor a(r).
-(r + 1)*(r + 2)/5
Let p(f) be the third derivative of -f**6/420 + f**5/105 - f**4/84 + 6*f**2. Find n such that p(n) = 0.
0, 1
Let p(o) be the first derivative of -o**8/6720 + o**7/3360 + o**6/1440 - o**5/480 + 2*o**3/3 + 1. Let s(n) be the third derivative of p(n). Factor s(z).
-z*(z - 1)**2*(z + 1)/4
Let t(f) = 52*f**2 - 18*f + 2. Let k(v) = 261*v**2 - 89*v + 10. Let b(q) = -2*k(q) + 11*t(q). Factor b(d).
2*(5*d - 1)**2
Let v be 1 + (-10)/3*42/(-35). Let f(d) be the third derivative of -3*d**2 + d**3 + 0 + 1/8*d**4 - 1/20*d**v + 0*d. Factor f(m).
-3*(m - 2)*(m + 1)
Let k(d) be the third derivative of d**6/300 + d**5/50 + d**4/30 - 11*d**2. Factor k(f).
2*f*(f + 1)*(f + 2)/5
Let q(c) be the first derivative of -c**6/7 - 8*c**5/35 + 2*c**4/7 + 4*c**3/7 - c**2/7 - 4*c/7 - 7. Let q(z) = 0. What is z?
-1, 2/3, 1
Determine o so that -5/2*o**2 - 4*o - 1/2*o**3 - 2 = 0.
-2, -1
Let v(o) be the first derivative of o**5/25 - o**4/2 + 11*o**3/5 - 4*o**2 + 16*o/5 - 11. Solve v(g) = 0.
1, 4
Let a(w) = 5*w. Let z(o) = o**2 - 11*o + 4. Let s(f) = 15*a(f) + 5*z(f). Solve s(x) = 0 for x.
-2
Let a(l) = -l - 5. Let v be a(-5). Suppose -4*m + 2 + 10 = v. Suppose -2/3*h**2 + 2/3*h - 2/9 + 2/9*h**m = 0. Calculate h.
1
Suppose 0 + 3 = -3*h - 4*l, 2*h - 2*l - 12 = 0. Factor 4/3*s - 2/3*s**h - 2/3*s**2 + 0.
-2*s*(s - 1)*(s + 2)/3
Factor 1/4*o**5 + 7/4*o**4 + 0 + 9/4*o**2 + 15/4*o**3 + 0*o.
o**2*(o + 1)*(o + 3)**2/4
Let b be (3/2)/(3/8). Factor -2*t**2 + 11*t - 2 - 2 - b - 3*t.
-2*(t - 2)**2
Suppose -5*u - 10 = 0, 0 = 5*l + 2*u + 2*u - 2. Let w be (-1)/((-4)/3 - -1). Factor -l*k**3 + 0*k**2 + 3*k**3 - 2*k**w + 3*k**2.
-k**2*(k - 3)
Let q(z) be the second derivative of -z**6/15 + 3*z**5/10 - z**4/2 + z**3/3 - z. Find s such that q(s) = 0.
0, 1
Let s(i) be the third derivative of -i**6/180 - i**5/60 + i**3/3 - 3*i**2. Let b(w) be the first derivative of s(w). Let b(h) = 0. Calculate h.
-1, 0
Suppose -4*i - 8 = -16. Suppose -2/9*q**3 - 2/9*q**i + 2/9 + 2/9*q = 0. Calculate q.
-1, 1
Solve -1/3*m + 0 - m**2 = 0 for m.
-1/3, 0
Let q(d) be the second derivative of d**5/30 - d**4/3 + 4*d**3/3 - 8*d**2/3 - 3*d. Find g such that q(g) = 0.
2
Let z be (2 + -3)/((-1)/5). Suppose -z*r = k + 10, -5*k + 3*r + 3 = -3. Solve 2*y**4 - 2*y**3 - y**2 + 2*y**5 - y**2 + k*y**2 = 0.
-1, 0, 1
Let i(n) be the second derivative of n**6/75 + n**5/25 - 2*n**3/15 - n**2/5 + 9*n. Factor i(p).
2*(p - 1)*(p + 1)**3/5
Let 49 + 10*s**2 - s**3 - 32*s - 31*s + 5*s**2 = 0. Calculate s.
1, 7
Factor -19 + 4*w - 1 + 2*w + 2*w**2.
2*(w - 2)*(w + 5)
Let a(p) = 5*p**2 - 2 + 8 - 5*p**3 + 0*p - 7*p + 1. Let v(m) = -4*m**3 + 4*m**2 - 6*m + 6. Let h(b) = 5*a(b) - 6*v(b). Find s, given 