v) = -v - 1. Let y be o(-3). Suppose 0 = -b - 0 + y. Factor -4/3*m**4 - 2/3*m**2 - b*m**3 + 0 + 0*m.
-2*m**2*(m + 1)*(2*m + 1)/3
Let o(m) be the second derivative of m**5/120 - m**4/24 - 36*m. Factor o(r).
r**2*(r - 3)/6
Suppose -4*z + 6 = 2*y, -3*y = -2*z - 0*y + 15. Let h be (-33)/11 + z + 0. Suppose -1/3*m + 0 - 1/3*m**5 + 0*m**2 + 2/3*m**3 + h*m**4 = 0. Calculate m.
-1, 0, 1
Suppose m = 4*k - 64, 2*m + 12 = 4. Let a be ((-5)/k)/(2/(-12)). Suppose 0 - 2/3*s**a + 4/3*s = 0. Calculate s.
0, 2
Let p(f) be the second derivative of f**7/525 - f**2/2 + 3*f. Let x(d) be the first derivative of p(d). Suppose x(c) = 0. Calculate c.
0
Factor 6/7*v**3 + 0 + 6/7*v**2 + 2/7*v**4 + 2/7*v.
2*v*(v + 1)**3/7
Suppose 787*n - 803*n + 32 = 0. Factor 32/5*m**n + 16/5*m + 4*m**3 + 4/5*m**4 + 0.
4*m*(m + 1)*(m + 2)**2/5
Let t = -10 - -13. Find g, given that 2/7*g - 2/7*g**t + 0*g**2 + 0 = 0.
-1, 0, 1
Let i(u) = u**5 + 8*u**4 - 11*u**3 + 12*u**2 - 4*u - 2. Let r(p) = -4*p**5 - 25*p**4 + 32*p**3 - 36*p**2 + 12*p + 7. Let n(k) = 21*i(k) + 6*r(k). Factor n(x).
-3*x*(x - 2)**2*(x - 1)**2
Let a(x) = -9*x**4 + 14*x**3 + 2*x**2 - 7*x - 7. Let f(d) = -d**5 + d**4 - d**3 + d + 1. Let q(w) = 3*a(w) + 21*f(w). Suppose q(g) = 0. What is g?
-1, -2/7, 0, 1
Let s(i) be the third derivative of i**7/525 + i**6/150 + i**5/150 - 8*i**2. Determine b, given that s(b) = 0.
-1, 0
Let j be -6*(3 - (-15)/(-6)). Let k = -1 - j. Factor 4/5*s**3 + 2/5*s**5 + 4/5*s**k - 6/5*s**4 + 2/5 - 6/5*s.
2*(s - 1)**4*(s + 1)/5
What is t in -2/11*t**3 + 10/11*t**2 + 0 + 0*t = 0?
0, 5
Suppose 21*v + 57 = 40*v. Factor 3/2*l**2 + v*l + 0.
3*l*(l + 2)/2
Let t(k) be the third derivative of k**6/30 - k**5/5 + 30*k**2. Suppose t(d) = 0. What is d?
0, 3
Suppose 52*s**2 - 33*s**4 + 76*s**3 - 14*s**4 + 7*s**4 - 16 + 4*s**4 - 28*s**5 - 48*s = 0. Calculate s.
-2, -1, -2/7, 1
Let m(u) = 4*u**2 - 13. Let v(f) = -f**2 + 1. Let h(i) = m(i) + v(i). Let h(j) = 0. What is j?
-2, 2
Solve 1/2*k**4 - 1/2*k**3 + 1/2*k - 1/2*k**2 + 0 = 0.
-1, 0, 1
Let y be (-1 + 1 + -4)/(-2). Solve -8*v - 2*v**2 - 2*v**3 + 0*v**2 + 3*v**y + 7*v**2 = 0 for v.
0, 2
Let u(j) = -6*j**5 - 20*j**4 + 6*j**3 + 34*j**2 - 14*j + 14. Let t(a) = -a**5 - 4*a**4 + a**3 + 7*a**2 - 3*a + 3. Let h(w) = -14*t(w) + 3*u(w). Factor h(p).
-4*p**2*(p - 1)*(p + 1)**2
Let h(c) be the third derivative of 1/56*c**8 + c**2 - 1/30*c**5 + 0*c**3 + 0*c**4 + 1/60*c**6 + 0*c + 1/21*c**7 + 0. Determine k so that h(k) = 0.
-1, 0, 1/3
Let k(g) be the second derivative of 3*g + 1/42*g**4 + 1/70*g**5 + 0*g**3 + 0*g**2 + 0. Let k(s) = 0. Calculate s.
-1, 0
Determine q, given that 0 + 2/19*q + 4/19*q**2 + 2/19*q**3 = 0.
-1, 0
Let w(s) = -6*s**2 + 13*s - 7. Let q(v) = 0*v - 2*v + 4*v**2 - 7*v + 5. Suppose -3*d = -4*d + m + 4, -m + 21 = 4*d. Let z(p) = d*w(p) + 7*q(p). Factor z(o).
-2*o*(o - 1)
Factor -v**2 + 0 + 0*v + 7/2*v**3 + 2*v**4.
v**2*(v + 2)*(4*v - 1)/2
Let s(r) be the first derivative of r**8/112 + r**7/35 - r**5/10 - r**4/8 - 2*r**2 + 4. Let p(a) be the second derivative of s(a). Let p(v) = 0. Calculate v.
-1, 0, 1
Let z(g) = g**2 - 8*g + 21. Let k be z(5). Factor 2*j + 3/2*j**3 - 5/2*j**4 + 0 + k*j**2.
-j*(j - 2)*(j + 1)*(5*j + 2)/2
Let p be 0 + 1 + 3/4. Let m be 16/120 - (-67)/60. Factor m*x + p*x**2 - 1/2.
(x + 1)*(7*x - 2)/4
Solve 2/7*v**5 + 6/7*v + 0*v**4 - 8/7*v**3 + 4/7 - 4/7*v**2 = 0.
-1, 1, 2
Find j, given that -5*j**5 - 8*j**2 - 3*j**2 + j**2 + 5*j + 10*j**4 = 0.
-1, 0, 1
Let u(k) be the second derivative of k**6/120 + k**5/40 - k**4/48 - k**3/12 + 13*k. Factor u(j).
j*(j - 1)*(j + 1)*(j + 2)/4
Let q(u) = -14*u**3 - 4*u**2 - 24*u - 12. Let g(x) = -5*x**3 - x**2 - 8*x - 4. Let f(t) = 11*g(t) - 4*q(t). Factor f(a).
(a + 1)*(a + 2)**2
Solve 4/7*w + 2/7*w**2 + 2/7 = 0 for w.
-1
Let p(t) be the first derivative of 0*t + 4/33*t**3 + 6 + 1/33*t**6 + 0*t**4 - 4/55*t**5 - 1/11*t**2. Factor p(y).
2*y*(y - 1)**3*(y + 1)/11
Let h(b) = 15*b**3 - 15*b**2 - 12*b - 12. Let w(n) = n**2 - 8*n + 7*n - 1 + n**3 - 2*n**2. Let f(m) = h(m) - 12*w(m). Suppose f(a) = 0. What is a?
0, 1
Let j(d) be the second derivative of -d**7/294 + d**6/30 - 19*d**5/140 + 25*d**4/84 - 8*d**3/21 + 2*d**2/7 + 26*d. Factor j(s).
-(s - 2)**2*(s - 1)**3/7
Suppose 114 = -4*d - 274. Let j = d - -681/7. Factor 2/7*s**2 - j + 0*s.
2*(s - 1)*(s + 1)/7
Let m = 20 - 18. Let g(o) be the second derivative of 0 + 1/30*o**4 + 3/50*o**5 - 1/5*o**3 - o - 1/5*o**m. Solve g(k) = 0.
-1, -1/3, 1
Let w be 16/4 - (-3 + (-65)/(-10)). Suppose -o + 2 = -2. Find d, given that -1/4*d + 3/4*d**5 + d**o - w*d**3 + 0 - d**2 = 0.
-1, -1/3, 0, 1
Factor 24/5*j + 12/5*j**3 - 26/5*j**2 - 2/5*j**4 - 8/5.
-2*(j - 2)**2*(j - 1)**2/5
Let j(p) be the second derivative of -11*p**5/15 - 10*p**4/9 + 2*p**3/9 + 34*p. Factor j(h).
-4*h*(h + 1)*(11*h - 1)/3
Let g(y) be the third derivative of -y**6/120 - 3*y**5/20 + y**3/3 - 4*y**2. Let v be g(-9). Factor -3/4*i - i**v + 1/4.
-(i + 1)*(4*i - 1)/4
Let m = -85 + 153. Let a = -202/3 + m. Suppose a*n**3 - 2/3*n**5 - 1/3*n**4 + 0*n + 1/3*n**2 + 0 = 0. What is n?
-1, -1/2, 0, 1
Let k(l) be the second derivative of 0*l**6 + 1/231*l**7 - 1/55*l**5 + 1/33*l**3 + 0 - 7*l + 0*l**2 + 0*l**4. Factor k(m).
2*m*(m - 1)**2*(m + 1)**2/11
Let y(z) = z**3 + 5*z**2 - 2*z - 7. Let n be y(-5). Let t(j) be the first derivative of -9/8*j**4 + 7/10*j**5 + 1 + 1/3*j**n + 0*j + 0*j**2. Factor t(l).
l**2*(l - 1)*(7*l - 2)/2
Let u = 61 + -58. Suppose -8/7*n**2 - 4/7 - 2/7*n**u - 10/7*n = 0. What is n?
-2, -1
Let v(d) be the third derivative of -d**6/1080 + d**5/90 - d**4/24 + 5*d**3/6 - 5*d**2. Let o(i) be the first derivative of v(i). Factor o(s).
-(s - 3)*(s - 1)/3
Suppose -z + 7 = 2*z - 2*p, -11 = -4*z + p. Suppose -46 = -z*f + g, 2*g = f - 20 + 3. Find i, given that -2*i - 7/2*i**5 - 43/2*i**3 + f*i**4 + 0 + 12*i**2 = 0.
0, 2/7, 1, 2
Let o be -5 - ((-55)/15 - 2). Factor 4/9 + 0*p**2 + 2/9*p**3 - o*p.
2*(p - 1)**2*(p + 2)/9
Let n = 29 + -115/4. Let f be 1*-1 - (-1 + 0). Factor 1/4*g + f + n*g**3 - 1/2*g**2.
g*(g - 1)**2/4
Let m(w) be the second derivative of -3*w - 1/14*w**4 - 1/7*w**2 - 1/7*w**3 + 0 - 1/70*w**5. Factor m(u).
-2*(u + 1)**3/7
Let v(r) be the first derivative of r**6/3 - 2*r**5 + 5*r**4 - 20*r**3/3 + 5*r**2 - 2*r - 9. Factor v(l).
2*(l - 1)**5
Factor 0 - 1/4*o**2 - 1/2*o.
-o*(o + 2)/4
Let w(v) be the second derivative of 0 + 1/24*v**4 + 3*v - 1/2*v**3 + 9/4*v**2. Solve w(i) = 0.
3
Let 0 + 0*n + 2/7*n**3 + 0*n**2 = 0. Calculate n.
0
Let k(n) be the first derivative of -n**4/22 + 6*n**3/11 - 15*n**2/11 - 50*n/11 - 1. Suppose k(u) = 0. Calculate u.
-1, 5
Let o(m) = -m**2 - 5*m + 5. Let r be o(-5). Suppose -d**3 + d - 2*d**2 - 4*d**2 + 1 + r*d**2 = 0. What is d?
-1, 1
Let x = 4 + -3. Let a be 1 - 3/4*x. Factor -a*d**2 + 1/2*d + 0.
-d*(d - 2)/4
Let w be (-3)/12 - 1/(-4). Let h(i) be the third derivative of -i**2 + 1/60*i**5 - 1/120*i**6 + 0*i**4 + 0*i + 0 + w*i**3. Let h(t) = 0. Calculate t.
0, 1
Let c(v) be the second derivative of -v**6/255 + v**4/102 - 14*v. Solve c(m) = 0 for m.
-1, 0, 1
Let h = 24 - 46. Let f = 24 + h. Suppose 2/5*k**f + 0 - 2/5*k**4 - 2/5*k**3 + 2/5*k = 0. What is k?
-1, 0, 1
Find c such that -51*c - 165/4*c**3 + 9/4*c**5 - 30 - 3/2*c**4 + 207/2*c**2 = 0.
-5, -1/3, 2
Factor 5*j**2 + 6*j + 20 + 18*j - 4*j.
5*(j + 2)**2
Suppose -10 = -2*b - 2. Let 10/3*h**b - 16/3*h**3 + 0 + 4/3*h + 2/3*h**2 = 0. Calculate h.
-2/5, 0, 1
Let x = 4/31 - -665/372. Let a = x + -5/4. Factor 0 + 2/3*n**2 - a*n.
2*n*(n - 1)/3
Let p(f) = 19*f**2 - 9*f + 4. Let z(h) = -h**2 + h - 1. Let x(m) = p(m) + 4*z(m). Factor x(q).
5*q*(3*q - 1)
Suppose 2*n = -5*c + 7, -5*c + 3*n = -0*n - 27. Find p, given that 2/13 + 2/13*p - 2/13*p**2 - 2/13*p**c = 0.
-1, 1
Let c(l) = -2*l**4 - 3*l**3 - 1. Suppose 11 = -4*a - 0*u - 5*u, 5*a = -3*u - 4. Let d(t) = t**4 + t**3 - t**2 + 1. Let w(x) = a*d(x) + c(x). Factor w(r).
-r**2*(r + 1)**2
Let i = 38 + -34. Factor 0 - 2/5*c**3 + 7/5*c**2 - 7/5*c**i + 2/5*c.
-c*(c - 1)*(c + 1)*(7*c + 2)/5
Let n(c) = c**2 - c + 2. Let d be n(2). Factor -2*t**2 - t**4 - t**4 + d*t**4.
2*t**2*(t - 1)*(t + 1)
Suppose 2*p - 4*p - 4 = 0. Let u be p + 2/4 + 2. Factor -t - u*t**2 - 1/2.
-(t + 1)**2/2
Let k(h) = -15*h - 4. Let b be k(-6). Let q = b - 515/6. Determine o, given that -1/3*o - q - 1/6*o**2 = 0.
-1
Let s(