*s**2 - c*s**3 = 0.
-1, 0, 2/7
Let k = -1853/308 + -18/77. Let z = k + 83/12. Find h, given that z*h - 2/9*h**2 - 2/3*h**3 + 2/9 = 0.
-1, -1/3, 1
Let g(o) be the second derivative of 2*o**6/15 + 17*o**5/20 + 5*o**4/3 + 2*o**3/3 - 8*o. Let g(q) = 0. Calculate q.
-2, -1/4, 0
Suppose -24 + 16 = -l. Let i(d) be the second derivative of 1/15*d**6 - 20/3*d**3 + 2*d + 0 + l*d**2 + 3*d**4 - 7/10*d**5. Solve i(v) = 0 for v.
1, 2
Determine z so that -3/2*z**2 + 3/2*z**4 - 3/2*z**5 + 0 + 3/2*z**3 + 0*z = 0.
-1, 0, 1
Suppose -5*y + 29 = -36. Suppose 3*d + 4*c + 18 = 7, y = d - 2*c. Factor 3*b + b**2 + 4*b**3 - 7*b**3 - d*b**4 + 2*b**2.
-3*b*(b - 1)*(b + 1)**2
Let x(u) be the third derivative of 2*u**7/105 + 2*u**6/15 + u**5/5 - 2*u**4/3 - 8*u**3/3 - 11*u**2. Factor x(n).
4*(n - 1)*(n + 1)*(n + 2)**2
Let g(v) be the first derivative of -v**4 + 8*v**3/3 - 2*v**2 + 4. Factor g(s).
-4*s*(s - 1)**2
Factor h - 10*h**4 + 10*h**4 + 8*h**3 - 4 - 2*h**5 + 4*h**2 - 7*h.
-2*(h - 2)*(h - 1)*(h + 1)**3
Let k(w) be the second derivative of 0*w**3 - 2/15*w**6 + 0 - w - 1/7*w**7 + 0*w**4 + 0*w**2 + 0*w**5. Factor k(y).
-2*y**4*(3*y + 2)
Let g(w) = w**2 - 11*w + 12. Suppose o = -3*o + 40. Let j be g(o). Factor -4/5*q**j - 1/5*q**5 - 1/5*q + 0 - 6/5*q**3 - 4/5*q**4.
-q*(q + 1)**4/5
Let z(w) be the third derivative of 0*w + 1/3*w**3 - w**2 - 1/8*w**4 + 1/60*w**5 + 0. Factor z(r).
(r - 2)*(r - 1)
Let s = -5 - -4. Let y = 2 + s. Solve 1 - 2*b**2 + 4*b**2 - y = 0.
0
Let a(z) be the third derivative of 2/15*z**6 + 0 - 2/15*z**5 + 0*z + 2/105*z**7 + 6*z**3 - 2*z**4 + 9*z**2. Factor a(n).
4*(n - 1)**2*(n + 3)**2
What is u in -11/12*u**3 + 1/6*u + 1/3*u**4 + 0 + 5/12*u**2 = 0?
-1/4, 0, 1, 2
Let v(w) be the first derivative of -2*w**5/15 - 5*w**4/6 - 2*w**3 - 7*w**2/3 - 4*w/3 + 8. Factor v(a).
-2*(a + 1)**3*(a + 2)/3
Let a(w) be the first derivative of w**6/10 + 6*w**5/25 - 2*w**3/5 - 3*w**2/10 + 2. What is m in a(m) = 0?
-1, 0, 1
Let v(a) be the first derivative of 1/4*a**4 + 1/10*a**5 + 1 + 0*a**2 + 0*a + 1/6*a**3. Factor v(b).
b**2*(b + 1)**2/2
Let m = -4 - -7. Suppose -4*v + 31 = 3*h, -21 = -3*v - 3*h + 6. Factor 5*q**m + q**v - q**2 + q**3 - q**5 - 5*q**3.
-q**2*(q - 1)**2*(q + 1)
Let l be 33/77 - 0/((-5)/1). Determine p, given that -6/7*p**2 + 0*p + 0 + l*p**3 = 0.
0, 2
Let h = 3/49 - -4/49. Let y(k) be the first derivative of -2/35*k**5 + 0*k**3 + 0*k**2 + 0*k + h*k**4 + 1. Determine a so that y(a) = 0.
0, 2
Let v(m) be the second derivative of -m**5/40 - m**4/24 + 2*m. Factor v(l).
-l**2*(l + 1)/2
Let c(j) be the second derivative of 1/6*j**4 + 0 + 0*j**2 + 0*j**6 + 0*j**3 - 1/2520*j**7 + j + 0*j**5. Let m(x) be the third derivative of c(x). Factor m(o).
-o**2
Let m(t) = -t**5 + t**4 - t. Let r(f) = -f**5 - 2*f**3 + 8*f**2 - 9*f + 2. Let q be (2/6)/((-4)/(-24)). Let l(c) = q*r(c) - 4*m(c). Solve l(i) = 0.
-2, 1
Let b(o) be the third derivative of o**8/336 + o**7/42 + 7*o**6/120 - o**5/60 - o**4/3 - 2*o**3/3 - 6*o**2. Find v such that b(v) = 0.
-2, -1, 1
Let i be -1 + (-111)/(-54) + (-1 - 0). Let s(h) be the first derivative of -i*h**4 + 2/45*h**5 + 0*h**2 - 1 - 4/27*h**3 + 0*h. Factor s(l).
2*l**2*(l - 2)*(l + 1)/9
Let j(d) = 2*d**3 + 2*d**2 - d + 8. Let k be j(-2). Factor i**k - 1 + 1/2*i - 1/2*i**3.
-(i - 2)*(i - 1)*(i + 1)/2
Factor -2*o**2 - 38*o**4 + 4*o**2 + 39*o**4 + 3*o**3.
o**2*(o + 1)*(o + 2)
Determine l so that 12*l**2 + 2*l**5 - 12*l**4 + 2*l**5 + 12*l**3 - 9*l**2 - 7*l**2 = 0.
0, 1
Let -2/5*t**4 + 0*t**3 + 0*t + 2/5*t**2 + 0 = 0. Calculate t.
-1, 0, 1
Let n(u) = u + 13. Let m be n(-11). Let v be 0*(-4 - 28/(-8)). Let -1/3*t**3 + v - 2/3*t**m - 1/3*t = 0. What is t?
-1, 0
Suppose -6*f = -5*t - 3*f + 78, 110 = 5*t + 5*f. Suppose 3 - t = -5*n. Factor 2/13*u**n - 2/13 - 6/13*u**2 + 6/13*u.
2*(u - 1)**3/13
Suppose -8*y + 13*y**2 + 28*y**3 - 12*y**2 - 12*y**4 - 12*y**5 - 8*y**5 + 11*y**2 = 0. What is y?
-1, 0, 2/5, 1
Let b(n) be the second derivative of n**5/40 - n**4/24 - n**3/6 + 9*n. Suppose b(g) = 0. Calculate g.
-1, 0, 2
Let g be 94/210 + 28/(-70). Let a(y) be the second derivative of -y - g*y**7 + 1/2*y**2 + 1/3*y**4 + 0 - 1/6*y**6 + 2/3*y**3 - 1/10*y**5. Factor a(r).
-(r - 1)*(r + 1)**3*(2*r + 1)
Let t be -4 + (1 - (-759)/252). Let d(w) be the third derivative of t*w**4 + w**2 + 0*w + 0*w**3 + 0 + 1/210*w**5. Factor d(p).
2*p*(p + 1)/7
Let o(c) = c**3 - 4*c**2 - c + 4. Let l be o(0). Find v, given that -1/2 - 3*v - 6*v**2 - l*v**3 = 0.
-1/2
Let w(b) be the first derivative of 16*b + 140/3*b**3 + 52*b**2 - 49/2*b**4 - 1. Factor w(g).
-2*(g - 2)*(7*g + 2)**2
Let u(v) = 4*v**2 - 4*v + 4. Let m = -7 + 6. Let i(x) = -x**2. Let d(t) = m*u(t) - 3*i(t). Factor d(r).
-(r - 2)**2
Let u be 1 + 0 + 6/2. Suppose 0 = -2*l - 0*l - u*q - 2, l = -q + 1. What is b in 0*b - 2/3*b**4 + 0 - 4/3*b**l - 2/3*b**2 = 0?
-1, 0
Suppose w = d - 2*w + 9, -2*d = -3*w + 6. Let q be (-42)/63*(-1)/2. Factor 1/3 + q*g**d + g**2 + g.
(g + 1)**3/3
Let y(h) be the first derivative of -h**5 + 25*h**3/3 - 20*h - 43. Determine q, given that y(q) = 0.
-2, -1, 1, 2
Let g = -811/6 - -136. Factor 1/6*s + g*s**3 + 1/3 - 4/3*s**2.
(s - 1)**2*(5*s + 2)/6
Let l be 4/(-2) + 2/1. Let r(x) be the first derivative of 1 + 0*x**2 - 1/12*x**3 + l*x. Factor r(a).
-a**2/4
Suppose 3 = f + 5. Let i be (-5)/(-20) + f/(-56). Suppose 0*v - 4/7*v**3 - 2/7*v**4 + 0 - i*v**2 = 0. What is v?
-1, 0
Suppose 5*h**2 - 4*h**3 + 2*h**3 - 3*h**2 + 80*h - 76*h = 0. What is h?
-1, 0, 2
Let d(f) be the first derivative of -f**4/12 - 11. Let d(z) = 0. Calculate z.
0
Let c(t) = 2*t - 27. Let o be c(15). Let k(n) be the first derivative of -6*n + 2/3*n**o - 2*n**2 + 1. Factor k(s).
2*(s - 3)*(s + 1)
Let d(f) be the first derivative of 2/3*f + 2/3*f**3 - 3 - 4/3*f**2. Factor d(b).
2*(b - 1)*(3*b - 1)/3
Suppose -1/3*y**2 + 0 + 1/3*y**4 - 1/3*y + 1/3*y**3 = 0. What is y?
-1, 0, 1
Let s(n) be the third derivative of 0*n**6 - 1/315*n**7 + 1/30*n**5 - 4*n**2 - 1/18*n**4 + 0 + 0*n + 0*n**3. Let s(a) = 0. Calculate a.
-2, 0, 1
Let f(r) = r**2 + 1. Let g(a) = 3*a**3 - 24*a**2 - 18. Let l = 13 + -8. Let o = -4 + l. Let x(q) = o*g(q) + 18*f(q). Factor x(y).
3*y**2*(y - 2)
Let o(w) = w + 7. Let f(j) = 6*j + 36. Let k(t) = 2*f(t) - 11*o(t). Let b be k(5). Factor b*l - 2/5*l**2 + 2/5.
-2*(l - 1)*(l + 1)/5
Let u(n) be the second derivative of n**5/90 - 2*n**4/27 + 4*n**3/27 - 31*n. Factor u(v).
2*v*(v - 2)**2/9
Let f be (44/(-440))/((-1)/2). Solve 0*q**3 + f - 2/5*q**2 + 0*q + 1/5*q**4 = 0 for q.
-1, 1
Let h(m) be the third derivative of -m**9/10080 - m**8/2520 + m**7/2520 + m**6/180 + m**5/30 - 4*m**2. Let s(o) be the third derivative of h(o). Factor s(b).
-2*(b + 1)**2*(3*b - 2)
Suppose 4 = -5*i - 4*y - 0, 0 = 2*y + 2. Determine c, given that 0*c + i + 1/4*c**2 = 0.
0
Let o(m) be the second derivative of -2*m**6/105 - 4*m**5/35 + m**4/7 + 20*m**3/21 - 16*m**2/7 + 8*m + 2. Suppose o(d) = 0. What is d?
-4, -2, 1
Let m be 32/(-6) + (-4)/6. Let h = m - -11. Factor -2*r**5 - r**2 - 2*r**4 + 3*r**h + 3*r**2 - r.
r*(r - 1)**3*(r + 1)
Let n = 721 + -719. Factor 0*i + 4/3 - 1/3*i**n.
-(i - 2)*(i + 2)/3
Let g(q) be the third derivative of q**8/1176 + 4*q**7/735 + q**6/70 + 2*q**5/105 + q**4/84 + 3*q**2. Let g(z) = 0. Calculate z.
-1, 0
Let m(l) = -l**3 + 8*l**2 + 2. Let g be 4/((-2)/(-3 + -1)). Let d be m(g). Factor -2/5*w**d - 4/5 - 6/5*w.
-2*(w + 1)*(w + 2)/5
Let b(g) be the first derivative of 0*g**2 + 0*g + 3*g**4 + 16/5*g**5 + 4 - 4/3*g**3. Suppose b(x) = 0. What is x?
-1, 0, 1/4
Let b(y) = 7*y**5 + 9*y**4 - 5*y**3 - 12*y**2 + y. Let z(w) = -8*w**5 - 9*w**4 + 6*w**3 + 13*w**2 - 2*w. Let a(s) = 4*b(s) + 3*z(s). Solve a(m) = 0.
-2, -1, -1/4, 0, 1
Suppose -2*q + 12 = 8. Let n(p) = -6*p**3 + 23*p**2 - 12*p. Let b(h) = 3*h**3 - 11*h**2 + 6*h. Let x(s) = q*n(s) + 5*b(s). Let x(a) = 0. What is a?
0, 1, 2
Let u(v) be the first derivative of v**3/6 + v**2 - 11. Factor u(a).
a*(a + 4)/2
Let w(u) be the first derivative of -8*u**6/15 + 8*u**5/5 - u**4 - 4*u**3/3 + 2*u**2 + 8*u - 6. Let f(l) be the first derivative of w(l). Solve f(h) = 0.
-1/2, 1/2, 1
Let j(x) = x**2 + 12*x + 13. Let i be j(-11). Factor 28*o**5 - o**i + 64*o**4 - o**3 + 9*o**2 + 45*o**3.
4*o**2*(o + 1)**2*(7*o + 2)
Let x(j) = 2*j**4 - 8*j**3 - 21*j**2 - 32*j - 19. Let o(u) = 85*u**2 + 26 + 128*u +