 p(q) be the second derivative of q**6/15 - q**5/5 - 2*q**4/3 + 2*q**3/3 + 3*q**2 - 37*q. Find o such that p(o) = 0.
-1, 1, 3
Factor -1/3*j**2 + 4/3*j - 4/3.
-(j - 2)**2/3
Let x(p) be the first derivative of p**5/5 + 3*p**4/2 + 13*p**3/3 + 6*p**2 + 4*p + 12. Factor x(v).
(v + 1)**2*(v + 2)**2
Suppose 3*u + 3 = -3*h, -u = -5*h + 2*u + 19. Suppose -h*v = 2*q, 2*v - 4 - 5 = -5*q. Factor 4/3*a**2 + 4/3*a**q - 2/3*a**5 - 2/3*a - 2/3 - 2/3*a**4.
-2*(a - 1)**2*(a + 1)**3/3
Factor -40*h + 80 - 45*h + 15*h**2 - 5*h**3 + 30*h**2 - 35*h.
-5*(h - 4)**2*(h - 1)
Let t(x) be the second derivative of -x**4/36 - x**3/18 + x**2/3 + 10*x. Determine y so that t(y) = 0.
-2, 1
Let d = 4 + -2. Suppose 4 = r + d. Factor -t**3 - t**3 - t - 8*t**r - 7*t.
-2*t*(t + 2)**2
Let w(u) be the first derivative of -4*u**5/45 - 5. Factor w(n).
-4*n**4/9
Let n = -15 + 17. Factor 0*s**2 + 8/3*s + 0 + 2/3*s**4 - n*s**3.
2*s*(s - 2)**2*(s + 1)/3
Let j = 7 - 4. Let 6*z**4 + 3*z - 4*z**3 - 6*z**j + z**3 = 0. Calculate z.
-1/2, 0, 1
Let -3/4*w**2 + 3 + 0*w = 0. Calculate w.
-2, 2
Let d be (6/(-12))/(2/(-12)). Let x(p) be the second derivative of -2*p - 1/18*p**4 + 0*p**2 + 0 + 1/9*p**d. Factor x(y).
-2*y*(y - 1)/3
Let i be (2/(4 - 0))/(-13 + 15). Solve -i*o**3 + 1/4*o**2 + 1/4*o - 1/4 = 0.
-1, 1
Let w(z) be the second derivative of -z**7/147 + z**6/35 + z**5/70 - 11*z**4/42 + 4*z**3/7 - 4*z**2/7 + 10*z + 1. Suppose w(g) = 0. What is g?
-2, 1, 2
Let q = 4 - 3. Let t be (1 - q)/((-4)/(-2)). Determine d, given that 2*d**2 - 2*d**3 - 8*d**2 + t*d**2 - 2 - 6*d = 0.
-1
Let f(y) = y**3 - 8*y**2 + 4. Let u be f(8). Let k(s) be the second derivative of 0*s**3 - 1/60*s**5 + 0 + 2*s + 0*s**2 - 1/36*s**u. Factor k(c).
-c**2*(c + 1)/3
Let o(p) be the third derivative of 1/108*p**4 + 0 - 1/1512*p**8 + 0*p + 0*p**6 + 0*p**3 - 1/135*p**5 + 2/945*p**7 - p**2. Factor o(s).
-2*s*(s - 1)**3*(s + 1)/9
Let n(o) be the second derivative of -o**5/20 + o**4/12 - 4*o. What is p in n(p) = 0?
0, 1
Let m = -5 + 2. Let d be m/((-9)/(-8)) - -3. Determine t so that -1/3 - d*t + 1/3*t**3 + 1/3*t**2 = 0.
-1, 1
Let w(v) = -5*v**5 - 15*v**4 + 65*v**3 + 55*v**2 + 20*v. Let x(t) = -t**4 + t**3. Let m(r) = w(r) - 20*x(r). Factor m(k).
-5*k*(k - 4)*(k + 1)**3
Let d = -191 + 191. Factor 1/4*b**3 - 1/4*b**2 + d - 1/2*b.
b*(b - 2)*(b + 1)/4
Let l(g) be the first derivative of -g**5/10 - 3*g**4/16 + 50. Suppose l(m) = 0. What is m?
-3/2, 0
Let c be 3/(-6) - (-21)/6. Suppose 2*t**3 + 3*t**4 - c*t**3 + t**5 - 3*t**4 = 0. Calculate t.
-1, 0, 1
Let x(z) be the third derivative of -z**10/12096 + z**9/15120 + z**4/6 - 2*z**2. Let p(m) be the second derivative of x(m). Let p(g) = 0. What is g?
0, 2/5
Let l(b) be the third derivative of -b**6/40 + b**5/10 + 3*b**4/8 - 6*b**2. Determine j, given that l(j) = 0.
-1, 0, 3
Let v(f) be the second derivative of -9/50*f**5 + 1/20*f**4 + 2/5*f**3 - f + 3/10*f**2 + 0. Determine b, given that v(b) = 0.
-1/2, -1/3, 1
Let x(q) = -q**3 - 5*q**2 - 8*q - 4. Let j be x(-3). Let a(b) be the second derivative of j*b - 1/12*b**3 + 0 + 1/8*b**2 + 1/48*b**4. What is i in a(i) = 0?
1
Let p(a) = 3*a**4 - 3*a**3 - 12*a**2 - 13*a - 2. Let k(o) = -2*o**4 + o**3 + 6*o**2 + 7*o + 1. Let j(l) = 5*k(l) + 3*p(l). Factor j(f).
-(f + 1)**4
Let x(p) be the third derivative of p**6/40 + p**5/20 - p**4/24 - p**3/2 + 2*p**2. Let r(m) = m**2 + m - 1. Let y(w) = -2*r(w) + x(w). Let y(c) = 0. What is c?
-1, -1/3, 1
Let b(a) be the second derivative of 1/25*a**6 + 1/105*a**7 + 0 - 2/15*a**3 + 0*a**2 + 1/50*a**5 - 1/10*a**4 - 5*a. Solve b(c) = 0 for c.
-2, -1, 0, 1
Let j(r) = 3*r**2 - 12*r + 3. Let h(k) = -3*k**2 + 13*k - 4. Let s(y) = 3*h(y) + 4*j(y). Let s(p) = 0. Calculate p.
0, 3
Let -15*i**2 - 5 + 0*i**2 + 2*i**3 + 15*i + 3*i**3 = 0. Calculate i.
1
Let u(a) = a**3 + 5*a**2 - 2*a - 10. Let s be u(-5). Factor s*n + 0 - 1/2*n**3 + 0*n**2.
-n**3/2
Let t(z) = -z**3 + 8*z**2 - 4*z + 13. Let n be t(7). Factor -38*l**3 - 16*l**2 - 36*l - n*l**2 - 2*l**5 + 4*l - 5*l**4 - 8 - 9*l**4.
-2*(l + 1)**3*(l + 2)**2
Let i = 30 + -99. Let a = 209/3 + i. Solve -2*r**3 + 0 - 2/3*r + a*r**4 + 2*r**2 = 0.
0, 1
Suppose -66*o + 77*o = 22. Factor -8/7 + 4/7*a**o + 4/7*a.
4*(a - 1)*(a + 2)/7
Let j(i) = -39*i**5 + 165*i**4 - 189*i**3 + 93*i**2 - 12*i. Let z(u) = -10*u**5 + 41*u**4 - 47*u**3 + 23*u**2 - 3*u. Let f(t) = -2*j(t) + 9*z(t). Factor f(k).
-3*k*(k - 1)**3*(4*k - 1)
Suppose -2*s + 36 = s. Suppose -s = -g - 3*g. Factor 2*w**5 + w**5 - 2*w**4 + 2*w - 4*w**g - w**5 + 4*w**2 - 2.
2*(w - 1)**3*(w + 1)**2
Let a = 4/5 - 18/35. Find n such that 2/7 - a*n**2 + 0*n = 0.
-1, 1
Let j(m) = 3*m**4 - 3. Let v(i) = 3*i**4 - i**3 + i**2 + i - 4. Let a(l) = 4*j(l) - 3*v(l). Solve a(n) = 0.
-1, 0, 1
Let m(d) be the first derivative of 1/3*d**2 + 0*d - 2/9*d**3 + 9. Suppose m(n) = 0. What is n?
0, 1
Let i(o) = 7*o + 8*o - 16*o - o**3 + 1. Let n(f) = -9*f**4 + 29*f**3 - 16*f**2 + 12*f - 8. Let w(y) = 24*i(y) + 3*n(y). Determine h so that w(h) = 0.
0, 2/3, 1
Suppose 4*t = k - 6, 7*k - 3*k + 15 = 3*t. Let h = 10 + k. Factor -s**4 - 1/3 - h*s**2 + 2*s + 10/3*s**3.
-(s - 1)**3*(3*s - 1)/3
Let x(o) be the third derivative of o**8/672 - o**7/84 + 3*o**6/80 - 7*o**5/120 + o**4/24 + 24*o**2. Determine m, given that x(m) = 0.
0, 1, 2
Factor -p**2 + 1/2 - 1/2*p + p**3 + 1/2*p**4 - 1/2*p**5.
-(p - 1)**3*(p + 1)**2/2
Let r be 60/(-45)*(-3)/14. Factor 4/7*f**4 + r*f**3 + 2/7*f**5 + 0*f + 0 + 0*f**2.
2*f**3*(f + 1)**2/7
Let t(o) be the first derivative of 12*o**5/5 - o**4 + 3. Determine k so that t(k) = 0.
0, 1/3
Suppose 6 = -p - 2. Let h = -6 - p. Suppose -2/9*r**3 - 2/9*r**4 + 0 + 0*r + 2/9*r**5 + 2/9*r**h = 0. Calculate r.
-1, 0, 1
Suppose -2*w - 3 = d + 1, 36 = 5*d - 4*w. Let j(s) be the first derivative of -1/4*s**2 + 1/8*s**d + 1/2*s - 1/6*s**3 - 3. Factor j(h).
(h - 1)**2*(h + 1)/2
Factor 0*t + 0*t**4 + 0*t**3 + 0 - 4/7*t**5 + 0*t**2.
-4*t**5/7
Let n = 38 - 35. Suppose -n*f = f - 8. Find i such that 1/2 - 1/4*i**f + 1/4*i = 0.
-1, 2
Suppose 7*h = 13*h. Let n(f) be the second derivative of 1/48*f**4 + 1/120*f**6 - 1/40*f**5 + 0 - f + h*f**2 + 0*f**3. Factor n(l).
l**2*(l - 1)**2/4
Suppose -2*a + 4 = 2*a + 2*s, 15 = a - 3*s. Suppose 0*b**2 - 24/5*b**4 - 18/5*b + 4/5 + 38/5*b**a = 0. What is b?
-2/3, 1/4, 1
Let o(f) be the first derivative of f**6/180 + f**5/20 + f**4/6 + 5*f**3/3 + 2. Let d(l) be the third derivative of o(l). Solve d(r) = 0.
-2, -1
Let z = 60 + -58. Let v(w) be the third derivative of 0 - 1/72*w**4 + 0*w + 1/360*w**6 + z*w**2 - 1/90*w**5 + 1/9*w**3. Let v(r) = 0. What is r?
-1, 1, 2
Let q be (-324)/7 - (-14)/49. Let o be (-3 - q/16)*-2. Factor 0*k**2 + o*k - 1/4*k**3 + 0.
-k*(k - 1)*(k + 1)/4
Suppose 2*o + 8 + 8 = 0. Let x = 11 + o. Factor 1/3*y**x + 0*y + 0 - y**4 + 0*y**2.
-y**3*(3*y - 1)/3
Let c(j) be the first derivative of 16*j**5/5 - 2*j**4 - 13*j**3 - 17*j**2/2 - 2*j + 2. What is m in c(m) = 0?
-1, -1/4, 2
Let i(j) be the first derivative of -j**3/3 - j**2 + 3*j - 8. Factor i(g).
-(g - 1)*(g + 3)
Solve 4/5*y + 0 + 18/5*y**2 + 6*y**3 + 22/5*y**4 + 6/5*y**5 = 0.
-1, -2/3, 0
Let c be ((-5)/6)/(30/(-24)). Find u, given that c*u + 1/3 + 1/3*u**2 = 0.
-1
Let y = 81 - 809/10. Let u(o) be the second derivative of 0 + 3*o + 0*o**2 + 1/3*o**3 + 0*o**4 - y*o**5. What is j in u(j) = 0?
-1, 0, 1
Let n(s) = -8*s + s**2 - 2*s**2 - 6 - 3. Let p be n(-6). Factor -4/3*c - 14/3*c**2 + 2/3 - 8/3*c**p.
-2*(c + 1)**2*(4*c - 1)/3
Let o be -2*(-85)/(-50) + (-8)/(-2). Factor 3/5*w + 0 - o*w**3 + 0*w**2.
-3*w*(w - 1)*(w + 1)/5
Let f = 4 - 0. Factor -3*u**2 - u**f + 3*u**2 + 2*u + u**3 + 1 - 3*u**3.
-(u - 1)*(u + 1)**3
Let b be (-2*(5 - 9))/2. Factor 0*p**3 + 0*p + 1/9*p**b - 1/9*p**2 + 0.
p**2*(p - 1)*(p + 1)/9
Suppose 2*t + 1 = 5. Suppose t*y = -y. What is h in 0*h - 1/4*h**3 - 1/4*h**2 + y = 0?
-1, 0
Let y be (-1 + 2 - 3)*-1. Factor 1 - i**2 + 10*i**5 + 18*i**3 - 1 - 26*i**4 + 3*i**y - 4*i.
2*i*(i - 1)**3*(5*i + 2)
Let s(r) be the first derivative of 0*r + 8/5*r**5 + 1 + 4*r**3 + r**2 + 9/2*r**4. Factor s(i).
2*i*(i + 1)**2*(4*i + 1)
Factor 5*b**5 - 2*b**5 - 3*b**5 + b**5.
b**5
Suppose p + p = 0. Suppose -y + 5*y - 8 = p. Let -1/3*s**4 + 0 + 1/3*s**y + 0*s**3 + 0*s = 0. Calculate s.
-1, 0, 1
Determine b so that -2/11*b**2 + 0 - 6/11*b = 0.
-3, 0
Let z = -20722/135 + 3