Let r be (2/4)/(p/4). Find f, given that f - 1/4*f**2 - r = 0.
2
Let j(v) be the third derivative of v**6/24 + v**5/6 - 9*v**2. Solve j(t) = 0.
-2, 0
Suppose -3*d + 2 = -5*f, -16 = -d - 3*d. Suppose 13 - 9*i**4 + 20*i + 4*i**5 + 29*i**4 + 40*i**f - 9 + 40*i**3 = 0. What is i?
-1
Let m(q) be the second derivative of q**8/336 - q**7/210 - q**6/120 + q**5/60 - q**2/2 + q. Let o(u) be the first derivative of m(u). Factor o(j).
j**2*(j - 1)**2*(j + 1)
Suppose -15 = -7*j + 13. Let -6/5*w**5 + 0*w + 0 - 8/5*w**j - 2/5*w**3 + 0*w**2 = 0. What is w?
-1, -1/3, 0
Let a(v) = 6*v + 6 - 3*v**2 + 8*v**2 + 4*v**2 - v**2. Let d(o) = -7*o**2 - 5*o - 5. Let c(i) = -5*a(i) - 6*d(i). Factor c(s).
2*s**2
Let l(k) = -6*k**4 + 64*k**3 + 56*k**2 - 64*k - 28. Let w(n) = n**4 - 9*n**3 - 8*n**2 + 9*n + 4. Let a(s) = 6*l(s) + 44*w(s). Suppose a(c) = 0. Calculate c.
-1, -1/2, 1, 2
Let z(g) be the second derivative of -g**6/30 - 3*g**5/20 - g**4/4 - g**3/6 - 4*g. Factor z(i).
-i*(i + 1)**3
Let g(r) be the first derivative of r**4/28 + r**3/7 - 2*r**2/7 + 20. Let g(l) = 0. What is l?
-4, 0, 1
Let q = 92/25 - 2386/825. Let t = q + 6/11. Factor -2/3*v**5 - 1/3*v**2 - 5/3*v**4 + 0 + 0*v - t*v**3.
-v**2*(v + 1)**2*(2*v + 1)/3
Let p(n) be the first derivative of -n**6/24 - 3*n**5/20 - 3*n**4/16 - n**3/12 + 14. Factor p(u).
-u**2*(u + 1)**3/4
Factor -3*g**3 - 5*g**4 + 0*g**3 - 9*g**3 + 7*g**3.
-5*g**3*(g + 1)
Let o(g) be the first derivative of 0*g - 1/15*g**6 + 0*g**3 + 1/10*g**4 + 0*g**5 + 0*g**2 + 2. Factor o(u).
-2*u**3*(u - 1)*(u + 1)/5
Determine c, given that 8/15 - 16/5*c + 6*c**2 - 10/3*c**3 = 0.
2/5, 1
Suppose 21 = 4*d - 3. Let h be d/(-27) + (-29)/(-9). Factor 0 + 0*b - 1/4*b**2 + 1/4*b**4 - 1/4*b**h + 1/4*b**5.
b**2*(b - 1)*(b + 1)**2/4
Let w be 2/(-14)*-16 - 2. Factor -8/7*x**3 + w*x**2 + 0 + 0*x.
-2*x**2*(4*x - 1)/7
Let x(c) be the first derivative of c**6/3 - 6*c**5/5 + 3*c**4/2 - 2*c**3/3 + 7. Solve x(m) = 0.
0, 1
Let r(b) = b**3 - b**2 + b + 1. Let v(f) = -4*f**3 + 3*f**2 - 9*f + 3. Let s(l) = -5*r(l) - v(l). Factor s(q).
-(q - 2)**2*(q + 2)
Determine n so that 20 + 0*n - 18*n**2 + 11*n**2 + 2*n**2 + 15*n = 0.
-1, 4
Let o(w) be the second derivative of -7*w + 0*w**2 + 0 - 1/60*w**5 - 1/30*w**6 + 0*w**3 + 0*w**4. Solve o(v) = 0.
-1/3, 0
Suppose 1/9*i**4 + 0*i + 2/9*i**2 + 0 + 1/3*i**3 = 0. Calculate i.
-2, -1, 0
Let b(d) be the first derivative of 2/3*d**3 - 3 + 0*d + 0*d**2. Factor b(j).
2*j**2
Let s = -1 - 0. Let m(g) = -g**2 + g. Let q(l) be the first derivative of l**4/2 + 14*l**3/3 - 4*l**2 + 5. Let c(d) = s*q(d) - 10*m(d). Factor c(n).
-2*n*(n + 1)**2
Let l(d) be the third derivative of 0*d + 3/350*d**7 + 1/560*d**8 - 6*d**2 - 3/100*d**5 + 0*d**3 + 1/200*d**6 + 0 - 1/20*d**4. Let l(x) = 0. Calculate x.
-2, -1, 0, 1
Let y(z) be the first derivative of z**4/16 + z**3/12 - 19. Factor y(a).
a**2*(a + 1)/4
Let v(s) be the third derivative of s**6/1140 + 2*s**5/285 + 5*s**4/228 + 2*s**3/57 - 4*s**2 - 4. Let v(d) = 0. What is d?
-2, -1
Suppose -2*z + 6*p + 14 = 2*p, 0 = -4*p + 16. Let u = -15 + z. Let 2/3*q + u + 4/3*q**2 + 2/3*q**3 = 0. Calculate q.
-1, 0
Let n be -8 + 8 + (24 - 1). Solve n*j**4 + 2*j**3 - j**3 - 24*j**4 - 2*j**3 = 0.
-1, 0
Let x(r) be the second derivative of 5*r**4/12 - 10*r**3 + 90*r**2 - 13*r. Factor x(y).
5*(y - 6)**2
Factor 3/5*m**2 - 3 + 12/5*m.
3*(m - 1)*(m + 5)/5
Factor 1/3*z**5 + 0*z**4 - 2/3*z**2 - z**3 + 0*z + 0.
z**2*(z - 2)*(z + 1)**2/3
Find u such that -20/3*u**3 + 32/3 - 4/3*u**4 - 8*u**2 + 16/3*u = 0.
-2, 1
Suppose -42*m + 47*m - 15 = 0. Factor 0*t + 2/7*t**2 - 2/7*t**4 + 0 + 0*t**m.
-2*t**2*(t - 1)*(t + 1)/7
Let 2/5*q**3 - 2/5*q + 4/5*q**2 - 4/5 = 0. Calculate q.
-2, -1, 1
Let a be (-6)/4*(-270)/3. Let l = -943/7 + a. Let 0*k + l - 2/7*k**2 = 0. What is k?
-1, 1
Let k = 3194/11 + -286. Find y, given that -30/11*y + 46/11*y**2 - 32/11*y**4 + k*y**3 + 4/11 = 0.
-1, 1/4, 2
Let l be (-3 - ((-2)/(-6) + -3))*-4. What is r in 4/3*r**2 - l*r**3 + 2/3*r - 2/3*r**4 - 2/3 + 2/3*r**5 = 0?
-1, 1
Suppose 2*s - 17 = -3. Let m be -5 - -4 - -1*s. Factor -y**3 + 7*y - 3 - 4*y**2 - 3*y**3 + 1 + m*y**4 - y - 2*y**5.
-2*(y - 1)**4*(y + 1)
Let 4*p**2 + 41*p**3 - 38*p**3 - 2*p - 3*p - 2 = 0. Calculate p.
-2, -1/3, 1
Factor 0*y**2 + 0*y + 2/19*y**5 + 4/19*y**4 + 2/19*y**3 + 0.
2*y**3*(y + 1)**2/19
Let y be (-2)/(-2)*(2 + (-2)/1). Let k(s) be the third derivative of 0 + 0*s + 1/330*s**5 - 1/66*s**4 + y*s**3 + s**2. Solve k(f) = 0.
0, 2
Solve 4*h**3 + 8*h**2 + 2 - 5*h + h + 0*h**3 - 10 = 0.
-2, -1, 1
Let t(v) = -10*v**4 - 31*v**3 - 36*v**2 - 16*v. Let i(q) = 19*q**4 + 61*q**3 + 72*q**2 + 31*q. Let u(c) = 4*i(c) + 7*t(c). Determine n so that u(n) = 0.
-2, -1/2, 0
Suppose 4*v - a = 12, 2*v + 4*a + 7 = -5. Let 2*c - c**v + 4 - 7*c**2 - 6 + 8*c = 0. Calculate c.
1/4, 1
Suppose 9/2*d**4 + 1/2 - 5*d**2 - 4/3*d + 12*d**3 = 0. Calculate d.
-3, -1/3, 1/3
Let v be 6*1/((-4)/(-3)). Solve 0*u + 0 + 3/2*u**5 - v*u**3 + 3*u**2 + 0*u**4 = 0.
-2, 0, 1
Let j(z) = -z + 6. Let c be j(4). Suppose 0*s - c*s = -4. Determine y so that s - 2*y**4 - 6*y**3 + 4*y - 3*y**3 + 5*y**3 = 0.
-1, 1
Let o(l) be the first derivative of l**4/30 - l**2/5 - 3*l - 4. Let a(v) be the first derivative of o(v). Factor a(q).
2*(q - 1)*(q + 1)/5
Let t(y) be the first derivative of -5*y**3 - 9*y**2/2 + 11. Let t(l) = 0. What is l?
-3/5, 0
Suppose -6 = -2*f + 5*y - 3*y, 2*y = -5*f - 6. Let z(x) be the third derivative of 1/210*x**5 - 2*x**2 + 1/42*x**4 + 0 + 1/21*x**3 + f*x. Factor z(m).
2*(m + 1)**2/7
Let q = -115/7 - -17. Solve 0*r + 0*r**2 - 2/7*r**3 + 0 - q*r**4 - 2/7*r**5 = 0.
-1, 0
Let y(t) = 5*t**5 + 9*t**4 - t**3 - 9*t**2 - 4*t + 1. Let n(c) = c**4 + c**3 - c**2 - c - 1. Let z(p) = -n(p) - y(p). Let z(f) = 0. Calculate f.
-1, 0, 1
Let s = 973/5 - 194. Determine g so that s - 9/5*g**3 - 3*g**2 - 3/5*g = 0.
-1, 1/3
Let o(r) be the third derivative of -r**8/336 + r**7/70 - r**6/40 + r**5/60 - 32*r**2. What is g in o(g) = 0?
0, 1
Let z(b) be the second derivative of b**5/10 - b**4/3 + b**3/3 - 9*b. Factor z(d).
2*d*(d - 1)**2
Let y(n) be the second derivative of -4/3*n**2 + 7/30*n**5 + 0 + 1/2*n**4 - 4/3*n**3 + n. Find h, given that y(h) = 0.
-2, -2/7, 1
Let t(z) be the first derivative of -4*z**3/3 - 6*z**2 - 8*z + 46. Determine s, given that t(s) = 0.
-2, -1
Let a(v) = -2*v**4 + 10*v**3 + 9*v**2 - 3*v. Let i(d) = -d**4 + 7*d**3 + 6*d**2 - 2*d. Let z(u) = 5*a(u) - 7*i(u). Suppose z(n) = 0. What is n?
-1, 0, 1/3, 1
Let t(l) be the second derivative of l**7/15 + 3*l**6/20 - l**5/6 - 3*l**4/4 - 2*l**3/3 - l**2/2 + 6*l. Let p(b) be the first derivative of t(b). Factor p(v).
2*(v - 1)*(v + 1)**2*(7*v + 2)
Determine r so that -2/3*r**3 + 0*r**2 + 2/3*r - 1/3*r**4 + 1/3 = 0.
-1, 1
Let s(j) = 7*j - 4. Let f be s(1). Solve -6/7*m - 6/7*m**4 + 2/7 + 4/7*m**2 + 4/7*m**f + 2/7*m**5 = 0 for m.
-1, 1
Let c(h) be the third derivative of -h**8/560 + h**7/175 + h**6/50 - h**5/50 - 3*h**4/40 - 4*h**2. Suppose c(i) = 0. What is i?
-1, 0, 1, 3
Factor -4/3*p**3 - 2/3*p**4 + 4/3*p + 0*p**2 + 2/3.
-2*(p - 1)*(p + 1)**3/3
Let y(w) be the first derivative of 2 + 1/5*w**3 + 0*w + 0*w**2. Factor y(k).
3*k**2/5
Factor 0 + 0*j**2 + 5/3*j - 5/3*j**3.
-5*j*(j - 1)*(j + 1)/3
Factor -4 - l**3 + l + 16*l**2 - 9*l - 21*l**2.
-(l + 1)*(l + 2)**2
Let x = -79 + 79. Solve -2/5*q**5 + 0*q**3 + x*q + 2/5*q**4 + 0*q**2 + 0 = 0 for q.
0, 1
Suppose 4*l - 3*j - 3 = -7, 14 = l + 3*j. Let q = 1 - -1. Factor -3*g**q + 3*g**2 - 2*g**4 + 2*g**l.
-2*g**2*(g - 1)*(g + 1)
Suppose 213*t = 212*t. Factor -1/5*h**2 + t - 2/5*h**3 + 0*h.
-h**2*(2*h + 1)/5
Suppose 12 = s + 5*s. Let o(h) be the second derivative of 4*h + 1/100*h**5 + 0 + 0*h**s + 0*h**3 + 0*h**4. Factor o(i).
i**3/5
Let h = 9 + -25/3. Factor -h*t**3 - t**2 - 1/6 - 1/6*t**4 - 2/3*t.
-(t + 1)**4/6
Suppose -5*c - 15 = 5*t, -3*t - c - 15 = 2*t. Let w be (t/(-10))/(36/30). Determine z so that -w + 1/4*z**3 + 3/4*z - 3/4*z**2 = 0.
1
Let n(d) be the second derivative of -2*d + 11/9*d**4 - 4/9*d**3 + 0 - 7/6*d**5 + 5/18*d**6 + 0*d**2. Suppose n(w) = 0. Calculate w.
0, 2/5, 2
Let t(b) = -3*b**2 + 5*b**2 + b - 2*b + 1. Let w be t(1). Factor 1/5*x**w - 1/5*x**4 + 1/5*x**3 + 0 - 1/5*x.
-x*(x - 1)**2*(x + 1)/5
Solve 2/7*u**3 - 3/7*u - 4/7*u**2 + 1/7*u**5 + 0 + 4/7*u**4 = 0.
-3, -1, 0, 1
Let -16/3*