z).
-2*z**3*(z - 1)**2/11
Let w be 15/(-30) - (-7)/2. Find z, given that -1/4*z**2 + 0*z + 1/4*z**w + 0 = 0.
0, 1
Let a = -51 + 55. Find y, given that -2/5*y**2 + 6/5*y**3 + 4/5 - 2/5*y**a - 6/5*y = 0.
-1, 1, 2
Let y be 1/(((-5)/12)/(-5)). Suppose -m + 5 = -p + 6, -y = -2*p - 3*m. Find d, given that 0*d**2 - 2*d + 3*d - 2*d**2 + d**p = 0.
0, 1
Suppose 0*p = 2*p + 44. Let m = p + 24. Solve 4/9*o - 2/3*o**4 - 4/9*o**3 - 2/9 + 8/9*o**m = 0 for o.
-1, 1/3, 1
Let y = -59 - -59. Let i(h) be the second derivative of 0 - 2*h + y*h**2 + 1/21*h**3 + 1/42*h**4. Solve i(l) = 0.
-1, 0
Let w(y) = y**4 + 4*y**3 + 2*y**2 + 2*y + 3. Let n(r) = 2*r**4 + 9*r**3 + 5*r**2 + 5*r + 7. Let g(d) = 3*n(d) - 7*w(d). Determine v so that g(v) = 0.
-1, 0, 1
Factor 0*j + 3*j**2 + 2*j**2 - 2*j**3 + 2*j + 4*j**3.
j*(j + 2)*(2*j + 1)
Suppose n - 2 = 1. Suppose -f = -2, -4*p + 25 = 3*f + 3. Factor 3*w - p*w - w**n + 2*w.
-w*(w - 1)*(w + 1)
Let t be (0 - 2) + (-3 - -9). Factor 0 - 2*u + 2*u**t + 1/2*u**5 + 3/2*u**3 - 2*u**2.
u*(u - 1)*(u + 1)*(u + 2)**2/2
Let q be -3*(-3 - -4) - -7. Let b(p) = -p**2 + 4*p + 1. Let i(r) = -5*r**2 + 17*r + 4. Let m(w) = q*i(w) - 18*b(w). What is d in m(d) = 0?
-1
Let k = -21 - -27. Let y(s) = s**3 - 5*s**2 - 3*s + 6. Let i be y(k). Factor -9*q + 3/2 - i*q**3 + 21*q**2 - 3*q**5 + 27/2*q**4.
-3*(q - 1)**4*(2*q - 1)/2
Suppose -f - 3*f + 23 = 5*s, 3*f = 6. Let b(u) be the second derivative of -2/35*u**5 - 5/21*u**s + 1/7*u**2 + 4/21*u**4 + 0 - u. Solve b(d) = 0.
1/2, 1
Let h = -128 - -226. Let g be 2/(-9) + h/9. Factor 16/3*i + 2/3 + g*i**2.
2*(4*i + 1)**2/3
Let b = 7 + -3. Let g(l) be the first derivative of 1/12*l**b - 1/9*l**3 + 1/3*l - 1 - 1/6*l**2. What is a in g(a) = 0?
-1, 1
Factor -6*t - 113 + 113 + 2*t**2.
2*t*(t - 3)
Suppose 0*y + 0 + 4/7*y**2 + 0*y**4 + 2/7*y**5 - 6/7*y**3 = 0. Calculate y.
-2, 0, 1
Let o be (64/(-60) + 1)*-6. What is b in -o*b**2 - 1/5*b**5 + 0 + 2/5*b**4 + 0*b**3 + 1/5*b = 0?
-1, 0, 1
Let a = -76/3 + 392/15. Factor -6/5*t + 2/5*t**2 + a.
2*(t - 2)*(t - 1)/5
Let u(y) be the first derivative of 3*y**5/5 + 3*y**4 + 5*y**3 + 3*y**2 + 4. Factor u(c).
3*c*(c + 1)**2*(c + 2)
Let o(k) be the third derivative of k**6/200 - 4*k**2. Suppose o(s) = 0. What is s?
0
Let c be (-12)/(-40) - 1/(-2). Suppose 2*n + n = 15. Determine s, given that -c*s**2 + 0*s**3 + 4/5*s**4 - 2/5*s + 0 + 2/5*s**n = 0.
-1, 0, 1
Let r(z) be the first derivative of -z**6/105 + z**5/35 + 8*z - 3. Let u(f) be the first derivative of r(f). Solve u(s) = 0.
0, 2
Let d(u) = 2*u + 26. Let g be d(-13). Let w(p) be the third derivative of 0*p - 1/42*p**4 + g + 0*p**3 - 1/210*p**5 + p**2. Solve w(x) = 0.
-2, 0
Suppose 250 + 0*w**3 - 13*w**3 + 2*w**4 + 16*w**2 - 250 - 5*w = 0. Calculate w.
0, 1/2, 1, 5
Let o(i) be the second derivative of i**6/75 - i**4/10 + 2*i**3/15 - 14*i. Determine q so that o(q) = 0.
-2, 0, 1
Factor 24 + 4 - 42 - 48*v - 178 - 3*v**2.
-3*(v + 8)**2
Let h = 14 - 8. Let p be (-12)/((45/h)/(-5)). Factor 8*u**5 + p*u**2 + 45*u**3 - 15*u**3 + 6*u**2 + 26*u**4 + 2*u.
2*u*(u + 1)**3*(4*u + 1)
Let x(b) be the third derivative of b**5/150 + b**4/30 + b**3/15 - 5*b**2. Factor x(q).
2*(q + 1)**2/5
Suppose -4 = 6*r - 16. Let o(z) be the first derivative of 1/6*z**r - 1/12*z**4 - 1/9*z**3 + 1/3*z - 2. Let o(q) = 0. Calculate q.
-1, 1
Suppose -3*i + 2*u = -2*i + 17, 3*i - 5*u = -47. Let h be (-8)/(16/i) - 0. Let 3*j - 6*j**3 + 15/2*j**2 - h = 0. Calculate j.
-3/4, 1
Let h be 102/24 + -6 + 5. Suppose -h*t + 5/4*t**2 - 3/2 = 0. Calculate t.
-2/5, 3
Let z = -2 + 21. Suppose -1 - z = -5*i. Factor -2*x**5 - 6*x**i + 2 + 4*x**4 + 4*x**4 + 4*x**3 - 4*x**2 - 2*x.
-2*(x - 1)**3*(x + 1)**2
Let z(s) = s. Let o(d) = 5*d**3 - 45*d**2 + 85*d - 35. Let q(x) = -o(x) + 10*z(x). Determine w so that q(w) = 0.
1, 7
Let j(k) be the second derivative of k**4/3 + 14*k**3/3 + 12*k**2 - 37*k. Factor j(h).
4*(h + 1)*(h + 6)
Let n(j) be the first derivative of -125*j**6/2 + 360*j**5 - 810*j**4 + 864*j**3 - 1944*j**2/5 + 47. Factor n(t).
-3*t*(5*t - 6)**4/5
Let n(y) be the third derivative of 0*y**4 + 0*y - 8*y**2 - 3/28*y**8 - 26/35*y**7 + 0 + 0*y**3 - 4/3*y**6 - 4/5*y**5. Factor n(o).
-4*o**2*(o + 3)*(3*o + 2)**2
Factor 3*f**4 - 12*f**3 + 18*f**2 - 12*f - 8 - 10 + 21.
3*(f - 1)**4
Let -4/5*h - 2/5*h**2 - 2/5 = 0. Calculate h.
-1
Let s(n) be the second derivative of -2*n**6/15 - n**5/5 + 4*n**4/3 + 8*n**3/3 + 53*n. Find h such that s(h) = 0.
-2, -1, 0, 2
Suppose -5*h - 5 = -25. Suppose 0*w = w - 5*i, 0 = h*w - 4*i. Suppose w*z - z**2 - 3*z + 2*z = 0. Calculate z.
-1, 0
Let h = 7 - -3. Suppose 2*r - h = -3*r. Factor t**2 + 2*t**2 + 1 + r*t - 2*t**2 + 0.
(t + 1)**2
Solve 5*c - 73*c**3 + 5*c**2 - 5*c**4 + 63*c**3 + 5*c = 0.
-2, -1, 0, 1
Let d = 711 - 708. Factor -24/7*a - 2/7*a**d - 16/7 - 12/7*a**2.
-2*(a + 2)**3/7
Let s(x) = -11*x**3 - 16*x**2 - 5*x. Let k(f) = -12*f**3 - 17*f**2 - 5*f. Let v(j) = 6*k(j) - 7*s(j). What is p in v(p) = 0?
-1, 0
Let s = -973 - -6820/7. Determine g so that 8/7*g**3 + s*g**2 - 4/7 - 5/7*g**4 - 8/7*g = 0.
-1, -2/5, 1, 2
Let q(b) = -5*b**3 + 5*b**2 + 10*b. Let f(p) = 4*p**3 - 5*p**2 - 9*p. Let s(m) = -4*f(m) - 3*q(m). Factor s(z).
-z*(z - 6)*(z + 1)
Let s(d) be the second derivative of -1/8*d**4 - 1/12*d**6 + 0*d**2 - 5*d + 0 + 1/12*d**3 - 9/40*d**5. Let s(h) = 0. Calculate h.
-1, 0, 1/5
Let c(w) = 10*w**4 - 28*w**3 + 66*w**2 - 36*w - 6. Let d(n) = 19*n**4 - 56*n**3 + 131*n**2 - 72*n - 11. Let z(x) = 11*c(x) - 6*d(x). Factor z(q).
-4*q*(q - 3)**2*(q - 1)
Suppose -5*a + 16 + 14 = 0. Let b be 1/a*(2 - 0). Factor 7/3*x - 3*x**2 - 2/3 - b*x**4 + 5/3*x**3.
-(x - 2)*(x - 1)**3/3
Let l = 317 + -2217/7. Let x(d) = d + 3. Let t be x(0). Let -l*a**t + 0 + 6/7*a**2 - 4/7*a = 0. What is a?
0, 1, 2
Let p(z) be the first derivative of z**5 + z**4/2 - 5*z**3/3 + 2*z**2 + 5. Let w(u) = -u**4 + u**2 - u. Let t(b) = -p(b) - 6*w(b). Find n such that t(n) = 0.
-1, 0, 1, 2
Let j(t) = -5*t**5 + t**4 - t**3 + 5*t**2 - 3*t. Let v(z) = 4*z**5 - 4*z**2 + 2*z. Let a be -3*(-1 - 2 - -4). Let n(x) = a*v(x) - 2*j(x). Factor n(s).
-2*s**2*(s - 1)*(s + 1)**2
Let l(p) = -p**4 - p. Let r(m) be the third derivative of 11*m**7/210 + m**6/30 - m**5/10 + m**4/24 + 6*m**2. Let h(u) = -5*l(u) - r(u). Factor h(i).
-2*i*(i - 1)*(i + 1)*(3*i + 2)
Let n(r) = r**2 - 44*r + 230. Let c be n(38). Let 2/5 - 3/5*j**c + 1/5*j**3 + 1/5*j**4 - 1/5*j = 0. What is j?
-2, -1, 1
Let g(w) = w**3 + 3*w**2 + 4*w. Let r be g(-3). Let z = r + 12. Factor 1/4*h**2 + 1/4*h + z.
h*(h + 1)/4
Let v be 14/(-4)*-2 + -2. Suppose -10*z + 4 = -8*z. Factor -2*o**v + 2*o**4 - z*o**2 + 0*o**4 + o**3 + o**3.
-2*o**2*(o - 1)**2*(o + 1)
Determine y so that -2*y**4 + 0 + 0*y - 4*y**3 - 1/4*y**5 + 0*y**2 = 0.
-4, 0
Let w(b) be the second derivative of 2*b**7/105 + 6*b**6/25 + 31*b**5/25 + 17*b**4/5 + 16*b**3/3 + 24*b**2/5 + 6*b. Solve w(h) = 0.
-3, -2, -1
Let c(h) be the third derivative of h**6/160 - h**5/20 + h**4/8 - 9*h**2. Solve c(t) = 0 for t.
0, 2
Let l(d) be the first derivative of 3/4*d**2 + 2/3*d**3 - 3*d - 1/8*d**4 + 4. Let q(j) be the first derivative of l(j). Factor q(k).
-(k - 3)*(3*k + 1)/2
Solve -5*d**4 + 5*d**2 + 2*d**3 - 5*d**5 + d - d + 3*d**3 = 0.
-1, 0, 1
Let s(l) be the first derivative of 1/3*l**3 + 2 + 1/60*l**4 + 0*l - 1/900*l**6 + 0*l**5 + 0*l**2. Let w(f) be the third derivative of s(f). Factor w(h).
-2*(h - 1)*(h + 1)/5
Suppose -7 = -5*t + 18. Factor v**3 + 0*v**5 + 6*v**2 - 3*v + 3*v**t - 6*v**4 - v**3.
3*v*(v - 1)**3*(v + 1)
Let r(k) be the third derivative of -k**8/112 + k**7/70 + k**6/40 - k**5/20 - 6*k**2. Suppose r(p) = 0. What is p?
-1, 0, 1
Find t, given that 2*t**4 + 4*t**3 - t**4 + 5*t**2 - 3*t + 5*t = 0.
-2, -1, 0
Let z(u) be the second derivative of u**4/3 + 2*u**3 + 16*u. Factor z(x).
4*x*(x + 3)
Let p(c) be the second derivative of -3/5*c**2 - 5*c - 1/30*c**4 + 4/15*c**3 + 0. Factor p(u).
-2*(u - 3)*(u - 1)/5
Let p = 60 - 57. Let q(b) be the second derivative of 1/150*b**6 - 1/60*b**4 + 1/30*b**p - 2*b + 0*b**2 + 0 - 1/100*b**5. Factor q(j).
j*(j - 1)**2*(j + 1)/5
Let y(l) be the first derivative of -l**3/5 + 3*l**2/10 - 10. Factor y(n).
-3*n*(n - 1)/5
Let t = 61 + 19. Let 2 + 234*o**2 + 1 + t*o + 162*o**3 + 5 = 0. Calculate o.
-1, -2/9
Factor -47 - 50 - 4*v - 2*v**2 - 2*v**2 + 105.
-4*(v - 1)*(v +