 1
Factor -2*r**4 + 1/3*r**5 + 4*r - r**3 + 16/3*r**2 + 0.
r*(r - 6)*(r - 2)*(r + 1)**2/3
Let a(h) = 32*h - 1111. Let m be a(35). Factor 3/2*j + 9/2*j**3 + 15*j**2 - m.
3*(j + 1)*(j + 3)*(3*j - 2)/2
Let h(c) = -c**3 + 2*c**2 + 4*c - 20. Let b be h(5). Let x = b - -78. Factor -4/5*r**x + 6/5*r**4 - 2/5*r**5 - 2/5 + 6/5*r - 4/5*r**2.
-2*(r - 1)**4*(r + 1)/5
Solve -4/3*n + 52/3*n**3 + 8/3 - 12*n**2 - 20/3*n**4 = 0 for n.
-2/5, 1
Let l(d) be the second derivative of d**4/28 - 18*d**3/7 + 192*d**2/7 + d - 285. Factor l(z).
3*(z - 32)*(z - 4)/7
Let t = -1666 + 1671. Let p(d) be the first derivative of 4/5*d**3 - 24/5*d**t + 129/20*d**4 - 15/2*d**6 - 13 + 0*d - 6/5*d**2. Suppose p(o) = 0. Calculate o.
-1, -1/3, 0, 2/5
Suppose 12 = 4*u - 5*v, 3*u - v + 2*v = 9. Suppose -b + 0*b = -0*b. Factor x**u + 0 + b*x**2 - 1/2*x - 1/2*x**5 + 0*x**4.
-x*(x - 1)**2*(x + 1)**2/2
Let x be (-2 - 0)*-12*(-1)/8. Let i be -3 - (21/(-5) - x) - -2. Solve 7/5*n**3 + 0*n**4 - i - 4/5*n**5 - 3/5*n + 1/5*n**2 = 0 for n.
-1, -1/2, 1
Let b = -239 + 242. Find f, given that -2/5*f + 0 + 4/5*f**2 + 2/5*f**5 - 4/5*f**4 + 0*f**b = 0.
-1, 0, 1
Let r(c) = -5*c**2 - 6*c. Let z(i) be the first derivative of i**3/3 + i**2/2 + 19. Let d(u) = 5*r(u) + 20*z(u). Factor d(f).
-5*f*(f + 2)
Factor 2/3 - 26/9*n + 26/9*n**2 - 2/3*n**3.
-2*(n - 3)*(n - 1)*(3*n - 1)/9
Let h(m) = 17*m**2 - 150*m - 48. Let g(o) = 42*o**2 - 374*o - 120. Let l(r) = -5*g(r) + 12*h(r). Factor l(v).
-2*(v - 12)*(3*v + 1)
Let x(g) be the first derivative of g**6/60 + 9*g**5/20 + 9*g**4/2 + 18*g**3 + 11*g - 20. Let b(v) be the first derivative of x(v). Solve b(k) = 0.
-6, 0
Let p(t) be the third derivative of -t**3/6 - t**2. Let q(w) = -3*w - 6 + 42*w**2 - 92*w**2 + 49*w**2. Let v(o) = -6*p(o) + q(o). Find s such that v(s) = 0.
-3, 0
Factor 0*n + 0 - n**4 - 1/3*n**2 + n**3 + 1/3*n**5.
n**2*(n - 1)**3/3
Suppose 2*p = -5*z + 46, 2*z - 5*p + 4 - 5 = 0. Factor 18*h**3 - z*h**3 - 12*h**2 - 6*h**3.
4*h**2*(h - 3)
Let j(l) be the first derivative of 2*l**3/15 - 2*l**2/5 - 331. Factor j(r).
2*r*(r - 2)/5
Let q be 3*(5 - 2 - 2). Suppose 5*l - 7 = 3*y + 20, 4*l + q*y = 0. Solve 9*v**2 - 2*v**l + 0*v**3 - 11*v**2 + 4*v = 0.
-2, 0, 1
Suppose y - 11 = -3*c - 0, 0 = 2*c - 4*y + 16. Let 0 + 1/7*i - 1/7*i**c = 0. Calculate i.
0, 1
Let h(k) be the third derivative of k**8/84 + 2*k**7/35 - 3*k**6/10 + k**5/3 - 2*k**2 + 129*k. Determine d, given that h(d) = 0.
-5, 0, 1
Let m(x) = 5*x - 20. Let z be m(5). Let 12 + 8 - 21 - 4*n**2 + z = 0. Calculate n.
-1, 1
Let h(t) = -12*t**2 - 71*t - 20. Let n(x) = -2*x**2 + x - 4. Let b(l) = -h(l) + 5*n(l). Determine g so that b(g) = 0.
-38, 0
Let i be -2 - 7/((-7)/58). Factor -56 + i + 3*t - 3*t**2.
-3*t*(t - 1)
Let s = 1112/1667 - 2/5001. Factor 2/9*q**2 - s*q + 4/9.
2*(q - 2)*(q - 1)/9
Let y(m) = 36*m - 354. Let l be y(10). Let g(s) be the second derivative of -1/18*s**4 + 2/9*s**3 + l*s - 1/3*s**2 + 0. Find z such that g(z) = 0.
1
Let a(r) be the third derivative of -r**8/2520 - r**7/630 - r**6/540 - 5*r**3/3 - 3*r**2. Let p(l) be the first derivative of a(l). Factor p(y).
-2*y**2*(y + 1)**2/3
Let a(v) = -12*v. Let t be a(-1). Solve -t*h + 4*h - 12*h**4 - 32*h**3 - 28*h**2 + 0*h = 0.
-1, -2/3, 0
Determine l so that 2/17*l**3 + 576/17*l + 648/17 - 70/17*l**2 = 0.
-1, 18
Let t = -20 + 23. Suppose 4*h - 3*x = 87, 0 = -2*x - 4 - 6. Factor 8*m**3 + h*m**3 - 24*m**t.
2*m**3
Let v be -5*(-36)/120*2. Let d**2 + 2/3*d**v + 1/3*d + 0 = 0. Calculate d.
-1, -1/2, 0
Let w be (-23)/92 + 7/(-4). Let t(c) = -c**5 + c**3 - 3*c**2 - 3. Let i(u) = 2*u**2 + 2. Let r(n) = w*t(n) - 3*i(n). Find k such that r(k) = 0.
-1, 0, 1
Let l(r) be the third derivative of -r**7/735 + r**6/35 - 6*r**5/35 + 5*r**2 - 25*r. Determine n, given that l(n) = 0.
0, 6
Let v = -109 - -231. Suppose 0 = 5*z - v + 7. Suppose d**2 + 3*d + z + 2*d**2 - 29 = 0. Calculate d.
-2, 1
Let a(k) = 2*k**4. Let p(h) = -13*h**4 + 6*h**3 - 9*h**2. Let d(z) = -6*a(z) - p(z). Factor d(f).
f**2*(f - 3)**2
Let k be 2/(-4)*(-1 - (-36)/44). Let l(b) be the first derivative of k*b**2 + 2/33*b**3 + 0*b + 4. Factor l(o).
2*o*(o + 1)/11
Let d(c) be the third derivative of -c**9/25200 + c**8/5600 + 7*c**4/24 + 11*c**2. Let b(l) be the second derivative of d(l). Let b(p) = 0. What is p?
0, 2
Let 8*i**3 - 3*i - 5*i + 253*i**4 - i**2 - 252*i**4 = 0. What is i?
-8, -1, 0, 1
Let j(d) be the third derivative of d**5/360 + 23*d**4/72 - 47*d**3/36 - 14*d**2 + 2*d. Factor j(w).
(w - 1)*(w + 47)/6
Let c = 19 + -4. Suppose -d + 13 = 3*l, 5*l = c - 0. Factor 3*y**2 + 48 + d*y + 7*y + 13*y.
3*(y + 4)**2
Let l(c) be the second derivative of -4*c + 5/6*c**3 - 1/20*c**5 - 1/4*c**4 + 0 + 1/30*c**6 - c**2. Factor l(h).
(h - 1)**3*(h + 2)
Let f(k) be the first derivative of 8*k**5/25 - 21*k**4/10 - 12*k**3/5 - 435. Solve f(l) = 0 for l.
-3/4, 0, 6
Let x be ((-24)/60)/(1/(-15)). Let k = x + -1. Factor -r**k + r**5 - 3*r + 6*r**3 - 3*r**5.
-3*r*(r - 1)**2*(r + 1)**2
Let q = 1 - -3. Suppose -13 = -q*k + 3. Factor r - 2 + 2 - k*r - 2 + r**3.
(r - 2)*(r + 1)**2
Let d(f) = -2*f**3 - 3*f**2 - 3*f - 1. Let c be d(-1). Let b be (3/(-3))/(-2) - (1 - c). Suppose 0*m**3 - 4/3*m - b - m**2 + 1/6*m**4 = 0. What is m?
-1, 3
Let l be (-60)/(-126) - 6/42. Find r such that 1/9*r**2 + 1/9*r**4 + l*r - 2/9 - 1/3*r**3 = 0.
-1, 1, 2
Let b(i) = -i**3 - 14*i**2 - i - 12. Let w = 33 + -47. Let c be b(w). Solve 3*g - g**2 - g + c - g = 0 for g.
-1, 2
Let o(h) be the first derivative of 1/18*h**3 - 9 - 1/24*h**4 - 1/6*h + 1/12*h**2. Find z, given that o(z) = 0.
-1, 1
Let r be ((-188)/517)/(2/(-11)). Factor 1/2*x**4 + r + 2*x - 3/2*x**2 - x**3.
(x - 2)**2*(x + 1)**2/2
Let b(f) = -6*f**2 + 9*f - 9. Let h(v) = -11*v**2 + 19*v - 18. Let x(l) = -5*b(l) + 3*h(l). Factor x(g).
-3*(g - 3)*(g - 1)
Let f(z) = 15*z**3 + 7*z**2 - 8*z. Let v(k) = 8*k**3 + 4*k**2 - 4*k. Suppose -3*g + 35 = 23. Let n(o) = g*f(o) - 7*v(o). Factor n(l).
4*l*(l - 1)*(l + 1)
Let t(w) be the third derivative of -w**5/96 + 19*w**4/24 - 5*w**3/4 - 136*w**2. Let t(p) = 0. What is p?
2/5, 30
Suppose -2*j + 12 = 4*j. Let r(x) be the first derivative of 1/2*x**j + 3/2*x**3 - 10 + 7/8*x**4 + 0*x. Factor r(h).
h*(h + 1)*(7*h + 2)/2
Let n = -33 - -36. Determine m so that -3*m - m**n - 3*m**3 + 13*m - 8 + 2*m = 0.
-2, 1
Factor 60/7*q - 2/7*q**3 + 26/7*q**2 + 0.
-2*q*(q - 15)*(q + 2)/7
Let u be 3/(-12)*2/(-3). Let g(f) = f**3 - 4*f**2 + f - 74. Let c be g(6). Factor 0 - 1/6*v + u*v**2 - 1/6*v**c + 1/6*v**3.
-v*(v - 1)**2*(v + 1)/6
Let b(n) be the second derivative of n**7/126 - n**6/90 - 13*n**5/60 + 25*n**4/36 - 2*n**3/3 + 398*n. Factor b(k).
k*(k - 3)*(k - 1)**2*(k + 4)/3
Suppose -81*n + 85*n - 16 = 0. Let b(k) be the first derivative of 0*k + 0*k**2 + 1/22*k**n - 4/33*k**3 - 2 + 2/55*k**5. Find a, given that b(a) = 0.
-2, 0, 1
Let t(m) be the second derivative of -m**6/180 - 17*m**5/120 + 10*m**4/9 - 7*m**3/3 + 30*m. Determine x, given that t(x) = 0.
-21, 0, 2
Let q(d) be the third derivative of -d**8/840 + d**7/180 - d**6/108 + d**5/180 - 5*d**3/2 - 11*d**2. Let y(h) be the first derivative of q(h). Factor y(k).
-2*k*(k - 1)**2*(3*k - 1)/3
Let g be (-7)/3 - (-63)/27. Let u be (-2)/(14/(-4) + 3). Factor g + 1/5*r**3 + 0*r**2 + 2/5*r**u + 1/5*r**5 + 0*r.
r**3*(r + 1)**2/5
Let -k**5 + 45 + 217*k**4 - 32*k**4 + 727*k**2 - 15 + 215*k + 21*k**5 + 465*k**3 - 242*k**2 = 0. What is k?
-6, -1, -1/4
Suppose -4 - 77 = 9*d. Let i be (2 - (-16)/d) + 15/540. Determine c, given that 0 + i*c + 1/4*c**2 = 0.
-1, 0
Let d(r) be the first derivative of -r**7/126 + r**5/30 - r**3/18 + 9*r - 11. Let i(y) be the first derivative of d(y). Find l such that i(l) = 0.
-1, 0, 1
Suppose 126 = 2*q - 5*c, 5*c + 86 + 244 = 5*q. Let z be 23/6 - q/(-102). What is b in -z - 1/2*b**2 - 3*b = 0?
-3
Let b(q) be the second derivative of q**6/15 - q**4/2 - 2*q**3/3 - 20*q. Determine u so that b(u) = 0.
-1, 0, 2
Let a = -48060/7 + 6868. Find p, given that -a*p + 16/7*p**3 + 16/7 - 12/7*p**2 - 4/7*p**4 = 0.
-1, 1, 2
Let i(q) be the third derivative of q**7/840 + q**6/30 + 2*q**5/5 + 5*q**4/12 + 13*q**2. Let d(s) be the second derivative of i(s). Let d(h) = 0. Calculate h.
-4
Let o(b) be the first derivative of -13*b**2 - 9/2*b**4 + 2 + 4*b + 16*b**3. Factor o(n).
-2*(n - 2)*(3*n - 1)**2
Suppose 28/5*