 21/4*x**4 + 0*x**2 + z*x**3 + 6. Determine s, given that f(s) = 0.
0, 2/7
Solve 6*w**2 - 2*w + w**4 + 27/2*w**3 - 9/2*w**5 + 0 = 0 for w.
-1, 0, 2/9, 2
Let t be 6/3 + (-128)/65. Let i = t + 59/195. Determine k, given that k - i*k**3 + 0*k**2 + 2/3 = 0.
-1, 2
Let y be 1/(168/(-1673)) + 10. Let k(c) be the first derivative of 1/30*c**5 + 0*c + 0*c**2 - 1/36*c**6 + y*c**4 - 1/18*c**3 - 10. Factor k(v).
-v**2*(v - 1)**2*(v + 1)/6
Let o(p) = -p**3 - p**2 + p - 3. Let z be o(-4). Determine s, given that -4*s**4 - 7*s**2 - z*s + 3*s**3 + 5*s - 5*s**2 + 17*s**3 = 0.
-1, 0, 3
Suppose 2*h + 0*h = -4*r + 24, 5*r = 3*h - 36. Let i(g) = g**2 + 5. Let a be i(0). Factor 27*m**3 + h*m**a + 36*m**4 - 7*m**5 + 10*m**5 + 0*m**5 + 6*m**2.
3*m**2*(m + 1)**2*(5*m + 2)
Factor 0 - 1/3*k**5 + 0*k**4 - 2/3*k**2 + 0*k + k**3.
-k**2*(k - 1)**2*(k + 2)/3
Determine a, given that 2/3*a**2 - 1/3*a**3 + 0 - 1/3*a = 0.
0, 1
Factor -8*x - 50 - 2*x**2 + 17*x - 5*x + 16*x.
-2*(x - 5)**2
Let a(s) be the first derivative of -5*s**4/4 + 5*s**3/3 + 5*s**2/2 - 5*s + 26. Let a(j) = 0. Calculate j.
-1, 1
Let q = -787/4 + 199. Suppose 41 = -20*w + 81. Factor 1/4*d**w + q - 3/2*d.
(d - 3)**2/4
Let a(u) be the third derivative of 3*u**3 + 1/20*u**6 + 0 + 13/8*u**4 + 9/20*u**5 + 0*u - 26*u**2. What is x in a(x) = 0?
-2, -3/2, -1
Let w(m) = 3*m**2 - 4*m - 1. Let c be w(2). Factor -2*v**4 + 6*v**2 - 2*v - 4*v**2 + 4*v**3 - 2*v**3 + 0*v**c.
-2*v*(v - 1)**2*(v + 1)
Let v(p) be the third derivative of -p**3/3 - p**2. Let z = -497 + 495. Let g(u) = u**2 + u + 5. Let l(m) = z*g(m) - 5*v(m). Determine d so that l(d) = 0.
-1, 0
Let n(w) be the third derivative of -2*w**7/175 - 3*w**6/40 - 21*w**5/100 - 13*w**4/40 - 3*w**3/10 - 8*w**2 - w. Factor n(l).
-3*(l + 1)**3*(4*l + 3)/5
Factor -4*h**2 - 4*h**3 - 12 - 6*h**2 + 24*h + 2*h**2 + 5*h**2 - 5*h**3.
-3*(h - 1)*(h + 2)*(3*h - 2)
Let z(u) = -23*u**3 + 393*u**2 - 954*u - 1361. Let j(c) = -6*c**3 + 98*c**2 - 238*c - 340. Let y(t) = 9*j(t) - 2*z(t). Factor y(i).
-2*(i + 1)*(2*i - 13)**2
Let i(y) = 2*y + 14*y**3 + 4 + 8*y**4 + 6*y**2 + 4*y + 2*y**4. Let z(x) = 9*x**4 + 14*x**3 + 7*x**2 + 5*x + 3. Let v(k) = -3*i(k) + 4*z(k). Factor v(r).
2*r*(r + 1)**2*(3*r + 1)
Let p(m) = -2*m + 6. Let y = -49 - -51. Let v be p(y). Suppose -42/13*h - 20/13*h**v - 18/13 - 2/13*h**5 + 12/13*h**3 + 6/13*h**4 = 0. What is h?
-1, 3
Let q = 1991/798 + 2/399. Let k(r) be the first derivative of 8*r**2 - 5 - q*r**4 + 8*r - 14/3*r**3. Factor k(w).
-2*(w - 1)*(w + 2)*(5*w + 2)
Let h be 62/10 + -14 + 11 + 1. Factor -6/5*t - h*t**2 - 3*t**4 + 0 - 27/5*t**3 - 3/5*t**5.
-3*t*(t + 1)**3*(t + 2)/5
Let m(f) be the second derivative of -f**6/220 + 9*f**5/110 - 5*f**2 + 38*f. Let o(d) be the first derivative of m(d). Determine h, given that o(h) = 0.
0, 9
Let s = 7225/14 - 516. Let z(i) be the first derivative of 0*i**3 - s*i**4 + 0*i - 2/35*i**5 + 0*i**2 - 7. Determine j so that z(j) = 0.
-1, 0
Let -16/7 - 4/7*i**2 + 20/7*i = 0. What is i?
1, 4
Let x(c) be the first derivative of -c**5/5 - 2*c**4 + 4*c**3 + 72*c**2 + 339. Factor x(w).
-w*(w - 4)*(w + 6)**2
Let o = -1096/3 + 368. Factor o*a + 4 - 4/3*a**2.
-4*(a - 3)*(a + 1)/3
Let b(v) = -2*v**5 - v**4. Let o(p) = 8*p**5 - 5*p**4 + 6*p**3 + 8*p**2 - 8*p. Let d(t) = 6*b(t) + 2*o(t). Let d(j) = 0. Calculate j.
-1, 0, 1, 2
Let g(m) be the third derivative of 2*m**7/105 + m**6/6 + 7*m**5/15 + m**4/2 + 10*m**2 + m. Find k such that g(k) = 0.
-3, -1, 0
Let u(n) be the second derivative of -n**4/3 + 4*n**3/3 + 6*n**2 - 70*n + 2. Factor u(l).
-4*(l - 3)*(l + 1)
Let t = 609/68 - 148/17. Factor -1/4*y + 1/4*y**2 + 1/4*y**3 - t.
(y - 1)*(y + 1)**2/4
Let -152*r**2 - 295*r + 861*r + 4*r**3 - 2592 + 439*r + 202*r + 377*r = 0. Calculate r.
2, 18
Let h(v) be the second derivative of -2*v + 77/6*v**4 - 121/10*v**5 + 5 + 4*v**2 + 40/3*v**3. Determine w so that h(w) = 0.
-2/11, 1
Let n = 729 - 723. Let k(b) be the third derivative of -1/24*b**4 + 2/105*b**7 - 1/20*b**n + 0*b + 0 + 3*b**2 - 1/336*b**8 + 0*b**3 + 1/15*b**5. Factor k(f).
-f*(f - 1)**4
Let w = 712/595 - -2/595. Determine l, given that -72/5*l**2 - w - 9*l + 48/5*l**3 = 0.
-1/4, 2
Let u be 5 + 26/39 + 1/(-3). Let 13/3*i**3 - i**2 + 4/3 - u*i - 4/3*i**4 = 0. What is i?
-1, 1/4, 2
Factor -2*b**2 + 30/7*b - 2*b**3 + 0 - 2/7*b**4.
-2*b*(b - 1)*(b + 3)*(b + 5)/7
Let g(d) = -d**5 - d**4 + 10*d**3 - d**2 - 14*d. Let n(v) = -v**5 - v**4 + 10*v**3 - 16*v. Let i(h) = 4*g(h) - 5*n(h). Solve i(r) = 0.
-3, -2, 0, 2
Let w(k) be the first derivative of 1/2*k**2 + 0*k**5 + 2/3*k - 2/9*k**3 + 1/18*k**6 - 1/3*k**4 - 16. Suppose w(n) = 0. Calculate n.
-1, 1, 2
Factor 22/3*z + 16/3 - 1/3*z**3 + 5/3*z**2.
-(z - 8)*(z + 1)*(z + 2)/3
Let k(z) = -z**2 + z - 4*z - 10*z - 16. Let q be k(-11). What is w in -1 + 0 + q*w**3 - 27*w**4 + 21*w**5 + 1 = 0?
0, 2/7, 1
Let u(w) be the third derivative of w**8/40320 - w**7/15120 - w**6/4320 + w**5/720 - w**4/4 + 15*w**2. Let o(q) be the second derivative of u(q). Factor o(m).
(m - 1)**2*(m + 1)/6
Determine k so that 42/13*k**3 + 8/13*k**4 + 8/13*k**2 - 2/13*k**5 - 56/13*k + 0 = 0.
-2, 0, 1, 7
Let j(g) be the first derivative of -g**6/6 + 68*g**5/35 - 23*g**4/7 - 32*g**3/21 - 24. Suppose j(b) = 0. Calculate b.
-2/7, 0, 2, 8
Let x(i) be the second derivative of 42/5*i**5 + 3 - 6/5*i**6 - 24*i**3 + 23/3*i**4 - 3*i - 40*i**2. Suppose x(r) = 0. Calculate r.
-2/3, 1, 5
Let h(j) be the first derivative of -1/2*j**2 + 22 - 7/20*j**5 - 1/24*j**6 - 15/16*j**4 + 0*j - 13/12*j**3. Factor h(b).
-b*(b + 1)**3*(b + 4)/4
Factor -6/7*l**2 + 0*l + 6/7*l**3 + 0.
6*l**2*(l - 1)/7
Let m be (-3)/((-11)/((-220)/(-90))). Let d = -10 + 13. Factor 0 + m*c - c**2 + 1/3*c**d.
c*(c - 2)*(c - 1)/3
Let v(k) = -24*k - 360. Let r be v(-15). Determine i, given that -3/7*i**2 - 2/7*i + r - 1/7*i**3 = 0.
-2, -1, 0
Suppose -3*b + 88 = -5*u + 3*u, -b - 3*u + 11 = 0. Let k be ((-3)/(-11))/(-1)*b/(-39). Factor -6/11*l + k*l**2 + 0.
2*l*(l - 3)/11
Suppose -25*h + 38 = -6*h. Let d(n) be the third derivative of -2/5*n**3 + 9*n**h + 0*n**4 + 0*n + 1/100*n**5 + 0. Factor d(x).
3*(x - 2)*(x + 2)/5
Let p(r) be the third derivative of 0*r + 0 - 1/600*r**6 - 3/100*r**5 - 7/30*r**3 - 1/8*r**4 - 6*r**2. Factor p(d).
-(d + 1)**2*(d + 7)/5
Let v = 60 - 58. Let c be 2/10*(-10)/(-3). Factor 4/3 - 2/3*z - 4/3*z**v + c*z**3.
2*(z - 2)*(z - 1)*(z + 1)/3
Suppose -27 = -5*s - 2, 2*l + 5*s = 35. Let w(q) = 3*q**2 - 9*q + 1. Let v(g) = 8*g - 2*g**2 - g**2 + g. Let y(r) = l*v(r) + 6*w(r). Solve y(t) = 0 for t.
1, 2
Let r be 0 - (-2 - -1 - 3). Let 674*p**2 - 677*p**2 - 4*p + 5*p**3 + 4*p**r - p**4 - p**5 = 0. What is p?
-1, 0, 1, 4
What is u in 572*u - 644*u + 512*u + 4*u**2 = 0?
-110, 0
Let f(h) be the third derivative of -h**7/70 + 103*h**6/200 - 633*h**5/100 + 221*h**4/8 + 55*h**3 - 127*h**2. Find z such that f(z) = 0.
-2/5, 5, 11
Let c(s) be the second derivative of -9/10*s**3 - 27/10*s**2 + 14*s - 1/100*s**5 + 0 - 3/20*s**4. Find g such that c(g) = 0.
-3
Let y(j) be the third derivative of j**7/672 - j**6/480 - j**5/40 - j**4/24 - 7*j**3/3 - 12*j**2. Let z(u) be the first derivative of y(u). Factor z(v).
(v - 2)*(v + 1)*(5*v + 2)/4
Factor 4*h + 2 - 21/2*h**2.
-(3*h - 2)*(7*h + 2)/2
Suppose -421*o + 5 = -422*o + 4*w, -5*o + 2*w = -11. Let l = 16 + -47/3. Factor -1/3*h + l*h**o - 1/3 + 1/3*h**2.
(h - 1)*(h + 1)**2/3
Let c(b) = -8*b**2 + 8*b - 8. Let a(y) be the first derivative of 4*y**2 - 7/3*y**3 + 4 - 7*y. Let g(r) = 4*a(r) - 3*c(r). Let g(p) = 0. Calculate p.
1
Let a(z) be the second derivative of 0 + 7*z + 0*z**2 + 0*z**4 + 0*z**3 - 1/100*z**5 + 1/150*z**6. Factor a(w).
w**3*(w - 1)/5
Factor -340 + 56*h + 16*h**2 - 50*h**2 + 32*h + 12*h**2 + 18*h**2.
-4*(h - 17)*(h - 5)
Suppose -3*m + 5 = -8*m, -2*d + 2*m = -18. Suppose 3*b - d = b. Factor -8 + 5*c - 3*c + 2*c + b*c - 2*c**2.
-2*(c - 2)**2
Let p = 85 + -83. Let w be p/3*(4 - 7) + 4. Find u, given that -3/5*u - 1/5 - 1/5*u**3 - 3/5*u**w = 0.
-1
Suppose 3*a - 3*h = 15, a + a - h = 11. Suppose 5*g = 2*g + a. Factor -g*y**2 - 3*y**3 - 3*y**4 + 5*y**2 + 3*y + 0*y**2.
-3*y*(y - 1)*(y + 1)**2
Let q(f) be the first derivative of 1/15*f**5 + 1/3*f**3 + 0*f + 1/120*f**6 + 5/24*f**4 + f**2 + 5. Let x(u) be the second derivative of q(u). Factor x(b).
(b + 1)**2*(b + 2)
Let k = 677 + -675. Let s