Factor -43*s + 12*s**2 + 5*s**3 + 7*s - 2*s**3 + s**3 + 20.
4*(s - 1)**2*(s + 5)
Let p be ((-53)/25 + 2)*(-30)/12. Let r(s) be the third derivative of 9*s**3 + 1/60*s**6 + 0 + 9/4*s**4 - 2*s**2 + p*s**5 + 0*s. Factor r(n).
2*(n + 3)**3
Let w(o) be the second derivative of -o**7/20160 + o**6/320 - 27*o**5/320 - o**4/3 + 5*o. Let d(v) be the third derivative of w(v). Find c such that d(c) = 0.
9
Let p(x) be the first derivative of 2/13*x**2 + 2/13*x**3 + 0*x + 1/26*x**4 - 12. Factor p(s).
2*s*(s + 1)*(s + 2)/13
Let t(u) = u**2 - 7*u - 2. Let c(d) = -18*d**2 - 129*d - 21. Let h(m) = -c(m) + 3*t(m). Suppose h(w) = 0. What is w?
-5, -1/7
Let d = -79 + 79. Suppose d*a**2 - 14*a - 2*a**2 + 0*a**2 = 0. Calculate a.
-7, 0
Factor -653 + 297*p + 4*p**3 + 3*p - 68*p**2 + 84*p - 67.
4*(p - 6)**2*(p - 5)
Determine f so that -1/4*f**2 + 27/4 - 13/2*f = 0.
-27, 1
Let i(r) be the first derivative of r**5/360 + r**4/36 + r**3/12 + 5*r**2/2 + 14. Let p(j) be the second derivative of i(j). Suppose p(b) = 0. What is b?
-3, -1
Suppose 2*z = z + 3. Let g**4 - 4*g - 35*g**z - 3*g**4 + g**5 - 2*g**2 + 32*g**3 + 10*g**2 = 0. What is g?
-2, 0, 1, 2
Let f be (-9)/(-18) + 670/4. Solve -k**2 + k + 3*k**2 - 2*k - f*k**3 - 2 + 169*k**3 = 0.
-2, -1, 1
Factor -3/2*l**3 - 12*l**2 + 0 + 27/2*l.
-3*l*(l - 1)*(l + 9)/2
Let m(g) = 2*g - 3. Let t be m(3). Suppose 0 = 2*x - t - 3. Suppose -8*q**x + 8*q - 2 + 7/2*q**4 - 3/2*q**2 = 0. Calculate q.
-1, 2/7, 1, 2
Let g(k) = k**3 - 26*k**2 + 3. Let f be g(26). Suppose -8*q = -f*q. Find r, given that 4/9*r**4 + 2/3*r**3 + 1/9*r + q + 1/9*r**5 + 4/9*r**2 = 0.
-1, 0
Let n(x) = -10*x**2 + 1547*x - 62432. Let h(a) = 5*a**2 - 772*a + 31217. Let y(j) = -11*h(j) - 6*n(j). Suppose y(b) = 0. What is b?
79
Let u(w) be the first derivative of -w**5/35 + w**4/28 + 2*w**3/21 + 79. Factor u(b).
-b**2*(b - 2)*(b + 1)/7
Let f be (1 - -1)*-2 - 140/(-14). Let x be (f + (-205)/35)/((-2)/(-4)). Factor -4/7*a**2 + x*a**4 + 2/7 + 4/7*a**3 - 2/7*a**5 - 2/7*a.
-2*(a - 1)**3*(a + 1)**2/7
Suppose -5 = -5*i - h, 23*i - h + 5 = 24*i. Let y(s) be the second derivative of -2*s + 1/7*s**2 + i*s**3 + 0*s**5 + 1/105*s**6 - 1/21*s**4 + 0. Factor y(k).
2*(k - 1)**2*(k + 1)**2/7
Let v(s) = -8*s**2 + 5 + 8*s**2 + s**2 - 12*s + 15*s. Let u be v(-3). Factor 0*m + 3*m**u + 0*m**2 - 9/5*m**4 + 0 - 6/5*m**3.
3*m**3*(m - 1)*(5*m + 2)/5
Factor -28*p**3 + 0*p + 0 - 1/6*p**5 + 9/2*p**4 - 98/3*p**2.
-p**2*(p - 14)**2*(p + 1)/6
Let p(d) = -d + 12. Let h be p(9). Suppose 0*m + 3*m + h = -2*l, -4*l + 34 = -2*m. Factor -2*y - 2 - l*y**3 + 5*y**3 + y**2 + 1 + 3*y.
-(y - 1)**2*(y + 1)
Let c be (-3 + (-25)/(-10))*0. Find b such that c*b**2 + 20*b + 3*b**2 + 17*b**2 + 5*b**3 = 0.
-2, 0
Let q = 1931/1550 - 38/31. Let s(k) be the second derivative of -1/105*k**7 + 0*k**3 - 2/75*k**6 + 6*k + 0*k**4 + 0*k**2 + 0 - q*k**5. Factor s(o).
-2*o**3*(o + 1)**2/5
Let m(d) be the second derivative of 5/42*d**7 + 1/2*d**5 - 1/2*d**6 + 19*d + 0*d**2 + 0 + 0*d**4 + 0*d**3. Factor m(n).
5*n**3*(n - 2)*(n - 1)
Let t(v) be the first derivative of v**6/18 - v**5/3 - 20*v**4/3 - 280*v**3/9 - 200*v**2/3 - 208*v/3 - 82. Determine z, given that t(z) = 0.
-2, 13
Let c(d) be the third derivative of -d**6/30 + 8*d**5/15 - 2*d**4 + 157*d**2. Factor c(y).
-4*y*(y - 6)*(y - 2)
Factor 522*q**3 - 264*q**3 - 261*q**3 - 99*q**2.
-3*q**2*(q + 33)
Let i = 51 + -47. Let p be (-4 + 2)*((-12)/(-6) + -3). Factor a**i + 5/3*a**p + 7/3*a**3 + 1/3*a + 0.
a*(a + 1)**2*(3*a + 1)/3
Let a(d) = d**4 + d**3 + d**2 - 1. Let i(t) = -7 + 2*t**4 - 13*t**2 - 4*t**2 + 11*t - 2*t**3 + 15*t**2. Let b(j) = -5*a(j) + 5*i(j). Factor b(v).
5*(v - 3)*(v - 1)**2*(v + 2)
Let q(a) = 12*a - 78. Let g be q(7). Solve -g*j**4 + 0 + 9/2*j**3 + 3/2*j**2 + 0*j = 0.
-1/4, 0, 1
Let a(s) be the third derivative of s**9/141120 - s**8/9408 + s**7/1680 - s**6/560 + s**5/4 - 9*s**2. Let u(k) be the third derivative of a(k). Factor u(i).
3*(i - 3)*(i - 1)**2/7
Let a(h) = 120*h**5 - 65*h**4 - 100*h**3 - 110*h**2 - 130. Let t(l) = 11*l**5 - 6*l**4 - 9*l**3 - 10*l**2 - 12. Let y(s) = -6*a(s) + 65*t(s). Factor y(o).
-5*o**2*(o - 2)*(o + 1)**2
Let z(u) be the second derivative of -u**6/10 + 3*u**5/20 - 7*u + 11. Factor z(v).
-3*v**3*(v - 1)
Factor -45/2*a**3 + 505/2*a**2 + 0 - 55*a.
-5*a*(a - 11)*(9*a - 2)/2
Suppose -34 = 4*s - 42. Suppose 2*t + 4 = 3*j, -s*j - 2*j = -3*t - 6. Factor 0*p + 0*p**4 + 2/7*p**3 - 2/7*p**5 + 0*p**2 + j.
-2*p**3*(p - 1)*(p + 1)/7
Find m, given that 4*m**3 + 60 - 5*m**2 + 92*m + 22*m**2 + 19*m**2 = 0.
-5, -3, -1
Let c(h) = 14*h + 8. Let u(y) = y + 1. Let v(a) = c(a) - 12*u(a). Let k be v(4). Factor 18 - w**2 - k*w**2 + 5*w**2 + 2*w**2 - 12*w.
2*(w - 3)**2
Suppose 11*u - 9*u = 10. Let o be 10 - u - 2/2. Let -3*n**o - 3/4*n**3 + 0*n - 7/4*n**5 + 0 + 1/2*n**2 = 0. Calculate n.
-1, 0, 2/7
Let n = 1/1926 + 6739/3852. Factor -49/8 - 1/8*g**2 + n*g.
-(g - 7)**2/8
Let a(c) be the first derivative of -2/3*c**3 + 1/4*c**4 + 4 + 0*c + 1/2*c**2. Let a(z) = 0. What is z?
0, 1
Factor -20/3*d - 2/3*d**2 + 0.
-2*d*(d + 10)/3
Let c(m) be the first derivative of -m**6/180 + 7*m**5/60 + 5*m**3/3 + 30. Let a(j) be the third derivative of c(j). Determine s so that a(s) = 0.
0, 7
Let a(l) be the third derivative of l**7/350 - l**6/120 - 4*l**5/75 + l**4/10 + 4*l**2 - 36. Factor a(f).
f*(f - 3)*(f + 2)*(3*f - 2)/5
Let l(y) = -y + 1. Let q(c) = c**4 + 24*c**3 + 45*c**2 + 23*c - 1. Let w(f) = -4*l(f) - 4*q(f). Factor w(n).
-4*n*(n + 1)**2*(n + 22)
Let p = 274 + -1361/5. Suppose 0 = -u - 2*d + 44 - 42, -5 = -4*u - 5*d. Suppose 6/5*k**2 + p*k + u - 3/5*k**3 = 0. Calculate k.
-1, 0, 3
Let x(u) be the second derivative of 0 + 4*u**2 - u**5 - 4/21*u**7 + 14/3*u**3 + 5/3*u**4 - 19*u - 14/15*u**6. Suppose x(t) = 0. Calculate t.
-2, -1, -1/2, 1
Suppose 0 = 25*y + 17*y - 53*y. Determine a so that a + y - 1/8*a**2 = 0.
0, 8
Let x be 6 + (7 - 8) + 1. Let d(p) be the first derivative of 9/4*p**4 - x*p**2 - 4 + 0*p**3 + 0*p - 3/5*p**5. Determine a so that d(a) = 0.
-1, 0, 2
Suppose -12*c = -17*c - 300. Let h be (3/15)/((-24)/c). Find b, given that 0*b**2 + 0 + 1/2*b**5 + h*b + 0*b**4 - b**3 = 0.
-1, 0, 1
Let p(w) be the second derivative of -5*w**4/6 + 25*w**3/18 + 5*w**2/6 - w + 20. Suppose p(t) = 0. Calculate t.
-1/6, 1
Suppose 3/2*r + 6 + 3/4*r**4 - 27/4*r**2 - 3/2*r**3 = 0. Calculate r.
-2, -1, 1, 4
Let j be 38/(-247) - 12346/26. Let a = -1891/4 - j. Factor -a*m + 0 - 3/2*m**2 - 1/4*m**3.
-m*(m + 3)**2/4
Let t(v) = -v + 13 - 23 + 19. Let z be t(6). Factor -3*s**2 - 4*s - 3/2 + 0*s**z + 1/2*s**4.
(s - 3)*(s + 1)**3/2
Let a(p) be the third derivative of -p**5/420 + 5*p**4/28 + 264*p**2. Factor a(g).
-g*(g - 30)/7
Let v be 0 + ((-33)/(-9) - (-6)/18). Let l(z) be the third derivative of 1/9*z**3 - 6*z**2 + 0 - 1/90*z**5 + 0*z + 0*z**v. Find j, given that l(j) = 0.
-1, 1
Let k(l) = l**2 + 16*l + 4. Let j(r) = 4*r**2 + 63*r + 18. Let w(d) = 2*j(d) - 9*k(d). Suppose w(s) = 0. Calculate s.
-18, 0
Let a(k) = -4*k**2 - 177*k - 1955. Let y be a(-22). Let 27/2*d**2 + 45/2*d + 3/2*d**y + 21/2 = 0. Calculate d.
-7, -1
Let k = -11592233/748296 + 11/39384. Let b = -3/19 - k. Find p such that -4*p**5 - 2/3 - 16/3*p - 68/3*p**3 - 16*p**2 - b*p**4 = 0.
-1, -1/2, -1/3
Let m = 536 - 531. Let a(h) be the second derivative of -h**4 - 2*h**3 + 4*h - 2*h**2 + 0 - 1/5*h**m. Let a(k) = 0. Calculate k.
-1
Let s(f) = -f + 15. Let w be s(-12). Let u be (w/6)/((-6)/(-4)). Solve 4/5 - 2*q - 8/5*q**2 + 4/5*q**4 + 4*q**u - 2*q**5 = 0 for q.
-1, 2/5, 1
Suppose 99*d = d + 392. Let r(x) be the third derivative of 0 - 1/30*x**5 + 0*x**3 + 11*x**2 + 0*x + 1/36*x**6 - 1/18*x**d. Factor r(j).
2*j*(j - 1)*(5*j + 2)/3
Let b(w) = -w - 4. Let i(x) = -4*x**2 + 148*x - 184. Let k(q) = -8*b(q) + i(q). Let k(h) = 0. Calculate h.
1, 38
Let j(y) be the first derivative of -y**6/3 - 12*y**5/5 - 4*y**4 + 67. Factor j(t).
-2*t**3*(t + 2)*(t + 4)
Suppose -3*a + 28 = -2. Let x be (-35)/14*(-16)/a. Determine g so that -g**2 - 4 + 5*g + 5 - g**3 - x = 0.
-3, 1
Suppose -4*i + 8 = -5*o, -i - 3*i = -3*o - 8. Factor -21 + 5*f**5 + 21 + i*f**4 + 13*f**4.
5*f**4*(f + 3)
Let l(q) be the second derivative of q**7/126 - 2*q**6/45 - q**5/30 + 2*q**4/9 + q**3/18 - 2*q**2/3 - 79*q. Let l(s) = 0. What is s?
-1, 1, 4
Let s(a) = -2*a**2 + 29*a - 64. 